Dr Davide Tavernini

This paper presents a novel approach integrating motion replanning, path tracking and vehicle stability for collision avoidance using nonlinear Model Predictive Contouring Control. Employing torque vectoring capabilities, the proposed controller is able to stabilise the vehicle in evasive manoeuvres at the limit of handling. A nonlinear double-track vehicle model, together with an extended Fiala tyre model, is used to capture the nonlinear coupled longitudinal and lateral dynamics. The optimised control inputs are the steering angle and the four longitudinal wheel forces to minimise the tracking error in safe situations and maximise the vehicle-to-obstacle distance in emergency manoeuvres. These optimised longitudinal forces generate an additional direct yaw moment, enhancing the vehicle's lateral agility and aiding in obstacle avoidance and stability maintenance. The longitudinal tyre forces are constrained using the tyre friction cycle. The proposed controller has been tested on rapid prototyping hardware to prove real-time capability. In a high-fidelity simulation environment validated with experimental data, our proposed approach successfully avoids obstacles and maintains vehicle stability. It outperforms two baseline controllers: one without torque vectoring and another one without collision avoidance prioritisation. Furthermore, we demonstrate the robustness of the proposed approach to vehicle parameter variations, road friction, perception, and localisation errors. The influence of each variation is statistically assessed to evaluate its impact on the performance, providing guidelines for future controller design.

The literature shows increasing interest in the energy efficiency aspects of electric vehicles with multiple actuators, e.g., capable of individual wheel torque and rear-wheel-steering control, and proposes controllers considering the relevant vehicle power losses. However, the available studies lack systematic analyses on: i) the energy saving potential of the individual actuation methods, and their combinations; and ii) the operating conditions in which a set of actuators is particularly effective in reducing power consumption. This paper targets the identified gap. After providing background on the relevant power losses, three forms of actuation, i.e., torque-vectoring through two or four electric powertrains, active suspensions for front-to-total anti-roll moment distribution control, and rear-wheel-steering, are explored through a set of simulations in quasi-steady-state conditions, by using an experimentally validated high-fidelity non-linear vehicle model. The analysis covers a range of vehicle speeds, longitudinal and lateral accelerations, and tire-road friction conditions, and determines: a) the most energy-efficient understeer characteristics, i.e., the loci of the front steering angle as a function of lateral acceleration providing the minimum power consumption, for each set of actuators; b) the energy-efficient actuations for achieving given understeer characteristics; and c) the power consumption penalty of each considered configuration with respect to the one with the complete set of actuators.

Although the vehicle dynamics effects of variable anti-roll momentdistribution actuated through active suspension systems are widelydiscussed in the literature, their model-based control has only beenrecently analysed, given the highly nonlinear nature of the involveddynamics. 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, whichenables the prediction of the steering angle and reference yawrate profiles ahead. To address the gap, this paper introducesand assesses three optimal controllers for an electric vehicle withactive suspensions, multiple powertrains, and a brake-by-wire sys-tem. The formulations are: (a) a gain scheduled output feedbacklinear quadratic regulator (OFLQR); (b) a nonlinear model predictivecontroller using a three-degree-of-freedom prediction model, with-out and with preview of the steering angle and reference yaw rateahead, 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 resultson an experimentally validated model show that: (i) NMPC-8 pro-vides evident yaw rate tracking benefits with respect to (w.r.t) OFLQRand NMPC-3; and (ii) NMPC-8-Pre can bring∼20% yaw rate trackingimprovement w.r.t. an optimally tuned NMPC-8 configuration.

The introduction of active safety systems and advanced driver assistance systems has enhanced the control authority over the vehicle dynamics through specialized actuators, enabling, for instance, independent wheel torque control. During emergency situations, these systems step in to aid the driver by limiting vehicle response to a stable and controllable range of low longitudinal tire slips and slip angles. This approach makes vehicle behavior predictable and manageable for the average human driver; however, it is conservative in case of driving automation. In fact, past research has shown that exceeding the operational boundaries of conventional active safety systems enables trajectories that are otherwise unattainable. This paper presents a nonlinear model predictive controller (NMPC) for path tracking (PT), which integrates steering, front-to-total longitudinal tire force distribution, and direct yaw moment actuation, and can operate beyond the limit of handling, e.g., to induce drift, if this is beneficial to PT. Simulation results of emergency conditions in an intersection scenario highlight that the proposed solution provides significant safety improvements, when compared to the concurrent operation of PT algorithms and the current generation of vehicle stability controllers.

State-of-the-art antilock braking systems (ABS) are reactive, i.e., they activate after detecting that wheels tend to lock in braking. With vehicle-to-everything (V2X) connectivity becoming a reality, it will be possible to gather information on the tire–road friction conditions ahead, and use these data to enhance wheel slip control performance, especially during abrupt friction level variations. This study presents a nonlinear model predictive controller (NMPC) for ABS with preview of the tire–road friction profile. The potential benefits, optimal prediction horizon, and robustness of the preview algorithm are evaluated for different dynamic characteristics of the brake actuation system, through an experimentally validated simulation model. Proof-of-concept experiments with an electric vehicle prototype highlight the real-time capability of the proposed NMPC ABS, and the associated wheel slip control performance improvements in braking maneuvers with high-to-low friction transitions.

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.

The design and optimisation of a permanent magnet-assisted synchronous reluctance (PMaSynR) traction machine is described to improve its energy efficiency over a selection of driving cycles, when installed on a four-wheel-drive electrically powered vehicle for urban use, with two on-board powertrains. The driving cycle-based optimisation is defined with the objective of minimising motor energy loss under strict size constraints, while maintaining the peak torque and restricting the torque ripple. The key design parameters that exert the most significant influence on the selected performance indicators are identified through a parametric sensitivity analysis. The optimisation brings a motor design that is characterised by an energy loss reduction of 8.2% over the WLTP Class 2 driving cycle and 11.7% over the NEDC and Artemis Urban driving cycles, at the price of a 4.7% peak torque reduction with respect to the baseline machine. Additional analysis, implemented outside the optimisation framework, revealed that different coil turn adjustments would reduce the energy loss along the considered driving cycles. However, under realistic size constraints, the optimal design solutions are the same.

Thanks to their road safety potential, automated vehicles are rapidly becoming a reality. In the last decade, automated driving has been the focus of intensive automotive engineering research, with the support of industry and governmental organisations. In automated driving systems, the path tracking layer defines the actuator commands to follow the reference path and speed profile. Model predictive control (MPC) is widely used for trajectory tracking because of its capability of managing multi-variable problems, and systematically considering constraints on states and control actions, as well as accounting for the expected future behaviour of the system. Despite the very large number of publications of the last few years, the literature lacks a comprehensive and updated survey on MPC for path tracking. To cover the gap, this literature review deals with the research conducted from 2015 until 2021 on model predictive path tracking control. Firstly, the survey highlights the significance of MPC in the recent path tracking control literature, with respect to alternative control structures. After classifying the different typologies of MPC for path tracking control, the adopted prediction models are critically analysed, together with typical optimal control problem formulations. This is followed by a summary of the most relevant results, which provides practical design indications, e.g., in terms of selection of prediction and control horizons. Finally, the most recent development trends are analysed, together with likely areas of further investigations, and the main conclusions are drawn.

Previous research showed that the integration of realistic tyre-road friction characteristics into a brush model improves the accuracy of simulating tyre forces under pure slip conditions. Building on this finding, this paper explores the development of a simple friction-integrated brush-type tyre model for accurate simulation of combined slip conditions. A small passenger car tyre is used as the case study implementation, for which extensive experimental measurements were obtained from flat-track testing covering a range of combined slip sweeps (±12° and ± 25%) for vertical loads from 1000 to 4000 N. The friction characteristics were captured using an experimentally derived master curve. Simulation results show good agreement with experimental data over a broad range of operating conditions, highlighting the benefits of the integration of friction characteristics also for combined slip conditions.

This study presents a nonlinear model predictive control (NMPC) formulation for preview-based traction control, which uses the information on the expected tire-road friction coefficient ahead to enhance the wheel slip control performance, in the context of connected vehicles with V2X features. Proof-of-concept experiments on an electric vehicle prototype highlight the real-time capability of the controller, and the wheel slip control performance improvement brought by the tire-road friction coefficient preview. Finally, an experimentally validated simulation model is used in sensitivity analyses, to evaluate the performance benefit of the preview-based controller for different dynamic characteristics (e.g., time constant and pure time delays) of the electric powertrains.

Devising planning algorithms for autonomous driving is non-trivial due to the presence of complex and uncertain interaction dynamics between road users. In this paper, we introduce a planning framework encompassing multiple action policies that are learned jointly from episodes of human-human interactions in naturalistic driving. The policy model is composed of encoder-decoder recurrent neural networks for modeling the sequential nature of interactions and mixture density networks for characterizing the probability distributions over driver actions. The model is used to simultaneously generate a finite set of context-dependent candidate plans for an autonomous agent and to anticipate the probable future plans of human drivers. This is followed by an evaluation stage to select the agent plan with the highest expected utility for execution. Our approach leverages rapid sampling of action distributions in parallel on a graphic processing unit, offering fast computation even when modeling the interactions among multiple vehicles and over several time steps. We present ablation experiments and comparison with two existing baseline methods to highlight several design choices that we found to be essential to our model’s success.We test the proposed planning approach in a simulated highway driving environment, showing that by using the model, the agent can plan actions that mimic the interactive behavior of humans.

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.

V2X connectivity and powertrain electrification are emerging trends in the automotive sector, which enable the implementation of new control solutions. Most of the production electric vehicles have centralized powertrain architectures consisting of a single central on-board motor, a single-speed transmission, an open differential, half-shafts, and constant velocity joints. The torsional drivetrain dynamics and wheel dynamics are influenced by the open differential, especially in split- scenarios, i.e., with different tire-road friction coefficients on the two wheels of the same axle, and are attenuated by the so-called anti-jerk controllers. Although a rather extensive literature discusses traction control formulations for individual wheel slip control, there is a knowledge gap on: a) model based traction controllers for centralized powertrains; and b) traction controllers using the preview of the expected tire-road friction condition ahead, e.g., obtained through V2X, for enhancing the wheel slip tracking performance. This study presents nonlinear model predictive control formulations for traction control and anti-jerk control in electric powertrains with central motor and open differential, and benefitting from the preview of the tire-road friction level. The simulation results in straight line and cornering conditions, obtained with an experimentally validated vehicle model, as well as the proof-of-concept experiments on an electric quadricycle prototype, highlight the benefits of the novel controllers.

This study applies nonlinear model predictive control (NMPC) to the torque-vectoring and front-to-total anti-roll moment distribution control of a four-wheel-drive electric vehicle with in-wheel-motors, a brake-by-wire system, and active suspension actuators. The NMPC cost function formulation is based on energy efficiency criteria, and strives to minimize the power losses caused by the longitudinal and lateral tire slips, friction brakes, and electric powertrains, while enhancing the vehicle cornering response in steady-state and transient conditions. The controller is assessed through simulations using an experimentally validated high-fidelity vehicle model, along ramp steer and multiple step steer maneuvers, including and excluding the direct yaw moment and active anti-roll moment distribution actuations. The results show: i) the substantial enhancement of energy saving and vehicle stabilization performance brought by the integration of the active suspension contribution and torque-vectoring; ii) the significance of the power loss terms of the NMPC formulation on the results; and iii) the effectiveness of the NMPC with respect to the benchmarking feedback and rule based controllers.

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.

This study investigates the influence of the buried magnet arrangement on the efficiency and drivability performance provided by an on-board interior permanent magnet synchronous machine for a four-wheel-drive electric car with two single-speed on-board powertrains. The relevant motor characteristics, including flux-linkage, inductance, electromagnetic torque, iron loss, total loss, and efficiency, are analyzed for a set of six permanent magnet configurations suitable for the specific machine, which is controlled through maximum-torque-per-ampere and maximum-torque-per-voltage strategies. Moreover, the impact of each magnet arrangement is analyzed in connection with the energy consumption along four driving cycles, as well as the longitudinal acceleration and gradeability performance of the considered vehicle. The simulation results identify the most promising rotor solutions, and show that: (i) the appropriate selection of the rotor configuration is especially important for the driving cycles with substantial high-speed sections; (ii) the magnet arrangement has a major impact on the maximum motor torque below the base speed, and thus on the longitudinal acceleration and gradeability performance; and (iii) the configurations that excel in energy efficiency are among the worst in terms of drivability, and vice versa, i.e., at the vehicle level, the rotor arrangement selection is a trade-off between energy efficiency and longitudinal vehicle dynamics.

In passenger cars active suspensions have been traditionally used to enhance comfort through body control, and handling through the reduction of the tyre load variations induced by road irregularities. However, active suspensions can also be designed to track a desired yaw rate profile through the control of the anti-roll moment distribution between the front and rear axles. The effect of the anti-roll moment distribution relates to the nonlinearity of tyre behaviour, which is difficult to capture in the linearised vehicle models normally used for control design. Hence, the tuning of anti-roll moment distribution controllers is usually based on heuristics. This paper includes an analysis of the effect of the lateral load transfer on the lateral axle force and cornering stiffness. A linearised axle force formulation is presented, and compared with a formulation from the literature, based on a quadratic relationship between cornering stiffness and load transfer. Multiple linearised vehicle models for control design are assessed in the frequency domain, and the respective controllers are tuned through optimisation routines. Simulation results from a nonlinear vehicle model are discussed to analyse the performance of the controllers, and show the importance of employing accurate models of the lateral load transfer effect during control design.

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.

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.

The market penetration of electric vehicles (EVs) is going to significantly increase in the next years and decades. However, EVs still present significant practical limitations in terms of mileage. Hence, the automotive industry is making important research efforts towards the progressive increase of battery energy density, reduction of battery charging time, and enhancement of electric powertrain efficiency. The electric machine is the main power loss contributor of an electric powertrain. This literature survey reviews the design and control methods to improve the energy efficiency of electric machines for EVs. The motor design requirements and specifications are described in terms of power density, efficiency along driving cycles, and cost, according to the targets set by the roadmaps of the main governmental agencies. The review discusses the stator and rotor design parameters, winding configurations, novel materials, construction technologies as well as control methods that are most influential on the power loss characteristics of typical traction machines. Moreover, the paper covers: i) driving cycle based design methods of traction motors, for energy consumption reduction in real operating conditions; and ii) novel machine topologies providing potential efficiency benefits.

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.

In vehicle dynamics, yaw rate control is used to improve the cornering response in steady-state and transient conditions. This can be achieved through an appropriate anti-roll moment distribution between the front and rear axles of a vehicle with controllable suspension actuators. Such control action alters the load transfer distribution, which in turn provokes a lateral tire force variation. With respect to the extensive set of papers from the literature discussing yaw rate tracking through active suspension control, this study presents: i) A detailed analysis of the effect of the load transfer on the lateral axle force and cornering stiffness; ii) A novel linearized single-track vehicle model formulation for control system design, based on the results in i); and iii) An optimization-based routine for the design of the non-linear feedforward contribution of the control action. The resulting feedforward-feedback controller is assessed through: a) Simulations with an experimentally validated model of a vehicle with active anti-roll bars (case study 1); and b) Experimental tests on a vehicle prototype with an active suspension system (case study 2).

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.

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.

Vehicles equipped with multiple electric machines allow variable distribution of propulsive and regenerative braking torques between axles or even individual wheels of the car. Left/right torque vectoring (i.e., a torque shift between wheels of the same axle) has been treated extensively in the literature; however, fewer studies focus on the torque shift between the front and rear axles, namely, front/rear torque vectoring, a drivetrain topology more suitable for mass production since it reduces complexity and cost. In this paper, we propose an online control strategy that can enhance vehicle agility and “fun-to-drive” for such a topology or, if necessary, mitigate oversteer during sublimit handling conditions. It includes a front/rear torque control allocation (CA) strategy that is formulated in terms of physical quantities that are directly connected to the vehicle dynamic behavior such as torques and forces, instead of nonphysical control signals. Hence, it is possible to easily incorporate the limitations of the electric machines and tires into the computation of the control action. Aside from the online implementation, this publication includes an offline study to assess the effectiveness of the proposed CA strategy, which illustrates the theoretical capability of affecting yaw moment that the front/rear torque vectoring strategy has for a given set of vehicle and road conditions and considering physical limitations of the tires and actuators. The development of the complete strategy is presented together with the results from hardware-in-the-loop (HiL) simulations, using a high fidelity vehicle model and covering various use cases.

This paper presents a traction control (TC) system for electric vehicles with in-wheel motors, based on explicit nonlinear 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 on the order of microseconds. These are significantly lower than the required time step for a TC application. Hence, the explicit model predictive controller can run at the same frequency as a simple TC system based on proportional integral (PI) technology. High-fidelity model simulations provide: 1) a performance comparison of the proposed explicit nonlinear model predictive controller (NMPC) with a benchmark PI-based traction controller with gain scheduling and anti-windup features, and 2) a performance comparison among two explicit and one implicit NMPCs 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 NMPC formulations.

In this paper, the effect of both passive and actively-modified vehicle handling characteristics on minimum time manoeuvring for vehicles with 4-wheel torque vectoring (TV) capability is studied. First, a baseline optimal TV strategy is sought, independent of any causal control law. An optimal control problem (OCP) is initially formulated considering 4 independent wheel torque inputs, together with the steering angle rate, as the control variables. Using this formulation, the performance benefit using TV against an electric drive train with a fixed torque distribution, is demonstrated. The sensitivity of TV-controlled manoeuvre time to the passive understeer gradient of the vehicle is then studied. A second formulation of the OCP is introduced where a closed-loop TV controller is incorporated into the system dynamics of the OCP. This formulation allows the effect of actively modifying a vehicle's handling characteristic via TV on its minimum time cornering performance of the vehicle to be assessed. In particular, the effect of the target understeer gradient as the key tuning parameter of the literature-standard steady-state linear single-track model yaw rate reference is analysed.

The distribution of brake forces between front and rear axles of a vehicle is typically specified such that the same level of brake force coefficient is imposed at both front and rear wheels. This condition is known as ‘ideal’  distribution and it is required to deliver the maximum vehicle deceleration and minimum braking distance. For subcritical braking conditions, the deceleration demand may be delivered by different distributions between front and rear braking forces. In this research we show how to obtain the optimal distribution which minimises the pitch angle of a vehicle and hence enhances driver subjective feel during braking. A vehicle model including suspension geometry features is adopted. The problem of the minimum pitch brake distribution for a varying deceleration level demand is solved by means of a model predictive control (MPC) technique. To address the problem of the undesirable pitch rebound caused by a full-stop of the vehicle, a second controller is designed and implemented independently from the braking distribution in use. An extended Kalman filter is designed for state estimation and implemented in a high fidelity environment together with the MPC strategy. The proposed solution is compared with the reference ‘ideal’   distribution as well as another previous feed-forward solution.

The paper investigates the optimality of the handbrake cornering, a strategy widespread among rally drivers. Nonlinear optimal control techniques are used to mimic real driver behavior. A proper yet simple cost function is devised to induce the virtual optimal driver to control the car at its physical limits while using the handbrake technique. The optimal solution is validated against experimental data by a professional rally driver performing the handbrake technique on a loose off-road surface. The effects of road surface, inertial properties, center of mass position, and friction coefficient are analyzed to highlight that the optimality of the maneuver does not depend on the particular vehicle data set used. It turns out that the handbrake maneuvering corresponds to the minimum time and minimum (lateral) space strategy on a tight hairpin corner. The results contribute to the understanding of one of the so-called aggressive driving techniques.

This paper investigates the minimum time/limit handling car manoeuvring through nonlinear optimal control techniques. The resulting ‘optimal driver’ controls the car at its physical limits. The focus is on cornering: different road surfaces (dry and wet paved road, dirt and gravel off-road) and transmission layouts (rear-wheel-drive, front-wheel-drive and all-wheel-drive) are considered. Low-drift paved circuit-like manoeuvres and aggressive/high-drift even counter-steering rally like manoeuvres are found depending on terrain/layout combinations. The results shed a light on the optimality of limit handling techniques.

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.

Nonlinear model predictive control 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 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 guaranteed 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 facilitates feasibility checks and functional safety validation. This study presents a yaw and lateral stability controller based on explicit NMPC, actuated through the electrohydraulically 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.

The brake force distribution between front and rear axles of a vehicle is typically specified such that front and rear wheels operate at the same level of brake force coefficient (i.e. equal normalized by axle weight brake forces). It can be shown that this `ideal' distribution is required to deliver the maximum vehicle deceleration and minimum braking distance. In the case of subcritical braking, the deceleration demand may be delivered by different distributions between front and rear braking forces. In this work we obtain the optimal distribution which minimizes the pitch angle and hence enhances driver comfort during braking. This is a unique study in the literature. A vehicle model with appropriate consideration of the suspension geometry is adopted. A feed-forward controller (i.e. quasi-static map) for brake force distribution is generated and tested on a demonstrator vehicle. In addition, to address the problem of the undesirable rebound overshoot caused by a full-stop of the vehicle, an LQR, which can be applied independently from the braking distribution in use, is designed. A second LQR is proposed as an alternative to the feed-forward approach in the calculation of the minimum pitch force distribution.

Recent advances in the automotive industry have incorporated the latest technology in vehicle electrification, with the aim to reduce fuel consumption, pollutants emissions, as well as enhance vehicle performance and safety. As a result, Electric Vehicles (EV) and Hybrid Electric Vehicles (HEV) have become the imminent automotive future, establishing important challenges in vehicle systems integration and control. In these vehicles, the regenerative braking is currently the major technique of energy recovery, providing accurate control on the brake torque applied. However regenerative brakes still need the support of conventional friction brakes, mainly due to the battery limitations. Consequently, the coordination of both braking strategies becomes critical for the safe actuation of braking related systems such as: ABS and ESP. Unfortunately, the torque blending between friction and regenerative brakes is a complicated task due to the different systems inputs; the regenerative brakes receive torque inputs, whilst the friction brakes work with pressure inputs. This paper proposes the friction brake torque estimation to simplify the torque blending, and improve the energy recovery and driving safety. The brake torque is estimated not only considering the pressure developed at the calipers, but also the brake disc temperature, and the wheel speed effect on the friction coefficient. The torque is obtained without installing additional sensors in the vehicle platform, considering that only wheel speed sensors are available. The estimation is performed using the extended version of the Kalman Filter. The results obtained are very satisfactory, and can improve the performance of the named systems in a safe way.

The “Optimal Maneuver Method” is an application of the optimal control theory that basically simulates an ideal driver and computes the actions and the trajectory to complete a maneuver in the minimum time. As an application of this method a 125 cc motorcycle and a real race circuit, in both dry and wet conditions, have been simulated, and the validation of the results by means of a comparison with real telemetry data is discussed. Afterwards two significant quantities, the height and the longitudinal position of the centre of mass of the vehicle, have been considered. The influence of variation on the minimum lap time, in the two track conditions discussed above, is presented.

The aim of this paper is to investigate the optimality of the handbrake cornering technique for a Front Wheel Drive vehicle. Nonlinear Optimal Control theory is used to formulate the problem of optimal cornering and to simulate manoeuvres used by race drivers. Handbrake cornering is optimal with an appropriate selection of the minimization cost. The optimal solution is validated against data collected during the execution of the technique by an expert race driver on a loose off-road surface. Further optimization results considering high adhesion road surface are obtained to show that the optimality of the technique is not affected by the road conditions.

This paper presents an original approach to vehicle obstacle avoidance. It involves the development of a nonlinear Model Predictive Contouring Control, which uses torque vectoring to stabilise and drive the vehicle in evasive manoeuvres at the limit of handling. The proposed algorithm combines motion planning, path tracking and vehicle stability objectives, prioritising collision avoidance in emergencies. The controller’s prediction model is a nonlinear double-track vehicle model based on an extended Fiala tyre to capture the nonlinear coupled longitudinal and lateral dynamics. The controller computes the optimal steering angle and the longitudinal forces per each of the four wheels to minimise tracking error in safe situations and maximise the vehicle-to-obstacle distance in emergencies. Thanks to the optimisation of the longitudinal tyre forces, the proposed controller can produce an extra yaw moment, increasing the vehicle’s lateral agility to avoid obstacles while keeping the vehicle stable. The optimal forces are constrained in the tyre friction circle not to exceed the tyres and vehicle capabilities. In a high-fidelity simulation environment, we demonstrate the benefits of torque vectoring, showing that our proposed approach is capable of successfully avoiding obstacles and keeping the vehicle stable while driving a double-lane change manoeuvre, in comparison to baselines lacking torque vectoring or collision avoidance prioritisation.

Path tracking (PT) controllers capable of replicating race driving techniques, such as drifting beyond the limits of handling, have the potential of enhancing active safety in critical conditions. This paper presents a nonlinear model predictive control (NMPC) approach that integrates multiple actuation methods, namely four-wheel-steering, longitudinal tyre force distribution, and direct yaw moment control, to execute drifting when this is beneficial for PT in emergency scenarios. Simulation results of challenging manoeuvres, based on an experimentally validated vehicle model, highlight the substantial PT performance improvements brought by: i) vehicle operation outside the envelope enforced by the current generation of stability controllers; and ii) the integrated control of multiple actuators.

A broad literature deals with torque-vectoring (TV) algorithms based on direct yaw moment control (DYC), which continuously generate longitudinal tire forces that are different on the left and right vehicle sides. Such set-ups enable desirable yaw rate and sideslip responses in normal and extreme driving conditions. However, they imply two electric powertrains per axle, or controllable differentials, and therefore the related controllers are not applicable to typical production electric vehicle layouts with a single centralized electric machine and open differential per axle. Nevertheless, in proximity of the limit of handling, the cornering response of conventional all-wheel-drive electric vehicles with one motor per axle can benefit from front-to-rear axle torque-vectoring (ATV), which, by controlling the longitudinal force distribution between the front and rear axles, indirectly modifies the yaw moment contribution due to the lateral tire forces. Only a few studies exploit this option, with limited coverage, e.g., without considering the energy efficiency aspects and the electronic stability control (ESC) function actuating the friction brakes. To address the gap, this paper presents real-time capable nonlinear model predictive controllers (NMPCs) for ATV and ESC, targeting: i) energy consumption reduction in normal driving, through powertrain and tire slip power loss limitation; and ii) yaw rate, sideslip angle and wheel slip control at the limit of handling, by considering the trade-off between powertrain and friction brake actuation. The performance is assessed through simulations with a validated vehicle model, and experiments on a vehicle demonstrator. With respect to benchmarking rule-based controllers, the results show that the NMPCs bring significant reductions of the yaw rate errors and friction brake power losses, while increasing the exit speed in acceleration-during-cornering conditions.

The accurate prediction of tyre forces requires an understanding of the friction characteristics between the tyre and the ground surface. A friction master curve represents the dependency of rubber friction on sliding velocity and temperature, typically obtained using a bespoke friction test rig. To circumvent specialised friction testing, this paper presents a methodology for extracting friction characteristics from pure longitudinal tyre force measurements obtained on a flat-track test machine. The methodology is demonstrated for two tyre types – a radial-ply road tyre and a cross-ply racing tyre. The identified friction characteristics are validated against directly measured friction master curves. Results demonstrate that the friction characteristics can be successfully and accurately extracted from flat-track data in a repeatable manner. For the studied passenger car tyre, only two pure traction slip curves (one at approx. 13% and one at approx. 105% of the rated tyre load) were required to obtain the available information on the rubber-surface sliding friction coefficient.