Professor Patrick Gruber

Traction control (TC) plays a key role in improving vehicle safety, especially for driving scenarios involving extremely low levels of tyre-road friction. In this paper a novel deep reinforcement learning (DRL) based TC strategy is formulated and its performance is compared against a nonlinear model predictive control (NMPC) solution for a simulated straight-line acceleration manoeuvre on icy road conditions. The paper explores the design and assessment of the proposed controllers using a vehicle model experimentally validated on ice. The simulation results show that the DRL solution outperforms the NMPC strategy by reducing the wheel slip ratio peaks and oscillations at the start of an acceleration manoeuvre. Additionally, it converges more quickly to the reference slip and is more computationally efficient.

This paper presents a novel unscented Kalman filter (UKF) implementation with adaptive covariance matrices (ACMs), to accurately estimate the longitudinal and lateral components of vehicle velocity, and thus the sideslip angle, tire slip angles, and tire slip ratios, also in extreme driving conditions, including tyre–road friction variations. The adaptation strategies are implemented on both the process noise and measurement noise covariances. The resulting UKF ACM is compared against a well-tuned baseline UKF with fixed covariances. Experimental test results in high tyre–road friction conditions show the good performance of both filters, with only a very marginal benefit of the ACM version. However, the simulated extreme tests in variable and low-friction conditions highlight the superior performance and robustness provided by the adaptation mechanism. 

Active and semi-active suspensions for passenger cars traditionally enhance comfort through body control, and vehicle handling by reducing the tyre load variations induced by road irregularities. Active suspensions can also be designed to track a desired yaw rate profile through the control of the lateral load transfer distribution between the front and rear axles. This paper considers an integrated system including semi-active and active suspension actuation to control the yaw, roll, pitch and heave dynamics excited by the driving actions. To this purpose, two novel real-time-capable implicit nonlinear model predictive control (NMPC) formulations, excluding and including cost function weight adaptation, are proposed and compared with the passive vehicle, and the controlled vehicle with two combinations of skyhook and active roll control, the first based on a pseudoinverse decoupling transformation for obtaining the damping force contributions, and the second using an inverse formulation. The algorithms are assessed through an experimentally validated simulation model, along manoeuvres corresponding to sub-limit and limit handling operation, to analyse the trade-off between body motion reduction and cornering response enhancement. The results show that the adaptable NMPC configuration provides the best performance in all scenarios, also for significant variations of the main vehicle and tyre parameters.

Although the literature includes examples of model predictive controllers for trailer sway mitigation through direct yaw moment control in car-semitrailer configurations, the available studies do not consider the integration of direct yaw moment control and other actuations within the towing vehicle, e.g., anti-roll moment distribution control through active suspension (AS) systems. This study focuses on the integration of torque-vectoring (TV) and AS control on the towing car, to provide yaw rate tracking, sideslip angle limitation, and trailer sway reduction. Given the nonlinearity of the effect of the anti-roll moment distribution on the articulated vehicle dynamics, nonlinear model predictive control (NMPC) is selected as an effective technique for the specific problem. The paper presents and analyzes several alternative real-time implementable NMPC algorithms, using either the predicted trailer hitch dynamics or the estimated hitch joint forces for the control of an electric all-wheel-drive car towing a semitrailer. The simulation results, obtained through a high-fidelity simulation environment, including an optimization based tuning routine for a fair comparison of the controllers, show that: i) AS actuated in isolation brings higher semitrailer stability than a baseline TV controller focusing only on the towing car; ii) the best performance is provided by the integrated control of AS and TV, with respect to (w.r.t.) the other considered configurations; iii) the NMPCs based on car prediction models considering the current hitch joint forces can be a valuable alternative to the NMPCs embedding the hitch dynamics; and iv) all NMPC approaches are rather robust w.r.t. significant variations of semitrailer parameters.

In passenger cars, the ride characteristics are fundamental to the driver and passenger engagement, as they define the comfort and road holding performance. Therefore, the methods and tools to assess ride quality are of significant interest to the vehicle dynamics specialists, and are an important part of the internal know-how of each car maker and Tier 1 supplier, which is often kept confidential. Unfortunately, the available literature does not include a comprehensive survey on the evaluation of the objective and subjective aspects related to ride, and their correlation. This review targets the gap, and deals with: (i) the available tools and techniques to objectively assess primary and secondary ride, including typical manoeuvres, road profiles, required vehicle instrumentation, and key performance indicators (KPIs); (ii) the subjective attributes and their categorisation; (iii) the approaches and mathematical models to correlate the objective KPIs with the subjective evaluation; and (iv) future trends. The know-how of the authors on the ride assessment of high-performance passenger cars will also be used to cover the aspects that are currently overlooked by the available literature and standards. In summary, the manuscript provides the interested reader with useful guidance on the procedures to perform ride quality analyses.

A recently growing literature discusses the topics of direct yaw moment control based on model predictive control (MPC), and energy-efficient torque-vectoring (TV) for electric vehicles with multiple powertrains. To reduce energy consumption, the available TV studies focus on the control allocation layer, which calculates the individual wheel torque levels to generate the total reference longitudinal force and direct yaw moment, specified by higher level algorithms to provide the desired longitudinal and lateral vehicle dynamics. In fact, with a system of redundant actuators, the vehicle-level objectives can be achieved by distributing the individual control actions to minimize an optimality criterion, e.g., based on the reduction of different power loss contributions. However, preliminary simulation and experimental studies - not using MPC - show that further important energy savings are possible through the appropriate design of the reference yaw rate. This paper presents a nonlinear model predictive control (NMPC) implementation for energy-efficient TV, which is based on the concurrent optimization of the reference yaw rate and wheel torque allocation. The NMPC cost function weights are varied through a fuzzy logic algorithm to adaptively prioritize vehicle dynamics or energy efficiency, depending on the driving conditions. The results show that the adaptive NMPC configuration allows stable cornering performance with lower energy consumption than a benchmarking fuzzy logic TV controller using an energy-efficient control allocation layer.

This study discusses vehicle stability control based on explicit nonlinear model predictive control (NMPC) and investigates the influence of prediction model fidelity on controller performance. The explicit solutions are generated through an algorithm using multiparametric quadratic programming (mp-QP) approximations of the multiparametric nonlinear programming (mp-NLP) problems. Controllers with different prediction models are assessed through objective indicators in sine-with-dwell tests. The analysis considers the following prediction model features: 1) nonlinear lateral tire forces as functions of slip angles, which are essential for the operation of the stability controller at the limit of handling. Moreover, a simple nonlinear tire force model with saturation is shown to be an effective alternative to a more complex model based on a simplified version of the Magic Formula; 2) longitudinal and lateral load transfers, playing a crucial role in the accurate prediction of the lateral tire forces and their yaw moment contributions; 3) coupling between longitudinal and lateral tire forces, which has a significant influence on the front-to-rear distribution of the braking forces generated by the controller; and 4) nonlinear peak and stiffness factors of the tire model, with visible yet negligible effects on the results.

Integrated Chassis Control (ICC) is one of the most appealing subjects for vehicle dynamics specialists and researchers, due to the increasing number of chassis actuators of modern human-driven and automated cars. ICC ensures that the potential of the available actuators is systematically exploited, by overcoming the individual limitations, and solving conflicts and redundancies, which results into enhanced vehicle performance, ride comfort and safety. This paper is a literature review on ICC, and focuses on the topics that are left uncovered by the most recent surveys on the subject, or that are dealt with only by old surveys, namely: a) the systematic categorisation of the available ICC architectures, with the critical analysis of their strengths and weaknesses; b) the latest ICC approaches, which are becoming feasible with modern automotive microcontrollers; c) the driving performance requirements; and d) the procedures to objectively evaluate ICC performance. The manuscript aids the interested reader in the choice of the most appropriate ICC method for the specific requirements, and concludes with the recent developments and future trends.

Electric Vehicles (EVs) with multiple motors permit to design the steady-state cornering response by imposing reference understeer characteristics according to expected vehicle handling quality targets. To this aim a direct yaw moment is generated by assigning different torque demands to the left and right vehicle sides. The reference understeer characteristic has an impact on the drivetrain input power as well. In parallel, a Control Allocation (CA) strategy can be employed to achieve an energy-efficient wheel torque distribution generating the reference yaw moment and wheel torque. To the knowledge of the authors, for the first time this paper experimentally compares and critically analyses the potential energy efficiency benefits achievable through the appropriate set-up of the reference understeer characteristics and wheel torque CA. Interestingly, the experiments on a four wheel-drive EV demonstrator show that higher energy savings can be obtained through the appropriate tuning of the reference cornering response rather than with an energy efficient CA.

© IFAC.Using Lyapunov theory, Pontryagin's minimum principle, and affine quadratic stability, a novel robust optimal control strategy is developed for active suspension systems to enhance vehicle ride comfort and handling performance. The controller has a simple structure, making its suitable for real-time implementation. The required sensor configuration includes a six-axis IMU and four LVDTs. The proposed controller is suitable for on-road commercial vehicles where ride comfort over bump disturbances and handling performance are the most concerns. The effectiveness of the controller is verified through simulation results using IPG CarMaker software.

Most tyre models used in vehicle dynamics simulations are parameterised with data obtained on a flat-track test rig, where the tyre is commonly driven on sandpaper. The resultant models are typically very accurate at low to medium slip conditions. At high slip, the prediction of forces and moments of a tyre rolling on surfaces other than sandpaper is less reliable as this condition is dominated by the rubber-road friction characteristics. To extend the validity of tyre models derived from sandpaper surface measurements to road surfaces, this paper explores the use of frictional behaviour of tread rubber obtained with a purpose-built rubber friction measurement system. Since rubber friction depends on many variables, tests have been carried out under controlled conditions in order to obtain accurate and repeatable data. Friction measurements were performed on sandpaper and incorporated into a brush-type tyre model to recreate the flat-track measurements of the full tyre. Preliminary results indicate the benefits and potential of detailed knowledge on the frictional behaviour for accurately modelling tyre forces and moments.

This paper presents a traction controller for combined driving and cornering conditions, based on explicit nonlinear model predictive control. The prediction model includes a nonlinear tire force model using a simplified version of the Pacejka Magic Formula, incorporating the effect of combined longitudinal and lateral slips. Simulations of a front-wheel-drive electric vehicle with multiple motors highlight the benefits of the proposed formulation with respect to a controller with a tire model for pure longitudinal slip. Objective performance indicators provide a performance assessment in traction control scenarios.

Road irregularities induce vertical and longitudinal vibrations of the sprung and unsprung masses, which affect vehicle comfort. While the vertical dynamics and related compensation techniques are extensively covered by the suspension control literature, the longitudinal dynamics on uneven road surfaces are less frequently addressed, and are significantly influenced by the tires and suspension systems. The relatively slow response of internal combustion engines does not allow any form of active compensation of the effect of road irregularities. However, in-wheel electric powertrains, in conjunction with pre-emptive control based on the information on the road profile ahead, have some potential for effective compensation, which, however, has not been explored yet. This paper presents a proof-of-concept nonlinear model predictive control (NMPC) implementation based on road preview, which is preliminarily assessed with a simulation model of an all-wheel drive electric vehicle with in-wheel motors, including a realistic tire model for ride comfort simulation. The major improvement brought by the proposed road preview controller is evaluated through objective performance indicators along multiple maneuvers, and is confirmed by the comparison with two benchmarking feedback controllers from the literature.

Most tyre models used in vehicle dynamics simulations are parameterised with data obtained on a flat-track test rig, where the tyre is commonly driven on sandpaper. The resultant models are typically very accurate at low to medium slip conditions. At high slip, the prediction of forces and moments of a tyre rolling on surfaces other than sandpaper is less reliable as this condition is dominated by the rubber-road friction characteristics. To extend the validity of tyre models derived from sandpaper surface measurements to road surfaces, this paper explores the use of frictional behaviour of tread rubber obtained with a purpose-built rubber friction measurement system. Since rubber friction depends on many variables, tests have been carried out under controlled conditions in order to obtain accurate and repeatable data. Friction measurements were performed on sandpaper and incorporated into a brush-type tyre model to recreate the flat-track measurements of the full tyre. Preliminary results indicate the benefits and potential of detailed knowledge on the frictional behaviour for accurately modelling tyre forces and moments.

This study addresses the development and Hardware-in-the-Loop (HiL) testing of an explicit nonlinear model predictive controller (eNMPC) for an anti-lock braking system (ABS) for passenger cars, actuated through an electro-hydraulic braking (EHB) unit. The control structure includes a compensation strategy to guard against performance degradation due to actuation dead times, identified through experimental tests. The eNMPC is run on an automotive rapid control prototyping unit, which shows its real-time capability with comfortable margin. A validated high-fidelity vehicle simulation model is used for the assessment of the ABS on a HiL rig equipped with the braking system hardware. The eNMPC is tested in 7 emergency braking scenarios, and its performance is benchmarked against a proportional integral derivative (PID) controller. The eNMPC results show: i) the control system robustness with respect to variations of tire-road friction condition and initial vehicle speed; and ii) a consistent and significant improvement of the stopping distance and wheel slip reference tracking, with respect to the vehicle with the PID ABS.

Nonlinear model predictive control (NMPC) is proposed in multiple academic studies as an advanced control system technology for vehicle operation at the limits of handling, allowing high tracking performance and formal consideration of system constraints. However, the implementation of implicit NMPC, in which the control problem is solved on-line, poses significant challenges in terms of computational load. This issue can be overcome through explicit NMPC, in which the optimization problem is solved off-line, and the resulting explicit solution, with guaranteed level of sub-optimality, is evaluated on-line. This study presents a yaw and lateral stability controller based on explicit NMPC, actuated through the friction brakes of the vehicle. The controller performance is demonstrated during sine-with-dwell tests simulated with a high-fidelity model. The analysis investigates the influence of the weights in the cost function formulation and includes a comparison of different settings of the optimal control problem.

Future vehicle localisation technologies enable major enhancements of vehicle dynamics control. This study proposes a novel vehicle stability control paradigm, based on pre-emptive control that considers the curvature profile of the expected path ahead in the computation of the reference direct yaw moment and braking control action. The additional information allows pre-emptive trail braking control, which slows down the vehicle if the predicted speed profile based on the current torque demand is deemed incompatible with the reference trajectory ahead. Nonlinear model predictive control is used to implement the approach, in which also the steering angle and reference yaw rate provided to the internal model are varied along the prediction horizon, to account for the expected vehicle path. Two pre-emptive stability control configurations with different levels of complexity are proposed and compared with the passive vehicle, and two state-of-the-art nonlinear model predictive stability controllers, one with and one without non-pre-emptive trail braking control. The performance is assessed along obstacle avoidance tests, simulated with a high-fidelity model of an electric vehicle with in-wheel motors. Results show that the pre-emptive controllers achieve higher maximum entry speeds - up to ∼34% and ∼60% in high and low tyre-road friction conditions - than the formulations without preview.

Many tire models use a single value for the tire-road friction coefficient to produce tire force data. While this approach may provide sufficient accuracy at small to medium slip values, it can cause unrealistic force and moment predictions at large slip values. The inaccuracies primarily stem from an increase in tire temperature which, in turn, influences the friction characteristics between the tread rubber and the road surface. The friction relationship can be represented by the friction master curve, and commonly requires testing on a bespoke rubber friction test rig. This paper explores ways on how the friction master curve can be obtained from flat-track tire test data for pure longitudinal slip conditions.

Vehicle handling in steady-state and transient conditions can be significantly enhanced with the continuous modulation of the driving and braking torques of each wheel via dedicated torque-vectoring controllers. For fully electric vehicles with multiple electric motor drives, the enhancements can be achieved through a control allocation algorithm for the determination of the wheel torque distribution. This article analyzes alternative cost functions developed for the allocation of the wheel torques for a four-wheel-driven fully electric vehicle with individually controlled motors. Results in terms of wheel torque and tire slip distributions among the four wheels, and of input power to the electric drivetrains as functions of lateral acceleration are presented and discussed in detail. The cost functions based on minimizing tire slip allow better control performance than the functions based on energy efficiency for the case-study vehicle.

An oscillation control system of a vehicle includes a distribution control module configured to determine: a first front torque request for one or more front electric motors of the vehicle; and a first rear torque request for one or more rear electric motors of the vehicle; a first control module configured to: determine a second front torque request for the front electric motor(s) of the vehicle based on the first front torque request and a front wheel road profile; and control power flow to the front electric motor(s) based on the second front torque request; a second control module configured to: determine a second rear torque request for the rear electric motor(s) of the vehicle based on the first rear torque request and a rear wheel road profile; and control power flow to the rear electric motor(s) based on the second rear torque request.

The paper discusses novel computationally efficient torque distribution strategies for electric vehicles with individually controlled drivetrains, aimed at minimizing the overall power losses while providing the required level of wheel torque and yaw moment. Analytical solutions of the torque control allocation problem are derived and effects of load transfers due to moderate driving/braking and cornering conditions are studied and discussed in detail. Influences of different drivetrain characteristics on the front and rear axles are described. The results of the analytically-derived algorithm are contrasted with those from two other control allocation strategies, based on the off-line numerical solution of more detailed formulations of the control allocation problem (i.e., a multi-parametric non-linear programming problem). The solutions of the control allocation problem are experimentally validated along multiple driving cycles and in steady-state cornering, on an electric vehicle with four identical drivetrains. The experiments show that the computationally efficient algorithms represent a very good compromise between low energy consumption and controller complexity.

This review addresses efforts made within the field of vehicle dynamics to contribute to the energy efficient operation of road and rail vehicles. Selected investigations of the research community to develop technology solutions to reduce energy consumption are presented. The study explores the impact and potential of relatively mature technologies such as regenerative braking, but also recent research directions that are seeking to develop solutions such as regenerative suspensions, a concept common to both transport modes. Specifically for road vehicles, the study includes rear wheel steering, camber control and torque vectoring, and for rail vehicles active steering and light-weighting. Operationally, there would appear to be great potential for rail vehicles in the wider adoption of connected driver advisory systems, and automatic train control systems, including the application of machine learning techniques to optimise train speed trajectories across a route. Similarly, for road vehicles, predictive and cooperative eco-driving strategies show potential for significant energy savings for connected autonomous vehicles.

In contrast with conventional vehicles driven by an internal-combustion engine, the number of motors in fully electric cars is not fixed. A variety of architectural solutions, including from one to four individually controlled electric drive units, is possible and opens up new avenues in the design of vehicle characteristics. In particular, individual control of multiple electric powertrains promises to enhance the handling performance in steady-state and dynamic conditions. For the analysis and selection of the best electric powertrain layout based on the expected vehicle characteristics and performance, new analytical tools and metrics are required. This article presents and demonstrates a novel offline procedure for the design of the feedforward control action of the vehicle dynamics controller of a fully electric vehicle and three performance indicators for the objective comparison of the handling potential of alternative electric powertrain layouts. The results demonstrate that the proposed offline routine allows the desired understeer characteristics to be achieved with any of the investigated vehicle configurations, in traction and braking conditions. With respect to linear handling characteristics, the simulations indicate that the influence of torque-vectoring is independent of the location of the controlled axles (front or rear) and is considerably affected by the number of controlled axles.

This paper presents a novel four-wheel-drive electric vehicle layout consisting of one on-board electric drivetrain per axle. Each drivetrain includes a simplified clutch-less two-speed transmission system and an open differential to transmit the torque to the wheels. This drivetrain layout allows eight different gear state combinations at the vehicle level, thus increasing the possibility of running the vehicle in a more energy-efficient state for the specific wheel torque demand and speed. To compensate for the torque gap during gearshifts, a "torque-fill" controller was developed that varies the motor torque on the axle not involved in the gearshift. Experimental tests show the effectiveness of the developed gearshift strategy extended with the torque-fill capability. Energy efficiency benefits are discussed by comparing the energy consumptions of the case study vehicle controlled through a constant front-to-total wheel torque distribution and conventional gearshift maps, and the same vehicle with an energy management system based on an offline optimization. Results demonstrate that the more advanced controller brings a significant reduction of the energy consumption at constant speed and along different driving cycles.

The main question in eco-driving is – what speed or torque profile should the vehicle follow to minimize its energy consumption over a certain distance within a desired trip time? Various techniques to obtain globally optimal energy-efficient driving profiles have been proposed in the literature, involving optimization algorithms such as dynamic programming (DP) or sequential quadratic programming. However, these methods are difficult to implement on real vehicles due to their significant computational requirements and the need for precise a-priori knowledge of the scenario ahead. Although many predictions state that electric vehicles (EVs) represent the future of mobility, the literature lacks a realistic analysis of optimal driving profiles for EVs. This paper attempts to address the gap by providing optimal solutions obtained from DP for a variety of trip times, which are compared with simple intuitive speed profiles. For a case study EV, the results show that the DP solutions involve forms of Pulse-and-Glide (PnG) at high frequency. Hence, detailed investigations are performed to: i) prove the optimality conditions of PnG for EVs; ii) show its practical use, based on realistic electric powertrain efficiency maps; iii) propose rules for lower frequency PnG operation; and iv) use PnG to track generic speed profiles.

Electric vehicles with multiple motors allow torque-vectoring, i.e., the individual control of each powertrain torque. Torque-vectoring (TV) can provide: (i) enhancement of vehicle safety and handling, via the generation of a direct yaw moment to shape the understeer characteristics and increase yaw and sideslip damping; and (ii) energy consumption reductions, via appropriate torque allocation to each motor. The FP7 European project iCOMPOSE thoroughly addressed (i) and (ii). Theoretical analyses were carried out to design state-of-the-art TV controllers, which were validated through: (a) vehicle simulations; and (b) extensive experimental tests, which were performed at rolling road facilities and proving grounds, using a Range Rover Evoque prototype equipped with four identical on-board electric powertrains. This paper provides an overview of the TV-related contributions of iCOMPOSE.

The safety benefits of torque-vectoring control of electric vehicles with multiple drivetrains are well known and extensively discussed in the literature. Also, several authors analyze wheel torque control allocation algorithms for reducing the energy consumption while obtaining the wheel torque demand and reference yaw moment specified by the higher layer of a torque-vectoring controller. Based on a set of novel experimental results, this study demonstrates that further significant energy consumption reductions can be achieved through the appropriate tuning of the reference understeer characteristics. The effects of drivetrain power losses and tire slip power losses are discussed for the case of identical drivetrains at the four vehicle corners. Easily implementable yet effective rule-based algorithms are presented for the set-up of the energy-efficient reference yaw rate, feedforward yaw moment and wheel torque distribution of the torque-vectoring controller.

Next-generation accurate vehicle localization and connectivity technologies will enable significant improvements in vehicle dynamics control. This study proposes a novel control function, referred to as pre-emptive braking, which imposes a braking action if the current vehicle speed is deemed safety-critical with respect to the curvature of the expected path ahead. Differently from the implementations in the literature, the pre-emptive braking input is designed to: a) enhance the safety of the transient vehicle response without compromising the capability of reaching the cornering limit, which is a significant limitation of the algorithms proposed so far; and b) allow - in its most advanced implementation - to precisely constrain the sideslip angle to set levels only through the pre-emptive control of the longitudinal vehicle dynamics, without the application of any direct yaw moment, typical of conventional stability control systems. To this purpose, a real-time-capable nonlinear model predictive control (NMPC) formulation based on a double track vehicle prediction model is presented, and implemented in its implicit form, which is applicable to both human-driven and automated vehicles, and acts as an additional safety function to compensate for human or virtual driver errors in extreme conditions. Its performance is compared with that of: i) two simpler - yet innovative with respect to the state-of-the-art - pre-emptive braking controllers, namely an NMPC implementation based on a dynamic point mass vehicle model, and a pre-emptive rule-based controller; and ii) a benchmarking non-pre-emptive rule-based trail braking controller. The benefits of pre-emptive braking are evaluated through vehicle dynamics simulations with an experimentally validated vehicle model, as well as a proof-of-concept implementation on an automated electric vehicle prototype.

In the last three decades a relatively wide literature has discussed the potential vehicle dynamics benefits of the control of the front-to-total anti-roll moment distribution generated by active suspension systems, either based on actuators located within the individual corners or controllable anti-roll bars. However, because of the nonlinearity of the involved phenomena, there is a lack of systematic model based design routines to achieve the reference cornering response in steady-state and transient conditions through active suspension controllers, and for the integration of suspension control with direct yaw moment control. This paper targets such knowledge gap, by introducing design tools for front-to-total anti-roll moment distribution control, based on: i) optimizations using a quasistatic model for the computation of the non-linear feedforward contribution of the controller; ii) a novel linearized vehicle model formulation for linear control design in the frequency domain; and iii) a nonlinear vehicle model formulation to be used as prediction model for nonlinear model predictive control. A set of simulation and experimental results shows the benefits in terms of: a) understeer gradient tunability; b) increased maximum achievable lateral acceleration; c) increased yaw and sideslip damping; and d) energy consumption reduction.

This study presents a traction control system for electric vehicles with in-wheel motors, based on explicit non-linear model predictive control. The feedback law, available beforehand, is described in detail, together with its variation for different plant conditions. The explicit controller is implemented on a rapid control prototyping unit, which proves the real-time capability of the strategy, with computing times in the order of microseconds. These are significantly lower than the required sampling time for a traction control application. Hence, the explicit model predictive controller can run at the same frequency as a simple traction control system based on Proportional Integral (PI) technology. High-fidelity model simulations provide: i) a performance comparison of the proposed explicit non-linear model predictive controller with a benchmark PI-based traction controller with gain scheduling and anti-windup features; and ii) a performance comparison among two explicit and one implicit non-linear model predictive controllers based on different internal models, with and without consideration of transient tire behavior and load transfers. Experimental test results on an electric vehicle demonstrator are shown for one of the explicit non-linear model predictive controller formulations.

A significant challenge in electric vehicles with multiple motors is how to control the individual drivetrains in order to achieve measurable benefits in terms of vehicle cornering response, compared to conventional stability control systems actuating the friction brakes. This paper presents a direct yaw moment controller based on the combination of feedforward and feedback contributions for continuous yaw rate control. When the estimated sideslip exceeds a pre-defined threshold, a sideslip-based yaw moment contribution is activated. All yaw moment contributions are entirely tunable through model-based approaches, for reduced vehicle testing time. The purpose of the controller is to continuously modify the vehicle understeer characteristic in quasi-static conditions and increase yaw and sideslip damping during transients. Skid-pad, step-steer and sweep steer tests are carried out with a front-wheel-drive fully electric vehicle demonstrator with two independent drivetrains. The experimental test results of the electric motor-based actuation of the direct yaw moment controller are compared with those deriving from the friction brake-based actuation of the same algorithm, which is a major contribution of this paper. The novel results show that continuous direct yaw moment control allows significant "on-demand" changes of the vehicle response in cornering conditions and to enhance active vehicle safety during extreme driving maneuvers.

With the advent of electric vehicles with multiple motors, the steady-state and transient cornering responses can be designed based on high-level reference targets, and implemented through the continuous torque control of the individual wheels, i.e., torque-vectoring or direct yaw moment control. The literature includes several papers describing the application of the sliding mode control theory to torque-vectoring. However, the experimental implementations of sliding mode controllers on real vehicle prototypes are very limited at the moment. More importantly, to the knowledge of the authors, there is lack of experimental assessments of the performance benefits of direct yaw moment control based on sliding modes, with respect to other controllers, such as the proportional integral derivative controllers or linear quadratic regulators currently used for stability control in production vehicles. This paper aims to reduce this gap by presenting an integral sliding mode controller for concurrent yaw rate and sideslip control. A new driving mode, the Enhanced Sport mode, is proposed, inducing sustained high values of sideslip angle, which can be safely limited to a specified threshold. The system is experimentally assessed on a four-wheel-drive electric vehicle along a wide range of maneuvers. The performance of the integral sliding mode controller is compared with that of a linear quadratic regulator during step steer tests. The results show that the integral sliding mode controller brings a significant enhancement of the tracking performance and yaw damping with respect to the more conventional linear quadratic regulator based on an augmented single-track vehicle model formulation.

Electric vehicles with independently controlled drivetrains allow torque-vectoring, which enhances active safety and handling qualities. This paper proposes an approach for the concurrent control of yaw rate and sideslip angle based on a single input single output (SISO) yaw rate controller. With the SISO formulation, the reference yaw rate is firstly defined according to the vehicle handling requirements, and is then corrected based on the actual sideslip angle. The sideslip angle contribution guarantees a prompt corrective action in critical situations such as incipient vehicle oversteer during limit cornering in low tire-road friction conditions. A design methodology in the frequency domain is discussed, including stability analysis based on the theory of switched linear systems. The performance of the control structure is assessed via: i) phase-plane plots obtained with a non-linear vehicle model; ii) simulations with an experimentally validated model, including multiple feedback control structures; and iii) experimental tests on an electric vehicle demonstrator along step steer maneuvers with purposely induced and controlled vehicle drift. Results show that the SISO controller allows constraining the sideslip angle within the predetermined thresholds and yields tire-road friction adaptation with all the considered feedback controllers.

This article identifies tyre modelling features that are fundamental to the accurate simulation of the shear forces in the contact patch of a steady-rolling, slipping and cambered racing tyre. The features investigated include contact patch shape, contact pressure distribution, carcass flexibility, rolling radius (RR) variations and friction coefficient. Using a previously described physical tyre model of modular nature, validated for static conditions, the influence of each feature on the shear forces generated is examined under different running conditions, including normal loads of 1500, 3000 and 4500 N, camber angles of 0° and−3°, and longitudinal slip ratios from 0 to−20%. Special attention is paid to heavy braking, in which context the aligning moment is of great interest in terms of its connection with the limit-handling feel. The results of the simulations reveal that true representations of the contact patch shape, carcass flexibility and lateral RR variation are essential for an accurate prediction of the distribution and the magnitude of the shear forces generated at the tread–road interface of the cambered tyre. Independent of the camber angle, the contact pressure distribution primarily influences the shear force distribution and the slip characteristics around the peak longitudinal force. At low brake-slip ratios, the friction coefficient affects the shear forces in terms of their distribution, while, at medium to high-slip ratios, the force magnitude is significantly affected. On the one hand, these findings help in the creation of efficient yet accurate tyre models. On the other hand, the research results allow improved understanding of how individual tyre components affect the generation of shear forces in the contact patch of a rolling and slipping tyre.

Smart tires are systems that are able to measure temperature, inflation pressure, footprint dimensions, and, importantly, tire contact forces. The integration of this additional information with the signals ob-tained from more conventional vehicle sensors, e.g., inertial measure-ment units, can enhance state estimation in production cars. This paper evaluates the use of smart tires to improve the estimation performance of an Unscented Kalman filter (UKF) based on a nonlinear vehicle dynam-ics model. Two UKF implementations, excluding and including smart tire information, are compared in terms of estimation accuracy of vehicle speed, sideslip angle and tire-road friction coefficient, using experi-mental data obtained on a high performance passenger car.

The combination of continuously-acting high level controllers and control allocation techniques allows various driving modes to be made available to the driver. The driving modes modify the fundamental vehicle performance characteristics including the understeer characteristic and also enable varying emphasis to be placed on aspects such as tire slip and energy efficiency. In this study, control and wheel torque allocation techniques are used to produce three driving modes. Using simulation of an empirically validated model that incorporates the dynamics of the electric powertrains, the vehicle performance, longitudinal slip and power utilization during straight-ahead driving and cornering maneuvers under the different driving modes are compared. The three driving modes enable significant changes to the vehicle behavior to be induced, allowing the responsiveness of the car to the steering wheel inputs and the lateral acceleration limits to be varied according to the selected driving mode. Furthermore, the different driving modes have a significant impact on the longitudinal tire slip, the motor power losses and the total power utilization. The control and wheel torque allocation methods do not rely on complex and computationally demanding online optimization schemes and can thus be practically implemented on real fully electric vehicles. Copyright © 2014 SAE International.

Anti-jerk controllers compensate for the torsional oscillations of automotive drivetrains, caused by swift variations of the traction torque. In the literature model predictive control (MPC) technology has been applied to anti-jerk control problems, by using a variety of prediction models. However, an analysis of the influence of the prediction model complexity on anti-jerk control performance is still missing. To cover the gap, this study proposes six anti-jerk MPC formulations, which are based on different prediction models and are fine-tuned through a unified optimization routine. Their performance is assessed over multiple tip-in and tip-out maneuvers by means of an objective indicator. Results show that: i) low number of prediction steps and short discretization time provide the best performance in the considered nominal tip-in test; ii) the consideration of the drivetrain backlash in the prediction model is beneficial in all test cases; iii) the inclusion of tire slip formulations makes the system more robust with respect to vehicle speed variations and enhances the vehicle behavior in tip-out tests; however, it deteriorates performance in the other scenarios; and iv) the inclusion of a simplified tire relaxation formulation does not bring any particular benefit.

Anti-jerk controllers, commonly implemented in production vehicles, reduce the longitudinal acceleration oscillations transmitted to the passengers, which are caused by the torsional dynamics of the drivetrain during torque transients. Hence, these controllers enhance comfort, drivability, and drivetrain compo- nent durability. Although anti-jerk controllers are commonly implemented in conventional production internal-combustion-engine-driven vehicles, the topic of anti-jerk control has recently been the subject of increased academic and industrial interest, because of the trend towards powertrain electrification, and the distinctive features of electric powertrains, such as the high torque generation bandwidth and absence of clutch dampers. This paper reviews the state-of-the-art of automotive anti-jerk control, with particular attention to control structures that are practically implementable on real vehicles. The survey starts with an overview of the causes of the longitudinal vehicle acceleration oscillations that follow abrupt changes in the powertrain torque delivery. The main body of the text reviews examples of anti-jerk controllers, and categorizes them according to the adopted error variable. The ancillary functions of typical anti-jerk controllers, e.g., their activation and deactivation conditions, are explained. The paper concludes with the most recent development trends, and ideas for future work, including possible applications of model pre- dictive control as well as integration of anti-jerk controllers with autonomous driving systems and other vehicle control functions.

Tire forces are at the heart of the dynamic qualities of vehicles. With the advent of electric vehicles the precise and accurate control of the traction and braking forces at the individual wheel becomes a possibility and a reality outside test labs and virtual proving grounds. Benefits of individual wheel torque control, or torque-vectoring, in terms of vehicle dynamics behavior have been well documented in the literature. However, very few studies exist which analyze the individual wheel torque control integrated with vehicle efficiency considerations. This paper focuses on this aspect and discusses the possibilities and benefits of integrated, energy efficient torque vectoring control. Experiments with a four-wheel-drive electric vehicle show that considerable energy savings can be achieved by considering drivetrain and tire power losses through energy efficient torque vectoring control.

The main benefits of dual clutch transmissions (DCTs) are: (i) a higher energy efficiency than automatic transmission systems with torque converters; and (ii) the capability to fill the torque gap during gear shifts to allow seamless longitudinal acceleration profiles. Therefore, DCTs are viable alternatives to automated manual transmissions (AMTs). For vehicles equipped with engines that can generate considerable torque, large clutch-slip energy losses occur during power-on gear shifts and, as a result, DCTs need wet clutches for effective heat dissipation. This requirement substantially reduces DCT efficiency because of the churning and ancillary power dissipations associated with the wet clutch pack. To the knowledge of the authors, this study is the first to analyse the detailed power loss contributions of a DCT with wet clutches, and their relative significance along a set of driving cycles. Based on these results, a novel hybridised AMT (HAMT) with a single dry clutch and an electric motor is proposed for the same vehicle. The HAMT architecture combines the high mechanical efficiency typical of AMTs with a single dry clutch, with the torque-fill capability and operational flexibility allowed by the electric motor. The measured efficiency maps of a case study DCT and HAMT are compared. This is then complemented by the analysis of the respective fuel consumption along the driving cycles, which is simulated with an experimentally validated vehicle model. In its internal combustion engine mode, the HAMT reduces fuel consumption by >9% with respect to the DCT.

Many torque-vectoring controllers are based on the concurrent control of yaw rate and sideslip angle through complex multi-variable control structures. In general, the target is to continuously track a reference yaw rate, and constrain the sideslip angle to remain within thresholds that are critical for vehicle stability. To achieve this objective, this paper presents a single input single output (SISO) formulation, which varies the reference yaw rate to constrain sideslip angle. The performance of the controller is successfully validated through simulations and experimental tests on an electric vehicle prototype with four drivetrains

Electric vehicles with multiple motors allow torque-vectoring, which generates a yaw moment by assigning different motor torques at the left and right wheels. This permits designing the steady-state cornering response according to several vehicle handling quality targets. For example, as widely discussed in the literature, to make the vehicle more sports-oriented, it is possible to reduce the understeer gradient and increase the maximum lateral acceleration with respect to the same vehicle without torque-vectoring. This paper focuses on the novel experimentally-based design of a reference vehicle understeer characteristic providing energy efficiency enhancement over the whole range of achievable lateral accelerations. Experiments show that an appropriate tuning of the reference understeer characteristic, i.e., the reference yaw rate of the torque-vectoring controller, can bring energy savings of up to ~11% for a case study four-wheel-drive electric vehicle demonstrator. Moreover, during constant speed cornering, it is more efficient to significantly reduce the level of vehicle understeer, with respect to the same vehicle with even torque distribution on the left and right wheels.

This paper revisits Grosch's work on rubber friction with Persson's contact theory. Persson's model is implemented to replicate Grosch's experiments on silicon carbide paper and compute the physical mechanism that Grosch identified as one of the main contributors to rubber friction: deformation friction. Grosch did not provide all rubber compound and surface characteristics required for the simulation work and, in order to obtain a full data set, the missing properties were adapted from literature sources and from measurements. The simulation results show that the deformation contribution is modeled correctly by Persson's model in terms of peak magnitude and sliding velocity at which the peak is located. On the contrary, poor correlation is found for the shape of the deformation friction master curve.

Accurate simulation of tyre forces relies on the knowledge of the friction characteristics between the tyre and the ground surface. Integrating realistic friction characteristics into a simple brush model was shown to improve the accuracy of the longitudinal and lateral force simulation for pure slip conditions. This paper extends the capabilities of a friction-integrated brush-type tyre model to accurately simulate combined slip conditions. Simulation results are validated with experimental tyre data.

© 2012 WEVA.This paper deals with the description of current and future vehicle technology related to yaw moment control, anti-lock braking and traction control through the employment of effective torque vectoring strategies for electric vehicles. In particular, the adoption of individually controlled electric powertrains with the aim of tuning the vehicle dynamic characteristics in steady-state and transient conditions is discussed. This subject is currently investigated within the European Union (EU) funded Seventh Framework Programme (FP7) consortium E-VECTOORC, focused on the development and experimental testing of novel control strategies. Through a comprehensive literature review, the article outlines the stateof- the-art of torque vectoring control for fully electric vehicles and presents the philosophy and the potential impact of the E-VECTOORC control structure from the viewpoint of torque vectoring for vehicle dynamics enhancement.

This paper discusses the vehicle dynamics control system of an all-wheel-drive electric vehicle with four on-board motors. Each driveline is characterized by complex torsional dynamics caused by the gearbox and the half-shaft located between the electric motor and the wheel. Such a drivetrain configuration can benefit from a specific controller, i.e., the active vibration controller (AVC), which increases the damping ratio of the actuation system. The AVC enhances the effectiveness of the other vehicle dynamics controllers such as the direct yaw moment controller (DYC) and the wheel slip controllers (WSCs). This study introduces examples of AVC, DYC and WSC implementations, and their experimental validation on the electric vehicle demonstrator of the European Union FP7 E-VECTOORC project. The experimental results confirm that the powertrain architecture with individually controlled on-board motors significantly improves the traction, braking and cornering capabilities of the electric vehicle, while increasing comfort and active safety.

Steering control for path tracking in autonomous vehicles is well documented in the literature. Also, continuous direct yaw moment control, i.e., torque-vectoring, applied to human-driven electric vehicles with multiple motors is extensively researched. However, the combination of both controllers is not yet well understood. This paper analyzes the benefits of torque-vectoring in an autonomous electric vehicle, either by integrating the torque-vectoring system in the path tracking controller, or through its separate implementation alongside the steering controller for path tracking. A selection of path tracking controllers is compared in obstacle avoidance tests simulated with an experimentally validated vehicle dynamics model. A genetic optimization is used to select the controller parameters. Simulation results confirm that torque-vectoring is beneficial to autonomous vehicle response. The integrated controllers achieve the best performance if they are tuned for the specific tire-road friction condition. However, they can also cause unstable behavior when they operate in lower friction conditions without any re-tuning. On the other hand, separate torque-vectoring implementations provide consistently stable cornering response for a wide range of friction conditions. Controllers with preview formulations, or based on appropriate reference paths with respect to the middle line of the available lane, are beneficial to the path tracking performance.

Individually-controlled powertrains of fully electric vehicles present an opportunity to enhance the steady-state and transient cornering response of a car via continuously-acting controllers and enable various “driving modes” to be available. This study investigates the associated potential for energy savings through the minimization of power losses from the motor units via wheel torque allocation. Power losses in straight-ahead driving and a ramp steer maneuver for different motor types and under different wheel torque allocation schemes are analyzed in an offline simulation approach. Significant reductions in motor power losses are achieved for two motor types using an optimization scheme based on look-up tables of motor loss data. Energy loss minimization cannot be achieved through a direct quadratic approximation of the power losses.

Latest advances in road profile sensors make the implementation of pre-emptive suspension control a viable option for production vehicles. From the control side, model predictive control (MPC) in combination with preview is a powerful solution for this application. However, the significant computational load associated with conventional implicit model predictive controllers (i-MPCs) is one of the limiting factors to the widespread industrial adoption of MPC. As an alternative, this paper proposes an explicit model predictive controller (e-MPC) for an active suspension system with preview. The MPC optimization is run offline, and the online controller is reduced to a function evaluation. To overcome the increased memory requirements, the controller uses the recently developed regionless e-MPC approach. The controller was assessed through simulations and experiments on a sport utility vehicle demonstrator with controllable hydraulic suspension actuators. For frequencies

In track-oriented road cars with electric powertrains, the ability to recuperate energy during track driving is significantly affected by the frequent interventions of the antilock braking system (ABS), which usually severely limits the regenerative torque level because of functional safety considerations. In high-performance vehicles, when controlling an active rear wing to maximize brake regeneration, it is unclear whether it is preferable to maximize drag by positioning the wing into its stall position, to maximize downforce, or to impose an intermediate aerodynamic setup. To maximize energy recuperation during braking from high speeds, this paper presents a novel integrated open-loop strategy to control: (i) the orientation of an active rear wing; (ii) the front-to-total brake force distribution; and (iii) the blending between regenerative and friction braking. For the case study wing and vehicle setup, the results show that the optimal wing positions for maximum regeneration and maximum deceleration coincide for most of the vehicle operating envelope. In fact, the wing position that maximizes drag by causing stall brings up to 37% increased energy recuperation over a passive wing during a braking maneuver from 300 km/h to 50 km/h by preventing the ABS intervention, despite achieving higher deceleration and a 2% shorter stopping distance. Furthermore, the maximum drag position also reduces the longitudinal tire slip power losses, which, for example, results in a 0.4% recuperated energy increase when braking from 300 km/h to 50 km/h in high tire–road friction conditions at a deceleration close to the limit of the vehicle with passive aerodynamics, i.e., without ABS interventions.

This paper investigates a torque-vectoring formulation for the combined control of the yaw rate and hitch angle of an articulated vehicle through a direct yaw moment generated on the towing car. The formulation is based on a single-input single-output feedback control structure, in which the reference yaw rate for the car is modified when the incipient instability of the trailer is detected with a hitch angle sensor. The design of the hitch angle controller is described, including the gain scheduling as a function of vehicle speed. The controller performance is assessed by means of frequency domain and phase plane analyses, and compared with that of an industrial trailer sway mitigation algorithm. In addition, the novel control strategy is implemented in a high-fidelity articulated vehicle model for robustness assessment, and experimentally tested on an electric vehicle demonstrator with four on-board drivetrains, towing two different conventional single-axle trailers. The results show that: (i) the torque-vectoring controller based only on the yaw rate of the car is not sufficient to mitigate trailer instability in extreme conditions; and (ii) the proposed controller provides safe trailer behaviour during the comprehensive set of manoeuvres, thus justifying the additional hardware complexity associated with the hitch angle measurement.

E-mobility is a game changer for the automotive domain. It promises significant reduction in terms of complexity and in terms of local emissions. With falling prices and recent technological advances, the second generation of electric vehicles (EVs) that is now in production makes electromobility an affordable and viable option for more and more transport mission (people, freight). Current e-vehicle platforms still present architectural similarities with respect to combustion engine vehicle (e.g., centralized motor). Target of the European project EVC1000 is to introduce corner solutions with in-wheel motors supported by electrified chassis components (brake-by-wire, active suspension) and advanced control strategies for full potential exploitation. Especially, it is expected that this solution will provide more architectural freedom toward “design-for-purpose” vehicles built for dedicated usage models, further providing higher performances. Target of this paper are (a) to introduce the EVC1000 project and results achieved so far; (b) with the example of two vehicle platforms (AUDI E-tron and JAC iEV7) to discuss platform migration opportunities and challenges related to corner solutions, and (c) to present preliminary results (simulation based) with respect to expected performance increase.

This paper describes a torque-vectoring (TV) algorithm for the control of the hitch angle of an articulated vehicle. The hitch angle control function prevents trailer oscillations and instability during extreme cornering maneuvers. The proposed control variable is a weighted combination of terms accounting for the yaw rate, sideslip angle and hitch angle of the articulated vehicle. The novel control variable formulation results in a single-input single-output (SISO) feedback controller. In the specific application a simple proportional integral (PI) controller with gain scheduling on vehicle velocity is developed. The TV system is implemented and experimentally tested on a fully electric vehicle with four on-board drivetrains, towing a single-axle passive trailer. Sinusoidal steer test results show that the proposed algorithm significantly improves the behavior of the articulated vehicle, and justify further research on the topic of hitch angle control through TV.

Automotive suspension systems are key to ride comfort and handling performance enhancement. In the last decades semi-active and active suspension configurations have been the focus of intensive automotive engineering research, and have been implemented by the industry. The recent advances in road profile measurement and estimation systems make road-preview-based suspension control a viable solution for production vehicles. Despite the availability of a significant body of papers on the topic, the literature lacks a comprehensive and up-to-date survey on the variety of proposed techniques for suspension control with road preview, and the comparison of their effectiveness. To cover the gap, this literature review deals with the research conducted over the past decades on the topic of semi-active and active suspension controllers with road preview. The main formulations are reported for each control category, and the respective features are critically analysed, together with the most relevant performance indicators. The paper also discusses the effect of the road preview time on the resulting system performance, and identifies control development trends.

Among other variables, smart tyre systems are capable of determining tyre contact forces. Combining this information with the signals obtained from conventional vehicle sensors, e.g. inertial measurement units, wheel speed sensors and steering wheel angle sensors, improves the estimation accuracy of the states used by the vehicle dynamics controllers of production cars. This study assesses the performance improvement brought by the vertical and longitudinal tyre contact force signals, obtained through smart tyres, to an unscented Kalman filter (UKF) for vehicle speed and sideslip angle estimation, based on a nonlinear vehicle dynamics model. Two UKF designs, excluding and including smart tyre information, are compared by using experimental data from a purposely sensorised high-performance passenger car, along a comprehensive set of manoeuvres. The results show average ∼60% and ∼37% reductions of the root mean square values of the normalised vehicle speed and sideslip angle estimation errors for the filter design receiving the smart tyre information. In comparison with the more conventional UKF design without tyre force inputs, the smart tyre based estimator is also characterised by significantly enhanced robustness and adaptability to typical variations of vehicle and tyre parameters, such as the tyre-road friction coefficient.

The International Tyre Colloquium has a successful history in discussing the latest progress in the understanding and simulation of tyre-road-vehicle interactions. The first Tyre Colloquium was organised by Prof Pacejka in 1991 (Delft), the second one was in Berlin in 1997, organised by Prof Böhm and Prof Willumeit, and the third one was in Vienna in 2004, organised by Prof Lugner and Prof Plöchl. In line with the tradition, the 4th Tyre Colloquium was focused on topics related to modelling of tyres for vehicle dynamics analysis including: • Tyre measurements and measurement techniques • Tyre models • Application of tyre models to vehicle dynamics • Determination of tyre model parameters • Measurement and modelling of rubber friction • Tyre-road contact • Evaluation and verification of tyre models • Tyre design features and their consequences for the tyre behaviour

The benefits of individual wheel torque control, or torque vectoring, in terms of vehicle dynamics behaviour have been well documented in the literature. However, few studies analyse individual wheel torque control integrated with electric vehicle efficiency considerations. The possibilities and benefits of energy efficient torque vectoring control for electric vehicles with multiple drivetrains are discussed. In particular, energy consumption reductions can be obtained through specific design of the wheel torque control allocation algorithm and the reference yaw rate characteristics. Experiments with a four-wheel-drive electric vehicle demonstrate considerable energy savings.

Although the vehicle dynamics effects of variable anti-roll moment distribution actuated through active suspension systems are widely discussed in the literature, their model-based control has only been recently analysed, given the highly nonlinear nature of the involved dynamics. Moreover, the available studies do not discuss the trade-off between internal model complexity and controller performance, nor analyse the opportunities offered by vehicle connectivity, which enables the prediction of the steering angle and reference yaw rate profiles ahead. To address the gap, this paper introduces and assesses three optimal controllers for an electric vehicle with active suspensions, multiple powertrains, and a brake-by-wire system. The formulations are: (a) a gain scheduled output feedback linear quadratic regulator (OFLQR); (b) a nonlinear model predictive controller using a three-degree-of-freedom prediction model, without and with preview of the steering angle and reference yaw rate ahead, respectively referred to as NMPC-3 and NMPC-3-Pre; and (c) a nonlinear model predictive controller based on an eight-degree-of-freedom prediction model, referred to as NMPC-8 and NMPC-8-Pre depending on the absence or presence of preview. The results on an experimentally validated model show that: (i) NMPC-8 provides evident yaw rate tracking benefits with respect to (w.r.t) OFLQR and NMPC-3; and (ii) NMPC-8-Pre can bring ∼20% yaw rate tracking improvement w.r.t. an optimally tuned NMPC-8 configuration.

Individually-controlled power trains of fully electric vehicles present an opportunity to enhance the steady-state and transient cornering response of a car via continuously-acting controllers and enable various "driving modes" to be available. This study investigates the associated potential for energy savings through the minimization of power losses from the motor units via wheel torque allocation. Power losses in straight-ahead driving and a ramp steer maneuver for different motor types and under different wheel torque allocation schemes are analyzed in an offline simulation approach. Significant reductions in motor power losses are achieved for two motor types using an optimization scheme based on look-up tables of motor loss data. Energy loss minimization cannot be achieved through a direct quadratic approximation of the power losses.

This article is the second part of a two-part article looking at carcass deflections, contact pressure and shear stress distributions for a steady-rolling, slipping and cambered tyre. In the first part, a previously described and validated finite-element (FE) model of a racing-car tyre is developed further to extract detailed results which are not easily obtainable through measurements on an actual tyre. Generally, these results aid in the understanding of contact patch characteristics. In particular, they form a basis for the development of a simpler physical tyre model, which forms the focus of this part of the article. The created simpler tyre model has the following three purposes: (i) to reduce computational demand while retaining accuracy, (ii) to allow identification of tyre model features that are fundamental to an accurate representation of the contact stresses and (iii) to create a facility for better understanding of tyre wear mechanisms and thermal effects. Results generated agree well with the physically realistic rolling-tyre behaviour demonstrated by the FE model. Also, the model results indicate that an accurate simulation of the contact stresses requires a detailed understanding of carcass deformation behaviour.

Waterborne coatings emit a low amount of harmful volatile organic compounds (VOCs) into the atmosphere compared to solvent-cast coatings. A typical waterborne formulation for agricultural applications consists of colloidal thermoplastic particles (latex) as the binder, a thickener to raise the viscosity, inorganic filler particles with a water-soluble dispersant, and a colloidal wax to modify surface properties. The formulations typically contain hygroscopic species that are potentially subject to softening by environmental moisture. The hardness, tack adhesion, and coefficient of friction of formulated coatings determines their suitability in applications. However, the relationship of these properties to the components in a coating formulation has not been adequately explored. Furthermore, the relationship between hygroscopic components and properties is an added complication. Here, we have characterized the hardness and tack adhesion of model formulated coatings using a single micro-indentation cycle with a conical indenter under controlled temperatures (above and below the glass transition temperature of a latex binder) and relative humidities. In parallel, we measured the coefficient of kinetic friction, μk, for the same coatings using a bespoke testing rig under controlled environmental conditions. Across a range of temperatures, RH and compositions, we find an inverse correlation between the coating hardness and μk. Any correlation of μk with the roughness of the coatings, which varies with the composition, is less clear. Formulations that contain wax additives have a higher μk at a low RH of 10%, in comparison to formulations without wax. For the wax formulations, μk decreases when the RH is raised, whereas in non-wax formulations, μk increases with increasing RH. Wax-containing coatings are hydrophilic (with a lower water contact angle), however the wax has a lower water permeability. A lubricating layer of water can explain the lower observed μk in these formulations. The addition of wax is also found to planarize the coating surface, which leads to higher tack adhesion in dry coatings in comparison to coatings without wax. Greater adhesive contact in these coatings can explain their higher friction. Our systematic research will aid the design of seed coating formulations to achieve their optimum properties under a wide range of environmental conditions.

Electric vehicles (EVs) with four individually controlled drivetrains are over-actuated systems, and therefore, the total wheel torque and yaw moment demands can be realized through an infinite number of feasible wheel torque combinations. Hence, an energy-efficient torque distribution among the four drivetrains is crucial for reducing the drivetrain power losses and extending driving range. In this paper, the optimal torque distribution is formulated as the solution of a parametric optimization problem, depending on the vehicle speed. An analytical solution is provided for the case of equal drivetrains, under the experimentally confirmed hypothesis that the drivetrain power losses are strictly monotonically increasing with the torque demand. The easily implementable and computationally fast wheel torque distribution algorithm is validated by simulations and experiments on an EV demonstrator, along driving cycles and cornering maneuvers. The results show considerable energy savings compared to alternative torque distribution strategies.

This paper presents a novel gearshift controller to improve longitudinal acceleration and driver comfort of fully electric vehicles consisting of two drivetrains, one per each axle. In particular, a torque-fill controller is developed to provide seamless gearshifts on one axle by varying the torque on the other axle. The developed controller was experimentally tested on a prototype vehicle. Results are compared with acceleration performance of alternative fully electric vehicle configurations and demonstrate the benefit of enhanced ride comfort through a seamless gearshift.

Electric vehicles with multiple motors permit continuous direct yaw moment control, also called torque-vectoring. This allows to significantly enhance the cornering response, e.g., by extending the linear region of the vehicle understeer characteristic, and by increasing the maximum achievable lateral acceleration. These benefits are well documented for human-driven cars, yet limited information is available for autonomous/driverless vehicles. In particular, over the last few years, steering controllers for automated driving at the cornering limit have considerably advanced, but it is unclear how these controllers should be integrated alongside a torque-vectoring system. This contribution discusses the integration of torque-vectoring control and automated driving, including the design and implementation of the torque-vectoring controller of an autonomous electric vehicle for a novel racing competition. The paper presents the main vehicle characteristics and control architecture. A quasi-static model is introduced to predict the understeer characteristics at different longitudinal accelerations. The model is coupled with an off-line optimization for the a-priori investigation of the potential benefits of torque-vectoring. The systematic computation of the achievable cornering limits is used to specify and design realistic maps of the reference yaw rate, and a non-linear feedforward yaw moment contribution providing the reference cornering response in quasi-static conditions. A gain scheduled proportional integral controller increases yaw damping, thus enhancing the transient response. Simulation results demonstrate the effectiveness of the proposed approach.

In electric vehicles with multiple motors, the individual wheel torque control, i.e., the so-called torque-vectoring, significantly enhances the cornering response and active safety. Torque-vectoring can also increase energy efficiency, through the appropriate design of the reference understeer characteristic and the calculation of the wheel torque distribution providing the desired total wheel torque and direct yaw moment. To meet the industrial requirements for real vehicle implementation, the energy-efficiency benefits of torque-vectoring should be achieved via controllers characterised by predictable behaviour, ease of tuning and low computational requirements. This paper discusses a novel energy-efficient torque-vectoring algorithm for an electric vehicle with in-wheel motors, which is based on a set of rules deriving from the combined consideration of: i) the experimentally measured electric powertrain efficiency maps; ii) a set of optimisation results from a non-linear quasi-static vehicle model, including the computation of tyre slip power losses; and iii) drivability requirements for comfortable and safe cornering response. With respect to the same electric vehicle with even wheel torque distribution, the simulation results, based on an experimentally validated vehicle dynamics simulation model, show: a) up to 4% power consumption reduction during straight line operation at constant speed; b) >5% average input power saving in steady-state cornering at lateral accelerations >3.5 m/s2; and c) effective compensation of the yaw rate and sideslip angle oscillations during extreme transient tests.

The continuous, precise modulation of the driving and braking torque of each wheel is considered to be the ultimate goal for controlling the performance of a vehicle in steady-state and transient conditions. To do so, dedicated torque-vectoring controllers which allow optimal wheel torque distribution under all possible driving conditions have to be developed. Commonly, vehicle torque-vectoring controllers are based on a hierarchical approach, consisting of a high-level supervisory controller which evaluates a corrective yaw moment, and a low-level controller which defines the individual wheel torque reference values. The problem of the optimal individual wheel torque distribution for a particular driving condition can be solved through an optimization-based control allocation algorithm, which must rely on the appropriate selection of the objective function. With a newly developed off-line optimization procedure, this article assesses the performance of alternative objective functions for the optimal wheel torque distribution of a four-wheel-drive fully electric vehicle. Results show that objective functions based on minimum tire slip criterion provide better control performance than functions based on energy efficiency.

This paper presents a novel 4-wheel-drive electric vehicle layout consisting of one on-board electric drivetrain per axle. Each drivetrain includes a simplified clutch-less 2-speed transmission system and an open differential, to transmit the torque to the wheels. This drivetrain layout allows eight different gear state combinations at the vehicle level, thus increasing the possibility of running the vehicle in a more energy efficient state for the specific wheel torque demand and speed. Also, to compensate the torque gap during gearshifts, a ‘torque-fill’ controller was developed that varies the motor torque on the axle not involved in the gearshift. Experimental tests show the effectiveness of the developed gearshift strategy extended with the torque-fill capability. Energy efficiency benefits are discussed by comparing the energy consumptions of the case study vehicle controlled through a constant front-to-total wheel torque distribution and conventional gearshift maps, and the same vehicle with an energy management system based on an off-line optimization. Results demonstrate that the more advanced controller brings a significant reduction of the energy consumption at constant speed and along different driving cycles.

Electric vehicles with multiple motors permit continuous direct yaw moment control, also called torque-vectoring. This allows to significantly enhance the cornering response, e.g., by extending the linear region of the vehicle understeer characteristic, and by increasing the maximum achievable lateral acceleration. These benefits are well documented for human-driven cars, yet limited information is available for autonomous/driverless vehicles. In particular, over the last few years, steering controllers for automated driving at the cornering limit have considerably advanced, but it is unclear how these controllers should be integrated alongside a torque-vectoring system. This contribution discusses the integration of torque-vectoring control and automated driving, including the design and implementation of the torque-vectoring controller of an autonomous electric vehicle for a novel racing competition. The paper presents the main vehicle characteristics and control architecture. A quasi-static model is introduced to predict the understeer characteristics at different longitudinal accelerations. The model is coupled with an off-line optimization for the a-priori investigation of the potential benefits of torque-vectoring. The systematic computation of the achievable cornering limits is used to specify and design realistic maps of the reference yaw rate, and a non-linear feedforward yaw moment contribution providing the reference cornering response in quasi-static conditions. A gain scheduled proportional integral controller increases yaw damping, thus enhancing the transient response. Simulation results demonstrate the effectiveness of the proposed approach.

Some general observations relating to tyre shear forces and road surfaces are followed by more specific considerations from circuit racing. The discussion then focuses on the mechanics of rubber friction. The classical experiments of Grosch are outlined and the interpretations that can be put on them are discussed. The interpretations involve rubber viscoelasticity, so that the vibration properties of rubber need to be considered. Adhesion and deformation mechanisms for energy dissipation at the interface between rubber and road and in the rubber itself are highlighted. The enquiry is concentrated on energy loss by deformation or hysteresis subsequently. Persson's deformation theory is outlined and the material properties necessary to apply the theory to Grosch's experiments are discussed. Predictions of the friction coefficient relating to one particular rubber compound and a rough surface are made using the theory and these are compared with the appropriate results from Grosch. Predictions from Persson's theory of the influence of nominal contact pressure on the friction coefficient are also examined. The extent of the agreement between theory and experiment is discussed. It is concluded that there is value in the theory but that it is far from complete. There is considerable scope for further research on the mechanics of rubber friction.

Nonlinear model predictive control is proposed in multiple academic studies as an ad-vanced control system technology for vehicle operation at the limits of handling, allow-ing high tracking performance and formal consideration of system constraints. How-ever, the implementation of implicit nonlinear model predictive control (NMPC), in which the control problem is solved on-line, poses significant challenges in terms of computational load. This issue can be overcome through explicit NMPC, in which the optimization problem is solved off-line, and the resulting explicit solution, with guar-anteed level of sub-optimality, is evaluated on-line. Due to the simplicity of the explicit solution, the real-time execution of the controller is possible even on automotive control hardware platforms with low specifications. The explicit nature of the control law fa-cilitates feasibility checks and functional safety validation. This study presents a yaw and lateral stability controller based on explicit NMPC, actuated through the electro-hydraulically controlled friction brakes of the vehicle. The controller performance is demonstrated during sine-with-dwell tests simulated with a high-fidelity model. The analysis includes a comparison of implicit and explicit implementations of the control system.

Electric vehicles with individually controlled drivetrains allow torque-vectoring, which improves vehicle safety and drivability. This paper investigates a new approach to the concurrent control of yaw rate and sideslip angle. The proposed controller is a simple single input single output (SISO) yaw rate controller, in which the reference yaw rate depends on the vehicle handling requirements, and the actual sideslip angle. The sideslip contribution enhances safety, as it provides a corrective action in critical situations, e.g., in case of oversteer during extreme cornering on a low friction surface. The proposed controller is experimentally assessed on an electric vehicle demonstrator, along two maneuvers with quickly variable tire-road friction coefficient. Different longitudinal locations of the sideslip angle used as control variable are compared during the experiments. Results show that: i) the proposed SISO approach provides significant improvements with respect to the vehicle without torque-vectoring, and the controlled vehicle with a reference yaw rate solely based on the handling requirements for high-friction maneuvering; and ii) the control of the rear axle sideslip angle provides better performance than the control of the sideslip angle at the centre of gravity.

Model predictive control (MPC) is increasingly finding its way into industrial applications, due to its superior tracking performance and ability to formally handle system constraints. However, the real-time capability problems related to the conventional implicit model predictive control (i-MPC) framework are well known, especially when targeting low-cost electronic control units (ECUs) for high bandwidth systems, such as automotive active suspensions, which are the topic of this paper. In this context, to overcome the real-time implementation issues of i-MPC, this study proposes explicit model predictive control (e-MPC), which solves the optimization problem off-line, via multi-parametric quadratic programming (mp-QP). e-MPC reduces the on-line algorithm to a function evaluation, which replaces the computationally demanding on-line solution of the quadratic programming (QP) problem. An e-MPC based suspension controller is designed and experimentally validated for a case study Sport Utility Vehicle (SUV), equipped with the active ACOCAR suspension system from the Tenneco Monroe product family. The target is to improve ride comfort in the frequency range of primary ride (< 4 Hz), without affecting the performance at higher frequencies. The proposed e-MPC implementations reduce the root mean square (RMS) value of the sprung mass acceleration by > 40% compared to the passive vehicle set-up for frequencies < 4 Hz, and by up to 19% compared to the same vehicle with a skyhook controller on the 0-100 Hz frequency range.

This paper presents an H ∞ torque-vectoring control formulation for a fully electric vehicle with four individually controlled electric motor drives. The design of the controller based on loop shaping and a state observer configuration is discussed, considering the effect of actuation dynamics. A gain scheduling of the controller parameters as a function of vehicle speed is implemented. The increased robustness of the H ∞ controller with respect to a Proportional Integral controller is analyzed, including simulations with different tire parameters and vehicle inertial properties. Experimental results on a four-wheel-drive electric vehicle demonstrator with on-board electric drivetrains show that this control formulation does not need a feedforward contribution for providing the required cornering response in steady-state and transient conditions.

Fully electric vehicles with individually controlled drivetrains can provide a high degree of drivability and vehicle safety, all while increasing the cornering limit and the ‘fun-to-drive’ aspect. This paper investigates a new approach on how sideslip control can be integrated into a continuously active yaw rate controller to extend the limit of stable vehicle cornering and to allow sustained high values of sideslip angle. The controllability-related limitations of integrated yaw rate and sideslip control, together with its potential benefits, are discussed through the tools of multi-variable feedback control theory and non-linear phase-plane analysis. Two examples of integrated yaw rate and sideslip control systems are presented and their effectiveness is experimentally evaluated and demonstrated on a four-wheel-drive fully electric vehicle prototype. Results show that the integrated control system allows safe operation at the vehicle cornering limit at a specified sideslip angle independent of the tire-road friction conditions.