Predictive Anti-Jerk and Traction Control for V2X Connected Electric Vehicles With Central Motor and Open Differential

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-${\bm{\mu}}$ 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.

. V2X connectivity exploited to share the position of low-μ friction patches on the road.
ii) limit wheel slip, thus enhancing the longitudinal acceleration and cornering responses. Both functions are separately implemented in production electric vehicles (EVs) with centralized on-board powertrain architectures, which consist of a single electric motor per driving axle, a single-speed transmission, an open differential, half-shafts, and constant velocity joints [3].
In parallel, vehicle connectivity to other road users, the infrastructure, and the cloud, usually referred to as V2X, is a growing trend, which is confirmed by the number of recent review papers on the topic, e.g., see [4]- [7]. This technology has several potential applications, including cooperative tire-road friction estimation [7], achieved through the fusion, e.g., in the cloud, of the sensor information from multiple preceding vehicles. For example, in the simplified scenario in Fig. 1, the preceding vehicle (in grey) is used as a moving sensor, sending information to the cloud via V2X. The cloud elaborates the information from several connected vehicles, and determines the position of potential low tire-road friction patches, which is then communicated to the upcoming vehicles, such as the ego vehicle in the figure. This V2X-enabled technology is becoming reality; for example, Volvo tested a V2X system notifying the drivers about upcoming icy patches on a fleet of 1000 vehicles [7]. The tire-road friction estimation through V2X can be supported by the fusion of the information from optical sensors and cameras [8], as well as from conventional on-board state and parameter estimators [9].
This study proposes a set of novel proof-of-concept anti-jerk and traction controllers based on nonlinear model predictive control (NMPC), for next generation EVs with V2X connectivity This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ and centralized powertrain architectures. The focus is on the control formulation aspects and preliminary assessment of the potential benefits, while the connectivity and other implementation details are beyond the scope of the analysis. The main contributions are: 1) The inclusion of the predicted tire-road friction information coming from a V2X system in the optimal control problem formulation and the online algorithm. 2) An internal model formulation including accurate yet numerically non-stiff description of the open differential behavior.
3) The simulation-based comparison of traction controller implementations with and without V2X connectivity, with and without drivetrain dynamics in the internal model, and including or excluding anti-jerk capabilities, along extreme acceleration, cornering and split-μ scenarios. 4) The proof-of-concept experimental assessment of the benefits of tire-road friction condition preview on the wheel slip control performance. The manuscript is organized as follows: Section II is a short literature survey on the relevant topics, and identifies the knowledge gap; Section III describes the case study EVs; Section IV deals with the optimal control problem formulation, including the considered internal models, cost function, and constraints; Section V describes the simulated maneuvers and performance indicators; Section VI critically analyzes the different internal model formulations; Section VII discusses the simulation results, while Section VIII focuses on the proof-of-concept experiments; finally, Section IX summarizes the main conclusions.

II. LITERATURE REVIEW
Although a wide body of literature discusses aspects and possible applications of V2X technologies, the analysis of the connectivity benefits on the performance of traction and anti-jerk controllers is still in very preliminary stages.
A first important contribution is the study by Batra et al. [10], which proposes an integrated model predictive traction and antijerk controller for a connected vehicle, where the V2X system provides the appropriate reference slip ratio at the current time. However, the prediction associated with the internal model of the controller does not consider the mapping of the tire-road friction parameter (indicated as μ in the remainder) along the prediction horizon, nor the corresponding variation of the reference slip ratio. This is an important limitation, since the slip ratio at which the peak longitudinal force occurs for a given vertical tire load significantly varies with μ [11]. Hence, preview-based powertrain torque actuation could achieve the greatest benefits in scenarios with abrupt μ variations (see Fig. 1), leading to changes in the friction parameter and reference slip ratio used by the internal model of the controller along the prediction horizon. This is a similar philosophy to that of the existing preview-augmented suspension controllers [12]- [14].
Model predictive control (MPC), which solves an optimization problem along a finite horizon, is the natural control choice for preview-augmented traction control, as the information on the expected road characteristics ahead can be systematically integrated in the controller formulation. In the last 15 years, MPC has met increasing interest within the automotive industry [15].
The literature includes a variety of model predictive traction controllers [16]- [19] and anti-jerk controllers [2], [20] without road preview, all of them defining the wheel slip control problem only for a single wheel. In [21] Batra et al. propose a model predictive adaptive cruise controller with traction control capability, achieved through a hard constraint on the longitudinal tire slip. Although the implementations in [21] and [10] are for vehicles with central motor and open differential, the internal MPC model does not consider the differential dynamics, and the system is tested in straight line conditions with identical μ on the two wheels of the same axle. Several examples are also available of non-MPC model-based wheel slip controllers for centralized powertrain layouts, e.g., using linear controllers [22] or sliding mode controllers [23], [24], all of them designed through quarter-vehicle models, and assessed only in straight line with the same μ on the two vehicle sides. In general, the literature lacks experimental vehicle validations of the proposed traction controllers. For example, among the considered traction control papers, only references [17] and [19] include vehicle experiments, all of them executed from standstill or close-tostandstill conditions.
In summary, the available model-based traction control formulations use single-wheel models without tire-road friction condition preview. In case of powertrains with mechanical differentials, appropriate additional algorithms (not discussed in the literature) would be required for the management of: i) cornering conditions, in which the longitudinal slip of the two tires driven by the same powertrain is different because of the effect of the lateral load transfer; and ii) split-μ scenarios, i.e., with different friction conditions on the two tires of the axle. This is an important gap, especially when considering that the EV market is dominated by on-board centralized powertrain configurations with open differentials, e.g., see the Tesla models, Volkswagen ID3, Nissan Leaf, Honda e, BMW i3, and Renault Zoe. Moreover, the electric powertrain layout with central motor would benefit the most from the tire-road friction preview and related pre-emptive traction control function, given its typically significant torsional drivetrain dynamics that tend to reduce the effectiveness of wheel slip control.

A. Vehicle A
Vehicle A is a high-performance electric front-wheel-drive sport utility vehicle (SUV) with an on-board permanent magnet synchronous motor, providing high level of responsiveness, i.e., with an approx. 5 ms electric drive time constant.
The EV is simulated through an experimentally validated nonlinear Matlab-Simulink model for control system assessment, considering the longitudinal and lateral vehicle dynamics as well as the torsional drivetrain dynamics, including the dynamics of the differential internals and drivetrain backlash, which require a particularly low simulation time step, equal to 0.1 ms in the presented simulation results. The tires are modeled with the Pacejka magic formula (version 5.2), with longitudinal and lateral relaxation according to the formulation in [25]. The main vehicle parameters are reported in Table I. The simulation model of Vehicle A was validated in quasisteady-state and transient conditions with experimental test data from the reference vehicle, e.g., in terms of: i) understeer, sideslip angle, and wheel speed characteristics as functions of lateral acceleration, see the skidpad test results in Fig. 2; and ii) time histories of yaw rate, lateral acceleration and driving wheel speeds, see the obstacle avoidance test results in Fig. 3, from an initial EV speed of 65 km/h. In both tests, the results highlight the wheel speed difference caused by the different trajectory radii on the two EV sides (the outer wheels cover a longer distance than the inner wheels) as well as by the tire slip ratio difference induced by the lateral load transfers. Given the very good match between simulations and experiments, the model can be considered a reliable tool for control system assessment.

B. Vehicle B
Vehicle B is the prototype Zero Emission test Bed for Research on Autonomous driving (ZEBRA, see Fig. 4) of the University of Surrey, which is a modified Renault Twizy, i.e., an L7e rear-wheel-drive electric quadricycle, with a centralized on-board electric powertrain, single-speed transmission, open differential, half-shafts, and constant velocity joints. This EV has much slower powertrain dynamics than Vehicle A (the electric drive has a time constant in excess of  100 ms), and was used for the proof-of-concept experimental assessment of the benefit of wheel slip control with tireroad friction preview. Its main parameters are also reported in Table I. The ZEBRA is equipped with i) a set of vehicle dynamics sensors, including capability to monitor individual wheel speeds; ii) a Racelogic GPS (global positioning system) speed sensor; and iii) a dSPACE MicroAutoBox II system for the rapid control prototyping of the vehicle dynamics control functions, including a selection of the traction controllers presented in this paper. 1) A cloud-generated road μ condition map expressed in spatial coordinates, which is periodically transmitted to the on-board control system through V2X. 2) A conversion unit, which, starting from the μ condition map, the current vehicle position, e.g., obtained through a global navigation satellite system (GNSS), and motion condition, e.g., in terms of estimated velocity and yaw rate, generates the vectors of the expected tire-road friction coefficient values along the prediction horizon, In the preliminary implementations of this study, the online controller parameters are directly obtained from the simulation model or sensor measurements, without the inclusion of a state and parameter estimation layer, see the example in [9]. The following subsections present the prediction model formulations, the cost function, and the constraints of the considered nonlinear optimal control problems.

A. Evaluated Configurations
Several controller set-ups are assessed in the following sections. In the remainder, the notation 'P ' identifies the passive vehicle, i.e., with ΔT = 0, while the notations 'Base · ', 'B · ' or 'C · ' indicate the vehicle with the NMPC controllers respectively using the baseline model, model B or model C (see their description in Section IV.B) as internal models. The subscripts that follow the main controller identifier define the NMPC features; in particular: 1) '· U ' refers to a controller for the unconnected EV, i.e., the current values of tire-road friction coefficients, μ L/R (where the subscript 'L/R' indicates left or right), and reference slip ratios, k ref,L/R , are provided to the NMPC and are kept constant along the prediction horizon. 2) '· V 2X ' refers to a controller that receives the vectors with the expected potentially variable μ L/R and k ref,L/R profiles along the prediction horizon, thanks to the EV connectivity features. 3) '· V 2X,Δk ' indicates controller configurations based on the expected μ L/R and k ref,L/R profiles along the prediction horizon, where the cost function weights are varied online differently for the left and right sides of the vehicle, depending on the right-to-left slip ratio difference, Δk = k R − k L . 4) '· ·,AJ ' refers to a controller including anti-jerk functionality, on top of the traction control capability. All proposed controllers are based on realistic assumptions in terms of required state estimators. In fact, a wide literature covers state estimators of individual tire slip [9], [26], as well as halfshaft torsion and half-shaft torque [2], [20], [27], including examples of experimental validation on real vehicles [9], [26], [28].

B. Prediction Model Formulations
The NMPC formulations are based on an internal model of the plant, also referred to as prediction model, which consists of a system of first order differential equations, according to the following canonical form: where X is the state vector, t is time, and P is the parameter vector. In this paper, the notation d(·)/dt indicates a time derivative of a system state or variable, while the notation '·' indicates a time derivative that is incorporated in the definition of a system state or variable. This study considers five prediction model formulations. The two baseline formulations neglect the torsional drivetrain dynamics (yet they consider both wheels of the axle), and enable traction control implementations without anti-jerk control, while formulations A, B and C also include the torsional drivetrain dynamics, and therefore enable integrated traction and anti-jerk control. All prediction model formulations include some form of consideration of the open differential behavior. Fig. 6 shows a close-up of the differential, including the planetary gear, with mass moment of inertia J p , and the right and left sun gears, with moment of inertia J s . In the figure, the rest of the powertrain assembly corresponds to the equivalent mass moment of inertia, J mgd,s , of the motor rotor, single-speed gearbox, and differential case, calculated at the differential output. 1) Baseline model for unconnected EV: The prediction model for the baseline controller without EV connectivity, Base U , is designed for traction control applications without μ preview. The model is very similar to the one in [17], with the exception that the implementation of this study considers both wheels of the axle in a single formulation. The controlled variable is the slip speed on the driven wheels, k v,L/R , defined as: whereθ w,L/R is the angular left/right wheel speed; R w,r is the rolling radius of the tire; and v x is the speed of the wheel center along the longitudinal axis of the tire reference system, which can be normally approximated to be the same as the longitudinal vehicle speed. The slip ratio of the left/right tire is defined as: The time derivative of (3) is: in which the first term on the right-hand side is obtained from the wheel moment balance equation: where each driving wheel receives a torque contribution corresponding to half of the motor torque, T m , which is typical of drivetrains with an open differential; i t is the transmission gear ratio; J w is the wheel mass moment of inertia, which incorporates half of the drivetrain inertia; and F x,L/R is the left/right longitudinal tire force, which is calculated with a simplified version of the Pacejka magic formula [11]: where F z,L/R is the vertical tire load, considered constant along the prediction horizon; μ x,L/R is the longitudinal tire force coefficient; and B, C and D (where D = 1 for the specific implementation) are the magic formula coefficients. The longitudinal vehicle dynamics are modeled with a quarter-vehicle model: where M eq,c is the equivalent EV mass used in the corner model, which is chosen to obtain a realistic longitudinal vehicle acceleration. By substituting (6)-(9) into (5), the first equation of the internal model -describing the dynamics of the wheel slip speed -is obtained: An integral action is used to overcome steady-state errors and model uncertainties, which considers the error e I,L/R between the actual and reference slip speeds, where the latter are computed from the reference slip ratios k ref,L/R . Therefore, the second differential equation of the prediction model is defined as: where k ref,L/R is obtained from maps or functions of the estimated F z,L/R and μ L/R . By substituting (4), (7) and (8) into (6), the third equation of the internal model is obtained: The actual motor torque, T m , is considered equal to the reference torque: with T plant defined in (1). In summary, the model has three differential equations for each driving wheel, resulting in a total of six equations. The state vector, X base,U , is: 2) Baseline model for connected EV: A more advanced prediction model for traction control is developed for the connected vehicle case, referred to as Base V 2X , which, in addition to considering the preview of the tire-road μ condition, incorporates the electric drive dynamics, on top of the features of the Base U controller. Since Base V 2X modifies the motor torque demand in anticipation of μ variations, its internal model must consider some form of powertrain dynamics model, in order to achieve accurate pre-emptive control. In Base V 2X the motor dynamics formulation is based on a first order model: where T m is the actual electro-magnetic motor torque, and τ m is the time constant of the electric drive. The other equations of Base V 2X are (1) and (3)- (12). The state vector, X base,V 2X , is: Half-shaft torque formulation: Models A-C include the differential and half shaft dynamics, to enable the anti-jerk control function. The half-shaft torque formulation is common to the three models. As the adopted solver of the nonlinear optimal control problem cannot handle piecewise models, the drivetrain backlash is considered through the combination of hyperbolic tangent functions, which lump the whole drivetrain backlash and torsional damping behavior within the half-shaft model. In this way, the piecewise backlash behavior is converted into an equivalent continuous nonlinear model.
The left (T hs,L ) and right (T hs,R ) half-shaft torques (see Fig. 6) are calculated as: where T hsK,L/R is the torque related to the stiffness contribution; and T hsC,L/R is the torque associated with drivetrain damping. T hsK,L/R and T hsC,L/R are approximated as: where Δθ L/R is the relative angular displacement between the sun gear and the respective wheel: in which θ s,L/R and θ w,L/R are the sun gear and wheel positions.
f A , f B and f C are linear functions: where K hs and C hs are the half-shaft stiffness and damping coefficient; α BL is half of the backlash width; and f 1 and f 2 are switching functions: where a is the shape factor of the hyperbolic tangent function, i.e., the higher is a, the sharper is the shape of the function. a is selected according to a trade-off between: a) the need for an accurate approximation of a linear piecewise function, which would require a high value of a; and b) the requirement of preventing the system from becoming numerically stiff, and generating numerical errors in the solution of the nonlinear optimal control problem, which would need a low value of a. A typical example of T hsK and T hsC behavior is plotted in Fig. 7, as a function of the drivetrain torsion angle and torsion rate, Δθ and Δθ.

4) Model A:
Model A includes consideration of the differential internals and uses the motor dynamics formulation (15), while (26) and (27) from Galvagno et al. [29] describe the open differential dynamics: whereθ d is the angular speed of the differential case; Δθ s is the relative angular speed between the right and left sun gears, i.e., Δθ s =θ s,R −θ s,L ; and J d,eq,1 and J d,eq,2 are the equivalent mass moments of inertia: where J hs is the mass moment of inertia of a single half-shaft (in this study, the right and left half-shafts are assumed identical); i p is the gear ratio between the solar and planetary gears; and J mgd,s is given by: where J m , J g1 , J g2 , and J d are the individual mass moments of inertia of the motor rotor, gearbox input shaft, gearbox output shaft, and differential case; η t is the transmission efficiency in traction conditions; and i frr is the final reduction ratio. For simplicity, (27) neglects the friction in the differential internals.
Willis equation correlatesθ d with the right and left sun gear speeds,θ s,R andθ s,L :θ The left and right wheel moment balance equations are expressed as: where R w,l is the laden wheel radius. In this model, F x,L/R is calculated with the Pacejka magic formula (version 5.2) [11]: where k L/R is defined earlier in (3)-(4) and α L/R is the slip angle. Given that the vehicle dynamics are slower than the wheel and electric powertrain dynamics, α L/R and F z,L/R are considered constant along the prediction horizon, and are treated by the controller as external parameters. The introduction of α L/R allows consideration of the interaction between longitudinal and lateral tire forces in the prediction model, which is of the essence in maneuvers including acceleration in a turn, such as the pull-out of a junction case considered in this analysis.
Equations (17)-(34), (15), (1) and (3)-(4) were re-arranged through Maple to obtain the canonical form of the system according to (2). The state vector of model A, X A , is: The other equations of model B are (15), (17)-(25), (33)-(34), (1) and (3)-(4). The significant limitation of this model, consequence of the independent dynamics of the two sides of the drivetrain, is that in split-μ scenarios the two half-shafts unrealistically transmit different torque levels, corresponding to the tire-road friction condition of the respective side. The state vector of Model B, X B , is: 6) Model C: Differently from model A, model C avoids the description of the inertial contributions of the differential internals, while, differently from model B, model C is based on the assumption of identical drivetrain torque levels at the differential output ports.
The torque balance of the motor rotor, gearbox and differential case is: whereθ d is expressed according to Willis equation: Since in a first approximation an open differential provides the same torque to the right and left wheels, i.e., T hs,R = T hs,L , it is also true that:Ṫ hs,L =Ṫ hs,R which, under the assumption of neglecting the mechanical plays, results in the following relationship between the angular speeds and accelerations of the sun gears and the wheels, used in the model formulation: Model C also includes (15), (17)-(25), (33)-(34), (1) and (3)-(4). The model C state vector, X C , is identical to the one of model B, i.e., X C = X B .

C. Nonlinear Optimal Control Problem
The NMPC control law minimizes the cost function J, subject to appropriate equality and inequality constraints [30]. The nonlinear optimal control problem is defined in discrete time as: (42) where the notation U (·) indicates the control sequence, in which U (k) includes the motor torque correction and the slack variables; X in is the initial value of the state vector, obtained from the sensor measurements and state estimators; N is the number of steps of the prediction horizon H p , in this implementation equal to the control horizon H c , i.e., H c = H p = N T s , with T s being the discretization time; k indicates the discretization step along the prediction horizon; X andX are the lower and upper limits for X; U andŪ are the lower and upper limits for U ; is the discretized version of the models defined in Section IV.B; (X(k), U(k)) is the stage cost function associated to each time step, defined as a least-squares function; and N (X(N )) is the terminal cost, also called Mayer term. For k = 0 the variables are measured/estimated, while for k > 0 the variables are predicted. As the specific emphasis of this proof-of-concept analysis is on the resulting traction control and anti-jerk functionalities, no formal stability analysis is presented. Nevertheless, the term N (X(N )) forces the system to converge to the desired final state and enhances stability.
In the specific implementation, is defined as the sum of three contributions, which assume a different meaning depending on the considered controller: 1) Baseline controllers: For the controllers using the baseline models, the first Lagrange term in (43), 1 , tracks the reference wheel slip speeds: 2 (44) where W 1 is a weighting factor; and k vref,L and k vref,R are the left and right reference wheel slip speeds, calculated from the reference slip ratios, k ref,L (k) and k ref,R (k), as: Based on (45), the reference slip speed varies with the angular wheel speed, according to the reference slip ratio. As a consequence, the resulting controller behavior is the same as for a formulation directly including slip ratio tracking in the cost function. On the other hand, if the same controller had to be implemented in its explicit form, differently from the implicit form of this study, the slip speed based arrangement would bring a reduction of the size of the explicit solution, as observed in [17]. Therefore, to obtain formulations that are efficiently implementable in both implicit and explicit forms, the baseline controllers use the slip speed within the cost function.
The second Lagrange term reduces the time integral of the error, e I,L/R (k), between the slip speed of the left/right wheels and its desired value: where W 2 is the respective weighting factor. The last Lagrange term, with weight W 3 , penalizes the control effort: The Mayer term tracks the reference wheel slip speed and reduces the integral of its error at the end of the prediction horizon, defined by the time t N : where W M,e and W M,I are constant weights. The constraint is: which ensures that the resulting T plant is positive (as the implemented controller is a traction controller) and does not exceed the driver torque request.

2) Controllers based on models A-C:
For the controllers based on models A-C, 1 deals with the violation of the soft constraints on the right and left reference wheel speed errors: where W 1 , W Δk,R and W Δk,L are weighting factors; and sv L and sv R are slack variables, which indicate the violation of the respective wheel speed error constraint. 2 induces the tracking of the reference wheel speed, and is used to support and smoothen the torque regulation action of 1 : where v x,L/R (0) is the estimated longitudinal speed component of the wheel at the beginning of the prediction horizon. The last Lagrange term defines the anti-jerk control action: where Δθ R and Δθ L are the right and left drivetrain torsion rate, i.e., the time derivatives of (20), and W 3 is a constant. The anti-jerk functionality is turned off if W 3 = 0. The Mayer term tracks the reference wheel speed at the end of the prediction horizon: Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
where W M is a constant weight. The constraints include (49), as well as: where (55) and (56) are soft constraints on the wheel speeds, which should not exceed the reference level, according to the slack variables sv R and sv L , which must be non-negative according to (57) and (58). The weights W Δk,R and W Δk,L in (50)-(51) are equal, i.e., W Δk,R = W Δk,L , except when the subscript '· V 2X,Δk ' is used. In this scenario, W Δk,R and W Δk,L vary as functions of the right-to-left slip ratio difference, Δk = k R − k L , as shown in Fig. 8, and described in the following formulations: where W Δk0 , Δk 1 , and Δk 2 are constant parameters, and m and q are given by: The weight adaptation in (59)-(62) allows tuning the traction controller behavior in split-μ conditions, i.e., the weight decrease on the wheel with higher slip ratio limits the torque demand reduction at the axle level.

D. Controller Implementation
The controllers are set up through the ACADO toolkit [31], which uses Gauss-Newton iteration algorithms for fast implicit NMPC with constraints, generating locally optimal solutions. The selected solver parameters are: multiple shooting discretization method, fourth order Runge Kutta integrator, and qpOASES QP optimization algorithm.

A. Selected Maneuvers
The performance of the models and controllers is assessed along the following simulated maneuvers, with Vehicle A: 1) Maneuver 1, i.e., a split-μ tip-in from 50 km/h. At 0.5 s, T ref is increased from 10 to 80 Nm. At 1 s, the right wheel friction parameter decreases from 1 to 0.5, creating a split-μ condition. After further 0.5 s, also the left wheel μ drops, repristinating the same friction conditions on both vehicle sides. 2) Maneuver 2, i.e., a straight line tip-in from 20 km/h, with a sudden change of μ. T ref is increased from 10 to 120 Nm at the beginning of the maneuver. The maneuver starts on high-friction tarmac; after 2.5 m the EV meets a low-μ patch covering the whole lane.

3) Maneuver 3, i.e., a split-μ tip-in from 20 km/h. T ref is
increased from 10 to 120 Nm at the beginning of the maneuver. The maneuver begins on high-friction tarmac. After 2.5 m the EV meets a low-μ patch covering the right part of the lane. 4) Maneuver 4, i.e., a pull-out of a U.K. A-road junction.
This maneuver is designed to test the system in a realworld scenario. The reference junction is located between Shalford and Chilworth, see Fig. 9, and is reproduced in Matlab-Simulink. The initial EV speed is 35 km/h, and the steering angle is calculated by a path tracking controller to follow the center of the lane. T ref is increased from 10 to 140 Nm once the vehicle has covered 40% of the curved path. The test is performed with and without two low-μ patches positioned on the curved path, see Fig. 19 in Section VII for the details.

B. Performance Indicators
The performance of the EV set-ups has been assessed through the following set of performance indicators: 1) The integral of the wheel slip violation,ê k , averaged over time:ê where t end is the duration of the maneuver; and e k,R and e k,L are the right and left wheel slip violations, which define the extent by which the actual tire slip exceeds the reference value:   2) The maximum slip violation, e k,max , during the maneuver: e k,max = max (max (e k,R ) , max (e k,L )) 3) The maximum slip ratio, k max , during the maneuver: 4) v max , i.e., the maximum vehicle speed, achieved at the end of the maneuver.    value, V DV a * x : where a * x (t) is the zero-mean profile of the longitudinal vehicle acceleration, a x . a * x (t) is calculated by filtering a x through a Butterworth high-pass filter with a cut-off frequency of 8 Hz. 6) The integral of the path tracking error, averaged with time: where e t is the lateral distance between the vehicle center of mass and the reference trajectory. 7) The maximum lateral trajectory tracking error:

VI. ANALYSIS OF PREDICTION MODELS WITH DRIVETRAIN DYNAMICS
This section compares the performance of models A-C defined in Section IV.B, i.e., the models which consider the drivetrain dynamics for integrated traction and anti-jerk control, and selects the most suitable prediction model for Vehicle A. Model A, which includes consideration of the differential internals, represents the benchmarking model in terms of accuracy.

A. Model Comparison in Open-Loop Simulations
In this subsection, the model states are integrated in open-loop with the same variable step setting of the continuous forward Euler integration function of Matlab (ode45). Fig. 10 shows the speed of the differential case,θ d , and the difference between the right and left sun gear speeds, Δθ s , during maneuver 1, which is designed to assess the computational effort and the response of models A-C in split-μ conditions. The first subplot shows that both models B and C are aligned to model A. However, in Fig. 19. A-road junction cornering maneuver (maneuver 4). Trajectories for: the passive vehicle in high tire-road friction conditions (left); the passive vehicle on the course including low-μ patches (center); and the vehicle with C U / C V 2X on the course including low-μ patches (right). the split-μ phase of the test, from 1 to 1.5 s, the Δθ s profile highlights a mismatch between model B and the benchmarking model A, whilst model C behaves well throughout the maneuver. Moreover, the number of steps required by the ode45 algorithm to integrate the differential equations of model A (901337) in the considered maneuver is three orders of magnitude higher than for models B and C (425 and 437, respectively). This indicates that model A is much more numerically stiff than the other two models. Therefore, although accurate, model A is unsuitable for implicit NMPC, which requires computational efficiency, and will not be considered for the NMPC implementations in the remainder.

B. Model Comparison Through Controller Implementation
Models B and C are implemented as prediction models in controller configurations B U , C U , B V 2X , and C V 2X , to test how the model mismatches highlighted in the previous maneuver affect the NMPC performance during maneuver 3, evaluated through the model for control system assessment in Section III. In accordance with the results of [17], which highlight the importance of selecting a low controller implementation time for wheel slip control, in this proof-of-concept analysis all controllers are run at 1 ms. Table II reports the values of: a)ê k , calculated for the four considered NMPC configurations, for different values of the number of prediction steps, N ; and b) Δ%, i.e., the percentage reduction ofê k associated with the NMPC implementation based on model C, with respect to the corresponding one using model B. The results highlight that: 1) In the specific maneuver all controller configurations experience a major performance improvement when the number of prediction steps is increased from 10 to 20, while a further increase of N tends to be associated with a very marginal performance decay. Hence, in the performance analysis in Section VII, all simulated controller configurations will be evaluated for N = 20. 2) The model B approximation tends to compromise the resulting NMPC performance in almost all cases. In particular, the wheel slip tracking performance gain brought by model C with respect to model B amounts up to 30.2% for the unconnected EV configurations, and up to 72.3% for the connected EV. The important conclusion is that a realistic model of the open differential behavior is required for reliable and predictable traction control performance in split-μ conditions.

VII. SIMULATION RESULTS
The simulations of this section, for Vehicle A, comprehensively assess the performance of the NMPC configurations using the baseline models and model C as prediction models, with the main target of identifying the potential wheel slip control benefits enabled by V2X and the consideration of the torsional drivetrain dynamics, in case of a highly responsive electric drive. All controllers were calibrated through brute force analyses to provide desirable performance in the considered tests.
A. Maneuver 2: Straight Line Tip-In 1) Controller comparison: Fig. 11 reports the motor torque before and after the NMPC correction, as well as the reference and actual slip ratios, for Base U , Base V 2X , C U and C V 2X . For example, thanks to its pre-emptive nature, C V 2X keeps k below its reference without the oscillations arising in the C U configuration after the sudden change of μ happening at ∼0.52 s. C V 2X also achieves lower control effort.  and, therefore, optimizes its control action accordingly. Similarly, both baseline controllers in Fig. 11 reduce the torque to follow k ref , and Base V 2X has reduced k oscillations compared to Base U . However, they perform worse than the model C based controllers, as they lack the consideration of the drivetrain dynamics in their internal models.
The slip ratio tracking benefits of preview-based traction control are confirmed by the values ofê k and k max in Table III, which also highlights -through the v max valuesthe marginally better acceleration performance of C V 2X with respect to C U and the passive EV. Understandably, C V 2X is the best performing controller among the four, as it includes both pre-emptive capabilities and the drivetrain dynamics in the internal model. For vehicle A, with very fast electric drive actuation, if only one of the above functions can be implemented (due to hardware limitations, etc.), then the priority should be given to the drivetrain dynamics formulation. In fact, C U has significantly lowerê k than Base V 2X , while the k max values are similar.
Table III also includes the performance indicators for the C U,AJ and C V 2X,AJ configurations, with anti-jerk capabilities, achieved through the cost function term in (53). In terms of comfort assessment, Fig. 13 reports the percentage variation of RM S a * x and V DV a * x , with respect to the passive vehicle. The oscillations of T plant and k, evident for C U in Fig. 11, affect the RM S a * x and V DV a * x values, which are significantly higher than for the passive EV, while the gentler control action provided by the pre-emptive C V 2X set-up worsens the longitudinal comfort only by a small margin with respect to the passive case. Similarly, Base U and Base V 2X have higher RM S a * x and V DV a * x values compared to the passive vehicle, but, because of their less invasive torque correction, at the expense of the slip ratio tracking performance, they provide better comfort than C U . The anti-jerk configurations are beneficial to drivability, as C U,AJ and C V 2X,AJ have lower discomfort-related indicators than the other controllers. The comparison of the control action (left) and longitudinal acceleration a x (right) profiles for C V 2X and C V 2X,AJ in Fig. 14 confirms the significant reduction of the acceleration oscillations. Also, the smoother torque profile caused by the increased weight on the drivetrain torsional speed reduces the slip violation, as confirmed byê k and k max in Table III. As expected, the anti-jerk effect brings a marginal reduction of the acceleration performance, shown by v max , which nevertheless remains superior to that of the passive EV. Interestingly, the V2X connectivity also enhances the anti-jerk capabilities of the controller, which highlights the potential benefits of pre-emptive and integrated wheel slip and anti-jerk control.
Although being model-based, the proposed controllers, thanks to their feedback set-up, provide good robustness with respect to reasonable variations of the system parameters. For example, in the simulation results, the model for control system assessment includes the full formulation of the Pacejka magic formula, which is different from the simplified formulations adopted in some of the controllers.
To verify robustness, sensitivity analyses were carried out, in which the most relevant parameters were varied within the high-fidelity simulation model of the plant, while the parameters of the internal model of the NMPC were kept constant. For example, Fig. 15 reports the controlled vehicle response for different values of the scaling factors, LKX and G σ , of the magic formula model on the longitudinal slip stiffness and relaxation length. The scaling factors were varied from -20% to +20% with respect to their nominal values, which is a rather wide range for tires that can be mounted on a specific vehicle. The resulting variation of the slip ratio response for the controlled vehicle in the Base V 2X configuration is negligible, i.e., the controlled vehicle response is robust with respect to the parameter variation. The same trends were verified for the other controllers.
2) Effect of powertrain dynamics: A preliminary analysis showed the robustness of the proposed NMPC with respect to the variation of the electric powertrain dynamics, defined by τ m (5 ms for Vehicle A in nominal conditions), provided that the internal model is tuned for the worst case condition of the plant, i.e., with the longest expected time constant. For example, Fig. 16 reports k ref and k for C U and C V 2X for two time constant values of the electro-magnetic torque of the motor, while the internal NMPC model uses a fixed τ m = 10 ms. Although both controllers provide acceptable performance, C V 2X is less sensitive to τ m than C U , i.e., for C U , k max increases by 79% when τ m increases from 1 to 10 ms, whilst for C V 2X , the increment is limited to 45%, and the magnitude of the slip ratio peak remains negligible (∼0.015 with respect to ∼0.075 for C U ), which confirms the advantage of pre-emptive control.
3) Effect of motor torque ripple: Realistic motor torque ripple effects were added to the model for control system assessment in Section III.A to observe the variation in controller response. The torque ripple is described as a Fourier series (see [32]) as: whereθ m is the angular speed of the motor rotor; p lcm is the least common multiple of the stator slots and pole numbers of the electric motor; and A s1 , A c1 , A s2 and A c2 are coefficients dependent on the motor structure and design. The torque ripple is added to the motor torque generated through the first order  IV  PERFORMANCE INDICATORS FOR MANEUVER 4 Note: the bold fonts highlight the values for the configuration/s providing the best performance for each indicator in the cases with low-μ patches.
motor dynamics, T m,f o , to obtain T m : As an example, C U and C V 2X (with τ m = 10 ms) were tested on maneuver 2 with this additional torque ripple, with results shown in Fig. 17. The comparison of the relevant subplots in the bottom half of Fig. 17 with those in Fig. 16 shows that the wheel slip tracking response is identical, i.e., the torque ripple does not have any effect on the controller performance, as its effect is filtered by the drivetrain and the tires.

B. Maneuver 3: Split-μ Tip-In
In the split-μ tip-in in Fig. 18, differently from the C U case, the V2X prediction of C V 2X allows the controller to avoid the oscillations of k on the low friction side, after the sudden change of μ. The figure also highlights the adjustability offered by the Δk function of C V 2X,Δk , see (59)-(60), which relaxes the weights on wheel speed tracking and slip violation on the low-μ wheel when a differential right-to-left slip condition is detected. This allows the wheel on the slippery side to spin in a controlled way, and can momentarily increase the traction performance on the high friction side. Future developments of the C V 2X,Δk algorithm will include its evaluation for the management of the trade-off between acceleration time and direct yaw moment during wheel slip control in split-μ acceleration, including friction brake actuation as well.

C. Maneuver 4: Pull-Out of a U.K. A-Road Junction
As highlighted by the performance indicators in Table IV, in maneuver 4 on dry asphalt, no excessive slip occurs, i.e., e k = 0 and e k,max = 0, and the passive vehicle can follow the reference trajectory, see also the P − dry subplot in Fig. 19. When low-μ patches are included along the vehicle trajectory, the passive vehicle consistently violates the reference slip (ê k = 0.199 and e k,max = 0.753), and is not able to follow the reference path (ê t = 0.64 m and e t,max = 2.17 m). As shown in the P − patches subplot in Fig. 19, in this scenario the passive vehicle crosses the line between the two lanes with both front wheels, potentially crashing with an oncoming vehicle. C U and C V 2X reduce the slip violation and the reference path tracking error, with C V 2X performing better, i.e., with lowerê k , e k,max and a higher final speed than C U . This performance gain does not produce noticeable differences in the resulting trajectories (C U and C V 2X share the same subplot in Fig. 19). Base U and Base V 2X are significantly better than the passive vehicle when low-μ patches are encountered. As they lack drivetrain dynamics, they inherently perform worse than the Model C based controllers. As expected, C V 2X is the best performing controller in Table IV. Comparing the C U and Base V 2X controller results, C U has significantly lower values of bothê k and e k,max . Again, this shows that accurate modelling of drivetrain dynamics is more important than road μ condition preview for the specific case study EV.

D. Sensitivity to the μ Prediction Error
This section evaluates the sensitivity of the system performance to the μ prediction error during maneuver 2. In particular: 1) The error on the distance between the vehicle and the low friction patch, Δx, is varied between -1 m and +1 m. If Δx > 0, the distance between the vehicle and the patch is overestimated, and therefore the change of μ is communicated too early to the controller; whilst if Δx < 0, the change of μ is communicated with a delay. 2) The error on the friction coefficient of the low friction patch, Δμ, ranges from -0.08 to +0.08. Fig. 20 reports the values ofê k , k max , and v max , calculated in the straight line tip-in for different combinations of Δx and Δμ. The white dot on the resulting two-dimensional surfaces indicates the condition of the system without injected error, i.e., with Δx = 0 and Δμ = 0. The bottom right subplot shows μ L/R , i.e., the friction coefficient communicated by the V2X module (see Fig. 5). The black line represents μ L/R for Δx = 0 and Δμ = 0; the grey area shows the range of variation with the error injection. For Δx < 0 or Δμ > 0, the wheel slip tracking performance worsens, with an increase ofê k and k max ; on the contrary, if Δx > 0 and Δμ < 0, the slip tracking performance is not affected, but as shown in the bottom left graph, the final vehicle speed is penalized. These preliminary results highlight that some tolerance is allowed on the accuracy of the preview information provided to the controller, and that, for conservativeness, the algorithm generating the expected tire-road friction parameter and reference slip ratio profiles along the prediction horizon could marginally anticipate the transitions from high friction to low friction conditions, and delay the transitions from low to high friction. Detailed simulation and experimental analyses of these aspects will be the object of future research.

A. Real-Time Implementation of the Controllers
To confirm the real-time capability of all proposed controllers, the most advanced configuration, i.e., C V 2X,AJ , was run in real-time on a dSPACE MicroAutoBox II system (900 MHz, 16 Mb flash memory, see Fig. 21). Its real-time implementation is indicated as C V 2X,AJ,RT , and is based on 5 prediction steps, with the control input discretized at 4 ms, and a 1 ms integration step of the internal model, against the 20 prediction steps with the control action discretized at 1 ms of the simulated C V 2X,AJ . The relatively short prediction horizon is suitable for the highly responsive powertrain of Vehicle A. When applied to the highfidelity simulation model of Vehicle A, C V 2X,AJ,RT brings only very marginally deteriorated results with respect to C V 2X,AJ , see the bottom subplots of Fig. 14 and the performance indicators in Table III, which remain better than for the other simpler controller configurations.
Moreover, the baseline controllers were run in real-time on the same dSPACE MicroAutoBox II system, which was installed on the ZEBRA vehicle (Vehicle B). During the experimental controller calibration phase, following a sensitivity analysis to optimize results, Base U was set to run with an implementation time of 8 ms and 4 prediction steps, while Base V 2X was implemented at 15 ms with 7 prediction steps.
In general, the real-time versions of the proposed controllers can be considered conservative, as nowadays much more powerful real-time control prototyping hardware is available than the adopted version of the dSPACE system, i.e., see the dSPACE Mi-croAutoBox III system and computing platforms for automated driving and artificial intelligence applications.

B. Vehicle Testing Set-Up
Proof-of-concept experiments were conducted to demonstrate the benefits of road μ condition preview. The Base U and Base V 2X controllers were implemented on the ZEBRA vehicle (Vehicle B) in Fig. 4, and their performance was compared to that of the passive vehicle during straight line scenarios, with a step transition from high to low μ, similar to maneuver 2. The transition was implemented by fixing acrylic boards to the road through silicon adhesive, and by dividing the resulting surface into two sections (see Fig. 4). Sandpaper was attached to the first section of the acrylic boards, which represents the high-μ section, while soap was applied to the second section of the boards, representing the low-μ section of the experiment.
The two implemented tests focus on high wheel torque operation in rather low speed conditions (with tire-road friction transitions occurring at ∼2 and ∼7 m/s), which are those considered in the reference literature on traction control, see the description of the production system in [33]. This test set-up is not limitative, since the open-loop and closed-loop analyses of the slip dynamics based on the quarter car vehicle model, detailed in [34], as well as the numerical study on wheel slip dynamics modelling in [35], show that the most critical conditions from the viewpoint of wheel slip stability occur at very low speed. Moreover, a typical electric powertrain is characterized by a maximum constant torque region at low motor speed, and a constant power region at medium-to-high motor speed, which translates into decreasing torque as a function of vehicle speed, given the typical adoption of single-speed transmissions in EVs, such as the two case studies considered in this paper. Therefore, the wheels are likely to spin in traction especially in low speed conditions, at which the maximum wheel torque is higher. In the specific testing set-up phase, it was verified that for Vehicle B, no significant wheel spinning would have occurred on the prepared low friction surface above ∼7 m/s. In these tests, a map of the road μ condition was programmed in spatial coordinates a priori, while the current EV position was identified through the GPS antenna installed on the vehicle, and fed into the two baseline controllers.

C. Experimental Results
The results for the passive, Base U and Base V 2X configurations along the first test are shown in Fig. 22. The test begins from low speed when the rear driving wheels are on the sandpaper. The driver requests for maximum motor torque throughout the test, identified by the constant T ref profile in the third subplot. At t∼0.18 s (a very marginal variation occurs for the different configurations), the rear wheels transition from high μ to low μ, defined by the vertical dashed lines.
In the first subplot, the notation 'P v x,vhl ' indicates the linear speed of the passive vehicle, while 'Pθ w,RL R w,RL ' indicates the corresponding angular speed of the rear left wheel multiplied by the respective radius, i.e., the resulting signal is the tangential speed at the periphery of the tire. The comparison of the two profiles highlights that the rear driving wheels of the passive vehicle are spinning in the low-μ section. As expected, the Base U configuration shows reduced wheel spinning in the first subplot, even if the purely reactive nature of the controller implies an initial build-up of slip speed immediately after the friction level transition, while Base V 2X shows a consistently low level of wheel slip speed, confirming the potential benefit of pre-emption associated with vehicle connectivity. A similar trend is seen in the second subplot, where the passive vehicle has the highest slip ratio peak on the considered rear left wheel, with k RL reaching a value of ∼0.4, followed by Base U , which has a slip ratio peak of ∼0.32, after which a significant slip ratio reduction is achieved by the traction controller, and Base V 2X , having the lowest slip ratio peak of ∼0. 15.
The reason for these results can be appreciated in the third subplot, reporting the torque profiles for the considered configurations. The Base U controller imposes a torque reduction ΔT at time t∼0.25 s, once the slip ratio reaches a significant level, corresponding to the activation threshold of the traction controller, which is used in Base U to prevent unnecessary interventions. This control action reduces the reference torque T plant . However, because of the actuation delays of the plant, which are visible by comparing T plant with the actual motor torque T m , estimated from the motor current measurement on the real vehicle, the actual torque reduction occurs too late to prevent a slip ratio peak immediately after the tire-road friction transition, even if, after the peak, the slip ratio is rapidly brought back to its expected value. In contrast, the novel preview formulation of Base V 2X intervenes pre-emptively at t∼0.12 s, even if the magnitude of the slip ratio is still low, as the internal model predicts the wheel slip ratio increase associated with the friction coefficient reduction and the slow motor dynamics, which are embedded in the internal model. Therefore, the profile of T plant is characterized by a pre-emptive reduction with respect to the critical event, which corresponds to a timely reduction of T m . As a result, the pre-emptive controller achieves by far the better performance among the two compared configurations.
The second experimental test involves a tire-road friction condition transition occurring at a higher vehicle speed of ∼7 m/s. The electric powertrain is characterized by a very substantial pure time delay Δt delay , which exceeds 150 ms, in the generation of the actual torque T m , starting from the reference torque, T plant , from the traction controller. At higher speeds, the effect of the pure time delay becomes significant due to the greater distance covered, therefore, the non-pre-emptive Base U configuration is unable to bring any benefit in useful time, and is not reported in Fig. 23, as the corresponding slip ratio response would be the same as for the passive vehicle, since the torque reduction would occur too late.
On the contrary, the benefit of Base V 2X is very evident, with ∼40% reduction of the peak value of the slip ratio, which is less than 0.15 for the pre-emptive configuration, and ∼0. 25 for the passive and Base U ones. To limited extent, with a non-pre-emptive controller, the effect of the pure time delay of the powertrain could be addressed with a Smith/state predictor (see the examples in [16] and [17]), which, however, would significantly increase complexity, and could bring limited benefits with such a long delay with respect to the system dynamics. However, with the pre-emptive formulation, the delay can be directly addressed through a corresponding advance of the tire-road friction condition supplied to the algorithm, by an amount equal to the pure time delay of the powertrain. With this correction, the vehicle position entered in the road friction map corresponds to the actually traveled distance incremented by Δx delay ≈ v x Δt delay (under a constant speed v x assumption, which can be easily extended to a constant acceleration assumption) with respect to the real one, where Δx delay approximates the distance the vehicle would cover during Δt delay .
The delay compensation strategy corresponds to the results indicated as Base V 2X,DC in Fig. 23, in which the significant anticipation of the T plant reduction brings a T m reduction at the correct time, with a slip ratio peak of ∼0.08 (>40% reduction with respect to Base V 2X ). Hence, the pre-emptive formulations can also solve issues related to pure time delays without any additional formulation complexity.
From the experimental analysis on the second case study vehicle, the important conclusion is that pre-emptive traction control formulations are extremely beneficial for plants characterized by slow electric drive dynamics (i.e., the dynamics associated with the traction inverter and the electric machine), which is the case of the considered ZEBRA vehicle. The experimental results are particularly promising also in terms of controller robustness, since precise values of the magic formula coefficients for Vehicle B were not available, and reasonable calibrations were put in place to match the experiments. The same controllers were implemented also on another demonstrator vehicle, not discussed here, with similar very promising results for the pre-emptive formulations, which were empirically tuned without having the a priori knowledge of the exact values of the tire model coefficients.

IX. CONCLUSION
This study presented proof-of-concept real-time capable nonlinear model predictive controllers (NMPC) integrating the traction and anti-jerk control functions, for next generation V2X-connected electric vehicles with centralized powertrain architectures. With respect to the existing literature, the novelties are: a) the inclusion of prediction models considering the open differential behavior; and b) the pre-emptive control formulations accounting for the expected variations of tire-road friction coefficient and reference slip ratio ahead. The simulations (based on an experimentally validated vehicle model) and experiments brought the following main conclusions: 1) To achieve realistic behavior of the prediction model of the drivetrain in split-μ scenarios without having to implement a set of numerically stiff equations, it is necessary to impose the equality of the half-shaft torque values within the considered axle, while neglecting the dynamics of the differential internals.
2) The pre-emptive traction control formulations, Base V 2X and C V 2X , reduce the reference slip ratio violation and slip ratio oscillations in case of abrupt changes in the tire-road friction condition, in comparison with the corresponding implementations (Base U and C U ) without road friction condition preview. In particular, in the considered split-μ scenarios (Fig. 18), C V 2X fully compensates the slip ratio oscillations on the wheel experiencing the transition from high to low friction, while the peak of slip ratio is nearly ten times higher for C U .
3) The anti-jerk contribution reduces the longitudinal acceleration oscillations induced by torque transients (Fig. 14), and also has a noticeable positive effect on the reduction of the slip violation, at the expected price of a marginally weaker longitudinal acceleration performance. The preemptive V2X formulation including anti-jerk control, C V 2X,AJ , enhances both comfort and acceleration, with respect to the equivalent formulation (C U,AJ ) excluding connectivity, see Table III. 4) All proposed traction control formulations are very effective in limiting longitudinal slip during traction in a turn, and in facilitating trajectory tracking in scenarios with swiftly variable friction conditions, even in absence of direct yaw moment control, see Fig. 19 and Table IV. 5) To ensure good wheel slip tracking, both road friction condition preview and drivetrain dynamics modeling should be implemented in the controller. In particular, for highly responsive electric powertrains, such as the one of Vehicle A, the consideration of the drivetrain dynamics effects is more important than the inclusion of road preview, while, in case of slow electric drive dynamics, such as those of Vehicle B, the preview implementation brings major benefits. 6) Proof-of-concept experiments on an electric quadricycle (Vehicle B) have shown the real-time operation of a traction controller with road friction preview, and that this feature is able to pre-emptively reduce wheel slip in maneuvers with abrupt tire-road friction reductions, see Fig. 22 and Fig. 23, and to effectively compensate for pure time delays and powertrain dynamics. Future developments of this research will include the extension of the proposed controllers to the case of concurrent control of the electric motor and friction brake torque demands.