MOTION CONTROL IN MOTOR VEHICLES

Description

[0001] The invention relates to a method for controlling actuators acting on vehicle wheels of a motor vehicle.

[0002] The motion control system for autonomous and manual driving is designed to meet the increased demands for energy efficiency, safety, and driving dynamics of the future. The software is designed to integrate and control all available active and semi-active actuators—steering, braking, drive, and dampers—on a centralized computing platform, ensuring a harmonious driving experience. To achieve this, the vehicle's horizontal, longitudinal, and lateral dynamics must be coordinated as well as possible.

[0003] The horizontal vehicle movement is determined by the wheel steering angles and wheel torques at any given time, which also determine the horizontal tire forces. Another important aspect is the assignment of the motion commands to the individual actuators. In so-called overactuated systems, the number of control variables exceeds the number of degrees of freedom of the vehicle's movement.

[0004] A control system for vehicles is known from US 10407035 B1. A vehicle processing unit determines a motion plan, which is passed on to a vehicle motion controller. This controller uses information about technically possible chassis-level accelerations to determine a chassis-level motion request. A chassis control unit, in turn, uses this motion request to determine actuator commands for the actuators that can actually influence the chassis-level accelerations.

[0005] DE 10 2018 122 948 A1 discloses a method for controlling a motor vehicle in which a target longitudinal force, a target lateral force, and a target yaw moment are specified. Using a control algorithm, a target value for the drive torque and a target value for the steering torque are determined for each of the four wheels. This optimization problem is solved using model predictive control with a sliding horizon.

[0006] For example, DE 10 2009 049 635 A1 describes a motion control system for vehicles with more actuators than degrees of freedom, with a static, direct allocation of control variables for the actuators. The vehicle dynamics controller is separated from the actuator allocation, which can potentially lead to unimplementable controller output variables. Simple, rule-based allocations are widespread, such as the wheel pressure distributions in today's ESC control systems. These approaches generally do not find a global optimum and therefore do not exploit the full potential of the actuators.

[0007] It is therefore an object of the invention to provide an improved motion control.

[0008] The object is achieved by a method for controlling actuators acting on vehicle wheels of a motor vehicle according to claim 1, the method comprising the following steps: Determining a force to be applied to a reference point of the motor vehicle on the basis of driver inputs, determining wheel forces to be applied to the vehicle wheels to implement the force to be applied to the reference point of the motor vehicle by means of a first dynamic allocation by a model-based predictive control, determining target values ​​for wheel parameters from the determined wheel forces, and controlling the actuators of the motor vehicle to implement the target values ​​of the wheel parameters.

[0009] The motion control concept is based on the principle of inverse dynamics. This means that the desired kinematic motion is calculated backward, taking into account the inertial properties of the vehicle, to determine the corresponding control variables, namely the dynamic tire forces and the corresponding wheel torques and wheel steering angles. To compensate for disturbances, measures such as suitable closed-loop control and disturbance compensation are preferably used. When determining the controlled variables, the control system is preferably divided into several cascading levels connected by clearly defined interfaces.

[0010] To enable coordinated actuator operation, optimization-based allocation algorithms can be used.

[0011] Potential vehicle movements are influenced by a number of factors: the performance limits of actuators and sensors, road conditions, passenger comfort and safety, energy and emissions, driver preferences, and infrastructure factors. These factors will preferably be systematically considered during the design of the control system, already at the highest cascade level. According to the invention, continuous forecasting capabilities will also be incorporated. This is ensured by the advanced control method of model-based predictive control, which is capable of optimizing vehicle operation and reducing time to market for increasingly complex vehicle systems.

[0012] The predictive, optimal approach according to the invention controls the driving and wheel dynamics and allows for easy inclusion of constraints in the optimization process. These are primarily the friction-related limitations of the wheel forces and driving dynamics, as well as the limitations of the actuators. This ensures the coordination of longitudinal and lateral dynamics within the physically available limits. In addition, quality functions can be used to prioritize driving dynamic and energy-related variables.

[0013] In a preferred embodiment of the invention, the driver inputs are provided by a virtual driver and / or an assistance system. This can be done alternatively or in addition to a human driver, who can input the driver inputs, for example, using an accelerator pedal, a brake pedal, and a steering wheel. A virtual driver can also specify a rear-wheel steering angle, which is used for movement control.

[0014] In a preferred embodiment of the invention, the driver inputs are an acceleration and / or at least a steering angle. These are the core inputs for controlling a vehicle.

[0015] In a preferred embodiment of the invention, the target values ​​for the wheel parameters are torques acting on the wheels, slip values ​​of the wheels, rotational speeds of the wheels and / or steering angles of the wheels.

[0016] In a preferred embodiment of the invention, the method for implementing a target value for a torque acting on a vehicle wheel further comprises a second dynamic allocation that includes a slip control. This also allows the torque on a wheel to be distributed among the available actuators in an optimized manner.

[0017] In a preferred embodiment of the invention, the actuators are electric motors and / or friction brakes.

[0018] According to the invention, in an intermediate step, kinematic target motion variables are adapted via a virtually controlled single-track model and taken into account in the dynamic allocation of the wheel forces.

[0019] In a preferred embodiment of the invention, the dynamic allocation of wheel forces includes a vehicle dynamics control system. The combination of allocation and vehicle dynamics control ensures that the vehicle dynamics control system can maximize and optimally utilize the available capabilities without imposing specifications that cannot be implemented by the actuators.

[0020] In a preferred embodiment of the invention, preliminary wheel forces are determined using a static allocation, and these are fed into the dynamic allocation as input values ​​or starting values. An arbitration can then be performed between the determined wheel forces from the static and dynamic allocations.

[0021] In a preferred embodiment of the invention, the dynamic allocation takes into account a saturation of an assigned actuator, a reconfiguration to ensure fault tolerance in case of actuator failure, an increase in energy efficiency and a minimization of wear.

[0022] In a preferred embodiment of the invention, the determined wheel forces are converted into target values ​​for torques, wheel slippage, rotational speeds and steering angles of the wheels using an inverse tire force model.

[0023] Further features, advantages and possible applications of the invention will become apparent from the following description of embodiments based on calculations and the drawings. Fig. 1 shows a vehicle configuration with a motion control according to the invention, Fig.2 shows the structure in parent - child systems, Fig. 3 shows schematically the motion control concept, Fig. 4shows the forces of the motor vehicle, Fig. 5 shows the forces on a tire, Fig. 6 shows a first test maneuver, Fig. 6 shows a second test maneuver, Fig. 6 shows a third test maneuver,

[0024] Figure 1 shows a vehicle configuration for the motion control (MC) of the vehicle. The motion control (MC) has access to all brakes (b), which can be electromechanical, and both electric motors (m) on the front axle, which are suitable for regenerative braking. This configuration enables improved torque vectoring and blending, which improves the vehicle's energy efficiency, stability, and handling. The steering (s) cannot be controlled by the motion control (MC).

[0025] Regenerative braking improves the comfort of the driver and passengers while driving and extends the vehicle's range.

[0026] The motion control concept uses elements inspired by object-oriented design. The elements used have a structure that maps the overall system into parent systems 13 and child systems 2 (parent / child system pairs) along various chains of effects, as shown in Figure 2is shown. The causal chains are either constructed for specific purposes or represent external influences such as waste heat. Examples of parent / child system pairs are vehicle / chassis, chassis / corner, or corner / actuator. Each system distinguishes internally between information providers / observers 3 (observer functions) and managers 4. Observer functions 3 provide estimated or measured actual values ​​9 for their own and parent levels 13 and coordinate the boundary conditions 10 they receive from the child level 2. They can also provide estimated or measured disturbances ("counters") 12 that are used by their own or subordinate systems to improve control quality. Manager functions determine requirements 8 for controlling the respective child system. They can also receive desired commands 11 from child levels and offset these against their own requirements 8.

[0027] At the vehicle level, the longitudinal and lateral demands are determined by dynamic feedforward control with customizable vehicle response and damping characteristics. The central element at the chassis level is a model predictive controller (MPC), which requests the forces from the cornering module while taking stability and energy limits into account. A two-track model is used to describe the chassis dynamics. Time-variant system matrices are generated by linearization and discretization at each sampling time. Friction circles between tire and road, which limit the permissible forces at the wheels, are approximated by polytopes. These measures are intended to ensure the applicability of convex quadratic programming, which is suitable for embedded real-time optimization. At the corner level, the modules process the incoming stream of chassis demands and generate a stream of corresponding demands for the actuators.An MPC framework for corner modules is capable of optimally distributing wheel braking torque among the redundant actuators on the front axle, while providing traction control and anti-lock braking functions to all wheels through wheel slip control. This approach offers fast transient response without compromising the energy recovery efficiency of the electric motors, taking into account the different dynamic authorities of the friction brake and the electric motor.

[0028] Figure 3shows the overall structure of the motion control concept. The system incorporates modern methods such as electronic stability control (ESC), active yaw control (AYC), anti-lock braking system (ABS), and traction control system (TCS). Arbitrator blocks (Arb) and an inverse tire model (iTire) are used for this purpose. The remaining blocks in the control chain are the human driver (Drv), a single-track model (STM) with a virtual controller (VC), a feedforward control (FF), a static control map (CA), observers (Obs), and the actuators (Act), i.e., two electric motors on the front axle and friction brakes on each wheel. The specific variables are explained below. A virtual driver (Virt. Drv) can be used in special situations to override the driver, thus allowing direct integration of autonomous driving (AD).

[0029] In the following, a general overview is given, followed by an increasing discussion of the systematic derivation and structure of the models as well as the generic structure of the optimization problem, which forms the basis for model predictive control.

[0030] Model predictive control is an advanced optimization-based control method. Unlike linear-quadratic (LQ) control, MPC offers the explicit treatment of process constraints arising from natural requirements, such as energy efficiency, safety, actuator limits, and others. The control decisions in MPC are calculated online using an internal model of the plant dynamics.

[0031] All models in the motion control concept are generally based on linear time-variant discrete models with n state variables in the vector x, m inputs or control actions in u and p Exits in y. Every discrete-time model is derived from a nonlinear continuous-time model in state-space form x ˙ = f x u , x t 0 = x 0 y = h x u

[0032] The nonlinear state space model is linearized along a reference trajectory for the state xd and the control action ud, resulting in f x u ≈ f x d u d + ∂ f ∂ x T x d , u d ︸ A x − x d + ∂ f ∂ u T x d , u d ︸ B u − u d , h x u ≈ h x d u d + ∂ h ∂ x T x d , u d ︸ C x − x d + ∂ h ∂ u T x d , u d ︸ D u − u d . The result is an affine linear approximation of the nonlinear system with the system matrices A, B, C , D and the affine vectors hx and hy , which are generally time-variant, x ˙ = Ax + Bu + h x , h x = f x d u d − A x d − B u d , y = Cx + Du + h y , h y = h x d u d − C x d − D u d .

[0033] The affine approximation is advantageous because the system variables can be used directly in the optimization and the problematic mixture of absolute values ​​and difference-to-setpoint values ​​is avoided. Two discretization methods are used in the motion control concept: the cost-effective but less accurate Euler forward method and the more accurate but also more expensive Tustin (trapezoidal) method. A discrete model is characterized below by an index k. With the sampling time T s, the Euler discretization for the affine system leads to A k = I n + A T s , B k = B T s , C k = C , D k = D , h xk = h x T s , h yk = h y

[0034] The Tustin discretization is used only for non-affine systems and is given by the following transformation. This generally results in a direct implementation matrix D k . A k = I n − A T s 2 − 1 I n − A T s 2 , B k = I n − A T s 2 − 1 B T s , C k = C I n − A T s 2 − 1 , D k = D + C I n − A T s 2 − 1 B T s 2

[0035] So far, it has been assumed that the predictive controller calculates the control input uk in its absolute form. However, this is not the only way to generate inputs for the system. In certain applications, it is advantageous to calculate changes uk in the input. This formulation is also called a rate-based or integral action formulation. The reason for using an integral action controller formulation is to obtain offset-free tracking. There are several ways to express the controller model in its incremental, integrating form. Using the incremental vectors Δ x k = x k − x k − 1 , Δ u k = u k − u k − 1 , Δ y k = y k − y k − 1 In the following, the integral action form of the state-space system is given, assuming that the time-varying system matrices and affine vectors do not differ very much between two consecutive time samples. Δ x k + 1 = A k Δ x k + B k Δ u k + Δ h xk , y k = y k − 1 + C k Δ x k + D k Δ u k + Δ h yk

[0036] The above system description does not correspond to the generic form we introduced earlier. To restore the generic form for integral actions, the system state is extended with the output of the previous sampling interval. The extended system is then as follows: Δ x k + 1 y k = A k 0 C k I p Δ x k y k − 1 + B k D k Δ u k + Δ h xk Δ h yk , y k = C k I p Δ x k y k − 1 + D k Δ u k + Δ h yk

[0037] Another advantageous use of the state-space model is to provide a prediction of the system state and output over a given time period into the future. Using the so-called "batch" approach, it is possible to express the dynamics of the state and output vector for a given time horizon N by backward multiplying the linear matrices and vectors. The batch form for discrete linear time-varying affine systems is denoted as follows and must be rebuilt at each sampling interval: x 1 x 2 x 3 ⋮ x N = A ¯ x 0 + B ¯ u 0 u 1 u 2 ⋮ u N − 1 + H ¯ x h x 0 h x 1 h x 2 ⋮ h xN − 1 , y 0 y 1 y 2 ⋮ y N − 1 = C ¯ x 0 + D ¯ u 0 u 1 u 2 ⋮ u N − 1 + H ¯ yx h x 0 h x 1 h x 2 ⋮ h xN − 1 + h y 0 h y 1 h y 2 ⋮ h yN − 1 A ¯ = A 0 A 1 A 0 A 2 A 1 A 0 ⋮ ∏ j = 0 N − 1 A N − 1 − j , C ¯ = C 0 C 1 A 0 C 2 A 1 A 0 ⋮ C N − 1 ∏ j = 0 N − 1 A N − 1 − j , H ¯ x = I n 0 0 … 0 A 1 I n 0 … 0 A 2 A 1 A 2 I n … 0 ⋮ ⋮ ⋱ ⋱ ⋮ ∏ j = 0 N − 1 A N − j ∏ j = 0 N − 2 A N − j … A N − 1 I n B ¯ = B 0 0 0 ⋯ 0 A 1 B 0 B 1 0 ⋯ 0 A 2 A 1 B 0 A 2 B 1 B 2 ⋯ 0 ⋮ ⋮ ⋱ ⋱ ⋮ ∏ j = 1 N − 1 A N − j B 0 ∏ j = 1 N − 2 A N − j B 1 ⋯ A N − 1 B N − 2 B N − 1 D ¯ = D 0 0 0 ⋯ 0 C 1 B 0 D 1 0 ⋯ 0 C 2 A 1 B 1 C 2 B 1 D 2 ⋯ 0 ⋮ ⋮ ⋱ ⋱ ⋮ C N − 1 ∏ j = 1 N − 2 A N − 1 − j B N − 2 C N − 1 ∏ j = 1 N − 3 A N − 1 − j B N − 2 ⋯ C N − 1 B N − 2 D N − 1 , H ¯ yx = 0 0 0 ⋯ 0 C 1 0 0 ⋯ 0 C 2 A 1 C 2 0 ⋯ 0 ⋮ ⋮ ⋱ ⋱ ⋮ C N − 1 ∏ j = 1 N − 2 A N − 1 − j C N − 1 ∏ j = 1 N − 3 A N − 1 − j ⋯ C N − 1 0

[0038] Essentially, an MPC controller is based on an iterative finite-horizon (constrained) optimization of a plant model. At each discrete sampling time (k), the plant is sampled, and the actual state xk is measured or estimated using observers. The performance of the controller is expressed by a so-called cost function. Based on a dynamic model of the plant, this cost function is formulated to express the future behavior of the MPC controller given a current plant state xk and a sequence of future inputs uk. In other words, this predicted cost function provides a numerical indicator of the quality of the control, assuming that the current plant state is influenced by a specific sequence of inputs from the past.The question is not what the controller's performance will be, but rather what the sequence of inputs uk will look like that produces the best performance. To calculate the optimal sequence of inputs, one must minimize the cost function at each sampling interval using a numerical optimization algorithm. As with most real-world plants, the inputs, outputs, and states may be limited by physical constraints that can easily be incorporated into the numerical minimization task. Of the sequence of future inputs uk, only the first is applied, then the process is repeated based on brand-new measured state information. This type of repeated cycle of measure-predict-optimize-apply is called receding-horizon control.

[0039] The MPC optimization approach used in the present motion control concept includes the following generic form, where N denotes the prediction horizon and M the control horizon, min u c 0 : M − 1 , ε J T x k u k + γJ E x k u k + Pε 2 x k + 1 = A k x k + B k u k + h xk y k = C k x k + D k u k + h yk w k = C wk x k + D wk u k + ε V w u 0 T , … , u N − 1 T T = M ⊗ I m u c 0 T , … , u cM − 1 T T x 0 = x k u min ≤ u k ≤ u max y min − ε V y , min ≤ y k ≤ y max + ε V y , max Δ u min − ε V Δ u , min ≤ Δ u k ≤ Δ u max + ε V Δ u , max H xk x k + H uk u k ≤ b Hk + ε V H 0 ≤ ε ∀ k ∈ 0 , … , N − 1

[0040] The entire cost function is divided into a trajectory tracking part JT , an energy consumption part JE and a slack variable with the weight P εThe constraints of the MPC problem can be divided into equality and inequality constraints. The first three equality constraints are the state and output model of the vehicle dynamics in affine form and a general soft constraint as a linear combination of state and input, which is weakened by the slack variable. The target vector wk is either zero or must be externally specified. The next equality constraint is used to realize a control horizon shorter than the prediction horizon, namely by motion blocking. The matrix M determines the blocking scheme and the operator symbol is the Kronecker product. The last equality constraint maps the initial state to the current state of the sampling period. The inequality constraints determine the bounds for the input uk , the output yk , and the input rate uk .The latter two are weakened to ensure the feasibility of the optimization.

[0041] A polytopic set constraint, which is optionally relaxed, and the non-negativity of the slack variables are the remaining inequality conditions. The cost function used for goal tracking is quadratic and allows the penalization of the output error, the input error, and the input rate by the symmetric positive semidefinite weight matrices Q, R, and R Δ . J T = ∑ k = 0 N y k − y dk T Q y k − y dk + ∑ k = 0 N − 1 u k − u dk T R u k − u dk + Δ u k T R Δ Δ u k

[0042] For the energy consumption part JE of the cost function, any energy- or power-related function can be used. The only restriction is that the cost function must be quadratic and / or linear. The weighting factor can be used to specify the relative importance of the energy costs. A typical power-related function is the power loss P loss of electric motors, which can be formulated based on the electric motor torque T m , the wheel speed w , and given efficiency maps for generation and propulsion. P loss = T m ω w − T m ω w η gen T m ω w , T m < 0 T m ω w η mot T m ω w − T m ω w , T m ≥ 0

[0043] The efficiency maps are generally not quadratic, so an approximation at a specific operating point with linear and quadratic terms can be applied in the following form J E = ∇ 2 P loss T m = T m 0 Δ T m 2 + ∇ P loss T m = T m 0 Δ T m

[0044] To solve the optimization problem online, the following convex quadratic program (QP) is used, which can be solved reliably and efficiently. min z 1 2 z T Hz + f T z subject to A eq z = b eq A ineq z ≤ b ineq

[0045] The optimization vector z is given by z = x 0 T , … , x N T , u 0 T , … , u N − 1 T , u c 0 T , … , u cM − 1 T , ε T .

[0046] The only free variables for optimization are the control interventions u c0..M-1 and the slip ε . Only the first controlled variable u c0 is used to control the system. The other variables, especially the state x, are also optimal in the sense of QP optimization and can be used for other purposes, e.g., for the transformation of data in subsequent steps. With this optimization vector, the optimization is in a so-called "sparse" or "recursive" form, in contrast to the "dense" or "batch" formulation. In the latter, the state is eliminated in the optimization problem, resulting in an alternative QP problem. The Hessian matrix H and the gradient vector f are given as H = Q CC Q CD 0 0 Q DC Q DD + R u + A Δ T R Δu A Δ 0 0 0 0 0 0 0 0 0 P , f = Q C 0 0 0 Q D R u 0 0 0 0 0 0 0 0 0 0 h y , pred − y d , pred − u d , pred 0 0 − 0 A Δ T R Δu A Δ u − 1 0 0

[0047] With the following vectors y d , pred = y d 0 T , … , y dN T T , h y , pred = h y 0 T , … , h yN T T , u d , pred = u d 0 T , … , u dN − 1 T T , u pred = u 0 T , … , u N − 1 T T , Δ u pred = Δ u 0 T , … , Δ u N − 1 T T = A Δ u pred − A Δ u − 1 , u − 1 = u k − 1 T , … , u k − 1 T T ︸ N − 1 times

[0048] And matrices of the cost function Q CC = C 0 T Q C 0 ⋱ C N T Q C N , Q CD = C 0 T Q D 0 ⋱ C N − 1 T Q D N − 1 0 ⋯ 0 , Q DC = D 0 T Q C 0 0 ⋱ ⋮ D N − 1 T Q C N − 1 0 , Q DD = D 0 T Q D 0 ⋱ D N − 1 T Q D N − 1 , R u = R ⋱ R , R Δ u = R Δ ⋱ R Δ , A Δ = I m 0 ⋯ I m I m ⋯ ⋮ ⋮ ⋱ I m I m ⋯ − 1 , Q C = C 0 T Q ⋱ C N T Q , Q D = D 0 T Q 0 ⋱ ⋮ D N − 1 T Q 0

[0049] The linear equality constraints are given by the matrix A eq and the vector b eq given, A eq = − I n 0 ⋯ 0 0 ⋯ 0 0 A 0 − I n B 0 0 ⋯ 0 0 ⋱ ⋱ ⋱ ⋮ ⋱ ⋮ ⋮ A N − 1 − I n B N − 1 0 ⋯ 0 0 C w 0 0 D w 0 0 ⋯ 0 V w ⋱ ⋮ ⋱ ⋮ ⋱ ⋮ ⋮ C wN − 1 0 D wN − 1 0 ⋯ 0 V w 0 ⋯ 0 0 I m − I m 0 ⋱ ⋮ ⋮ ⋱ ⋮ ⋮ ⋱ − I m 0 ⋮ ⋮ 0 ⋯ 0 0 I m − I m 0 , b eq = x k − h x 0 ⋮ − h xN − 1 w 0 ⋮ w N − 1 0 ⋮ 0 ⋮ 0

[0050] The inequality conditions are defined in the matrix A room and the vector b room collected, A ineq = 0 0 diag I m 0 0 0 0 − diag I m 0 0 0 diag C k + 1 diag D k 0 − V ¯ y , max 0 − diag C k + 1 − diag D k 0 − V ¯ y , min 0 0 A Δ 0 − V ¯ Δ u , max 0 0 − A Δ 0 − V ¯ Δ u , min 0 diag H xk + 1 diag H uk 0 − V ¯ H 0 0 0 0 − 1 , b ineq = u ¯ max − u ¯ min y ¯ max − h ¯ y , pred − y ¯ min + h ¯ y , pred Δ u ¯ max + A Δ u − 1 − Δ u ¯ min − A Δ u − 1 b ¯ H 0

[0051] The index k ranges from horizon step 0 to N-1, and the overline symbol denotes the corresponding vectors. The min and max bounds are repeated here for each step of the horizon, but if a prediction along the horizon is available, the bounds can be different from step to step. Note that enforcing output constraints in the initial step only makes sense if the input directly affects the constrained outputs. Conversely, enforcing output constraints in the final step only makes sense if there is no direct flow from the input to the output. These constraints also apply mutatis mutandis to the cost function.

[0052] The motion control requirements are as follows: In straight-line driving or braking situations, energy efficiency should be prioritized. In such cases, the maximum regenerative braking torque should be provided.

[0053] In cornering situations, agility should be improved under normal driving conditions, and at the limit of tire-road friction, vehicle stability should have absolute priority.

[0054] Stability has priority in the event of a brake actuator failure and the drive train should support the deceleration process (stabilization and maximum deceleration performance)

[0055] The following sections describe the tasks of all modules of the motion control concept and explain the models and all necessary data in more detail.

[0056] The task of the vehicle manager is to determine setpoints for the vehicle state and the global forces acting on the body at the center of gravity (CoG). The vehicle manager is designed as a model-based feedforward control system. The reference vehicle state is determined using a planar linear single-track model, in which the coupling between longitudinal and lateral motion is achieved only by the vehicle speed. The input to the single-track model is the front steering angle and the acceleration requested by the driver. Optionally, a virtual driver can also request a rear steering angle. In this case, the virtual control (VC) described below is deactivated.

[0057] The vehicle's longitudinal state, i.e., the reference vehicle speed vd , is simply determined from the integration of the requested driver acceleration a xd less an estimated resistance, i.e., the disturbance a dis . Without considering the disturbance, the reference vehicle speed would be less realistic and unattainable by a tracking controller. The longitudinal reference model and its state-space representation is given by v ˙ d = a xd − a dis x = v d , u = a xd a dis T , y = v ˙ d , A = 0 , B = 1 − 1 , C = 0 , D = 1 − 1

[0058] The lateral vehicle condition is determined by the sideslip angle β d and the yaw rate ω d To enable the driver to individually adjust the lateral vehicle dynamics, the lateral single-track model is supplemented by a virtual rear axle steering angle δ rd,VCVirtually controlled (VC). The idea behind the virtually controlled single-track model is to provide the electric vehicle driver with improved lateral agility and yaw damping. The virtual rear-axle steering angle controller is implemented as a linear quadratic (LQ) state-space controller with gain K x , along with a feedforward filter K w and disturbance compensation K s . The input to the feedforward filter is a quasi-static yaw rate. ω stat , which is limited by the road grip conditions. The front steering angle δ fd The driver's input is treated as a disturbance and compensated for by creating a vanishing stationary virtual steering angle. This avoids the driver having to react adaptively to a changing stationary yaw gain caused by a non-zero virtual rear axle steering angle. The open-loop lateral reference model is given in state-space form by x = β d ω d , u = δ rd , VC , s = δ fd , A ol = a 11 a 12 a 21 a 22 , B u = b u 1 b u 2 , B s = b s 1 b s 2 , y = β ˙ d ω ˙ d a y , C ol = a 11 a 12 a 21 a 22 c 31 c 32 , D u = b u 1 b u 2 d u 3 , D s = b s 1 b s 2 d s 3

[0059] With the vehicle parameters mass m, yaw moment of inertia J z , lateral tire stiffness front and rear C f , C r and distance of center of gravity to the front and rear axle lf , lr the matrix elements of the uncontrolled lateral vehicle model are obtained a 11 = − C f + C r mv d , a 12 = − 1 − C f l f − C r l r mv d 2 , b u 1 = C r mv d , b s 1 = C f mv d , a 21 = − C f l f − C r l r J z , a 22 = − C f l f 2 + C r l r 2 J z v d , b u 2 = − C r l r J z , b s 2 = C f l f J z , c 31 = − C f + C r m , c 32 = − C f l f − C r l r mv d , d u 3 = C r m , d s 3 = C f m

[0060] The control law for the virtual rear steering angle is given as follows, where all controller gains are given by the longitudinal reference speed, u = − K x x − K s s + K w ω stat

[0061] The matrices of the closed control loop taking into account the front steering angle and the static yaw rate as new inputs have the form A = A ol − B u K x , B = B s − B u K s B u K w , C = C ol − D u K x , D = D s − D u K s D u K w

[0062] The static yaw rate is derived from a stationary single-track model and is limited by the tire-road friction, which is characterized by the coefficient µ. The remaining parameters are the gravitational acceleration constant g and the wheelbase. l = l f +l r , ω stat = sign δ fd ⋅ min ω drv ω μ , ω drv = δ fd v d l + EGv d 2 , ω μ = μg v d , EG = m l l r C f − l f C r

[0063] The controlled single-track model, which includes both longitudinal and lateral motion, is processed in the batch form described above to provide the reference data for the entire forecast horizon.

[0064] The next step in the control chain is a nonlinear feedforward control with so-called reference global forces as the output. The reference global forces, i.e. the longitudinal force F xd , the lateral force F yd and the yaw moment M zd acting on the center of gravity, are derived from the following nonlinear vehicle dynamics model in state-space form. Of all possible disturbance forces, only the wind resistance is taken into account with the aerodynamic drag coefficient parameter kx. The vehicle dynamics are described in a body-fixed coordinate system whose origin is at the center of gravity. The nonlinear system dynamics in input-affine form and the nonlinear output equations are given by v ˙ x v ˙ y ω ˙ = v y ω − k x m v x 2 − v x ω 0 + 1 m 0 0 0 1 m 0 0 0 1 J z F xd F yd M zd , v d β d ω d = v x 2 + v y 2 a rctan v y v x ω

[0065] The flatness property the reference outputs vd , β d and ω d ,is used to calculate the global reference forces by a flatness-based inversion, i.e., the global forces are functions of the reference outputs and their first derivatives as inputs. In particular, for the longitudinal reference force, the inversion yields F xd = m v ˙ d cosβ d − v d β ˙ d + ω d sinβ d + k x v d 2 1 − sin 2 β d

[0066] Particular attention must be paid to the disturbances. The reference velocity vd already contains longitudinal disturbances, and using the previous equation can lead to driver confusion. A desired zero acceleration should result in a zero longitudinal reference force F xd. Therefore, all disturbance-related terms must be eliminated. For this purpose, the next section describes the estimated disturbance a dis and introduces a curve disturbance term into the equation. Overall, the following model describes the desired global forces, which is processed at each sampling time for an N-step prediction: F xd F yd M zd = m v ˙ d cosβ d − v d β ˙ d + ω d sinβ d + m a dis + β d a yd m v ˙ d sinβ d + v d β ˙ d + ω d cosβ d J z ω ˙ d

[0067] There are two tasks of the vehicle observer: determining the prediction horizon of the driver input and estimating a longitudinal disturbance a dis acting on the vehicle.

[0068] There are two main approaches to predicting the driver horizon, assuming no map or environmental sensor information is available. The first approach involves simply holding the current acceleration and steering values ​​over the prediction horizon. The second approach is based on curve fitting. A few recent samples are stored and a curve is fitted to the data using interpolation, e.g., a polynomial. The polynomial is then used for extrapolation over the entire prediction horizon. For simplicity, the first approach has been chosen below.

[0069] For disturbance estimation, a Luenberger disturbance observer with two states, estimated vehicle speed ve and longitudinal disturbance a dis, is designed, and the desired driver acceleration a xd is input. The output is the estimated vehicle speed ve , which is compared with the actual vehicle speed v to reduce the estimation error. The Luenberger observer has the following continuous-time, linear, time-invariant state space form v ˙ e a ˙ dis = 0 − 1 0 0 v e a dis + 1 0 a xd + L 1 L 2 v − v e , v e = 1 0 v e a dis

[0070] The observer gains L 1 and L 2 are designed using the linear quadratic (LQ) method, and the continuous disturbance observer is then discretized using the Tustin method. The estimated longitudinal disturbance provided by the vehicle observer is kept constant over the prediction horizon. The task of the chassis manager is to provide optimized longitudinal and lateral forces at each corner of the vehicle. Figure 4shows the geometric and kinematic quantities as well as the forces considered in the motion control concept. The vehicle motion is described in a horizontal, body-fixed coordinate system (index "b"). Two types of auxiliary coordinate systems are used below. The first type are systems that are fixed at each chassis corner (index "c") but have the same orientation as the body-fixed system. The second type are systems that are fixed at each wheel corner and rotated by the wheel steering angle (index "w"). At each wheel, the chassis corner system and the wheel corner system have the same origin. For the motion control concept of the described embodiment, it was decided that the chassis manager would provide the optimized corner forces specified in the chassis corner system. The use of wheel corner forces would be an alternative, although the equations of motion are more complex.

[0071] The first task of the chassis manager is to determine the desired reference chassis corner forces, which result from the global reference forces supplied by the vehicle manager. For this purpose, a static rule assignment approach based on a pseudo-inverse with a weighting matrix W u is selected. The relationship between the global forces and the chassis corner forces is given by the distribution matrix G and the parameters track width at the front and rear axles, bf and br , respectively, as F xd F yd M zd T = G u c , u c = F xd , fl F yd , fl F xd , fr F yd , fr F xd , rl F yd , rl F xd , rr F yd , rr T , G = 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 − b f l f b f l f − b r − l r b r − l r

[0072] The above relationship between global and chassis corner forces is an underdetermined linear system that cannot be uniquely solved for uc<. Numerous methods exist to exploit the remaining degrees of freedom. We chose a weighted Moore-Penrose pseudoinverse, which results from the minimization of the weighted 2-norm u T< W u T< W u u where W u is a positive diagonal matrix.

[0073] The transformation between chassis corner and wheel corner coordinates is possible with the rotation matrix T cw< , u c = T cw u w , u w = T wc u c = T cw T u c , v w w = T wc v w c T cw = cosδ f − sinδ f 0 0 0 0 0 0 sinδ f cosδ f 0 0 0 0 0 0 0 0 cosδ f − sinδ f 0 0 0 0 0 0 sinδ f cosδ f 0 0 0 0 0 0 0 0 cosδ r − sinδ r 0 0 0 0 0 0 sinδ r cosδ r 0 0 0 0 0 0 0 0 cosδ r − sinδ r 0 0 0 0 0 0 sinδ r cosδ r

[0074] As mentioned above, the reference corner forces are required in the chassis corner systems. However, for the static control assignment, it is more advantageous to weight the corner forces in the wheel coordinate systems and then transform them back to the chassis systems. The reason for this is that, to achieve the goal of energy efficiency, the primary purpose of the weighting matrix W u is to prioritize the electric motors on the front axle before the friction brakes are applied on both axles. The wheel longitudinal corner forces correspond directly to the torques at the wheels, so the rear wheel longitudinal corner forces are weighted lower than the other forces. The entire static control assignment procedure is then specified by u d = T cw W u − 1 B g T B g W u − 1 B g T − 1 F xd F yd M zd T , B g = G T cw , W u = diag 10 − 6 , 10 − 6 , 10 − 6 , 10 − 6 , 1 , 10 − 6 , 1 , 10 − 6 .

[0075] The second task of the chassis manager is to use model-based predictive control (MPC) to track the reference states and inputs, keeping all states and control actions within their limits. In a first step, the nonlinear vehicle model defined in the vehicle manager section above is linearized along the reference state and input trajectory. The reference input ud is represented by the reference longitudinal and lateral forces in chassis corner coordinates as explained above, and the reference state xd is calculated from the data provided by the vehicle manager. x d = v xd v yd ω d = v d cos β d v d sin β d ω d

[0076] The result of the linearization are the following matrices and vectors A = − 2 k x v xd m ω d v yd − ω d 0 − v xd 0 0 0 , B = 1 m 0 0 0 1 m 0 0 0 1 J z G , C = v xd v xd 2 + v yd 2 v yd v xd 2 + v yd 2 0 − v yd v xd 2 + v yd 2 1 v xd 2 + v yd 2 0 0 0 1 , D = 0 , h x = v yd ω d − k x m v xd 2 − v xd ω d 0 + B u d − A x d − B u d = − v yd ω d + k x m v xd 2 v xd ω d 0 , h y = v xd 2 + v yd 2 atan v yd v xd ω d − C x d

[0077] The state x, the output y and the control action u of the chassis manager MPC consists of x = v x v y ω T , y = v β ω T u = F xd , fl , MPC F yd , fl , MPC ⋯ F xd , rr , MPC F yd , rr , MPC T

[0078] Constraints can be defined for the state and the control action, which are described below. The equality conditions of the MPC are the above system equations, the driving lock, and a balance of the longitudinal corner forces of the chassis with the global force provided by the vehicle manager, i.e. w k = F xd , C wk = 0 D wk = 1 0 1 0 1 0 1 0 , V w = 1

[0079] The inequality constraints contain the absolute force limits F max specified by the chassis observer at each wheel as u min and zero at the rear axle and the maximum electric motor propulsion force at the front axle as u max . The rate limits are chosen to be symmetric with + / - 100 Nm at each sampling time. A polytope constraint approximates the friction circle at each wheel with octagons. The vertices of the octagon are calculated by P x , j P y , j = F max sin 2 π j 8 cos 2 π j 8 , j = 1 , … , 8

[0080] The edges of the octagon can be described by linear functions and pm and pb can be derived from the vertices, ie for Rad i the boundary is described by F xd , i , MPC = p mj , i F yd , i , MPC + p bj , i , j = 1 , … , 8 , i = 1 ,… 4

[0081] The control actions are limited by the edges, but can in principle be controlled to any desired value within the polytope. This leads to the following inequality condition, which is softened to ensure the feasibility of the optimization: H xj , i F xd , i , MPC + H yj , i F yd , i , MPC ≤ H j , i + V Hj , i ε , j = 1 , … , 8 , i = 1 , … , 4 H xj , i = sign p bj , i , H yj , i = − sign p bj , i p mj , i , H j , i = sign p bj , i p bj , i , V Hj , i = 1

[0082] The second type of polytope constraint is a stability envelope that determines the yaw rate ω and the rear slip angle α r limited to a stable driving range.

[0083] The corners of the envelope are determined by the tire-road friction µ , the gravitational constant g and the rear lateral tire stiffness C r defined by ω max = μg vd , α r , max = 3 F max , rl + F max , rr C r

[0084] The rear slip angle is a simple nonlinear function of the output, but a more complicated function of the state. To derive a linear constraint, the nonlinear function is approximated by linearization along the reference states. The result is an affine linear function of the state, where the details of the time-dependent coefficients are omitted here. α r = β − l r v ω = arctan v y v x − l r v x 2 + v y 2 ω ≈ c 1 v x + c 2 v y + c 3 ω + h α ,

[0085] Using the same method as for the friction circle, the envelope condition is as follows H 1 l v x + H 2 l v y + H 3 l ω ≤ H 0 l + V Hl ε , l = 1 , … , 4 , H 1 l = − sign p bl p ml c 1 , H 2 l = − sign p bl p ml c 2 , H 3 l = sign p bl 1 − p ml c 3 , H 0 l = sign p bl p ml h α + p bl , V Hl = 1

[0086] Collecting all constraints in the total matrices H xk and H uk and the vector b H introduced above leads to the following results, where the trailing and leading zeros each correspond to the non-zero block in the other matrix, H xk + 1 = H 11 H 21 H 31 ⋮ ⋮ ⋮ H 14 H 24 H 34 0 0 0 ⋮ ⋮ ⋮ 0 0 0 ,

[0087] At this point, a note is appropriate regarding vehicle configurations other than the one described here. In other configurations, the wheel is typically coupled to an axle by mechanical connections.

[0088] Steering or the powertrain are typical examples. For example, if one considers a vehicle with a single electric motor coupled to a differential gear on the front axle, additional equality constraints can represent the coupling effects between the left and right wheels. These couplings can be modeled with the equality constraints, assuming a gear ratio of 1. ω m = 1 2 ω w , fl + ω w , fr , T w , fl = 1 2 T m , T w , fr = 1 2 T m

[0089] These constraints must be expressed with equivalent states or inputs, i.e., forces, from the vehicle and chassis observer so that the generic equality condition from above can be applied.

[0090] The main task of the chassis observer is to provide estimates of the maximum allowable forces at each corner. The maximum forces F max are functions of the wheel load F z and the friction µ , a tire parameter k Fz and the nominal wheel load F z0 =mg / 4 according to F max , fl F max , fr F max , rl F max , rr = F z , fl μ fl 1 + k Fz F z 0 − F z , fl F z 0 F z , fr μ fr 1 + k Fz F z 0 − F z , fr F z 0 F z , rl μ rl 1 + k Fz F z 0 − F z , rl F z 0 F z , rr μ rr 1 + k Fz F z 0 − F z , rr F z 0

[0091] The vertical tire forces are estimated with a quasi-stationary model without suspension dynamics based on the measured longitudinal and lateral acceleration using the height h of the CoG according to the following model F z , fl F z , fr F z , rl F z , rr = m l l r g − ha x 1 2 − h 2 b f g a y m l l r g − ha x 1 2 + h 2 b f g a y m l l f g + ha x 1 2 − h 2 b r g a y m l l f g − ha x 1 2 + h 2 b r g a y

[0092] Ideally, the friction coefficient between tire and road is known, e.g., through road condition observers. A conceptual solution based on connectivity is already available. Vehicles equipped with vehicle-to-infrastructure (V2I) connectivity publish their road condition data, which is generated by on-board fusion of vehicle dynamics sensor data, camera data, and other sensor data. Data subscribers are connected to the cloud-based road condition database eHorizon and benefit from frequently updated friction data. If road conditions are not homogeneous, a rough estimate of wheel-specific friction can be derived from the split detection of modern ABS and TCS.

[0093] The Corner Manager has three tasks: tracking the optimal horizontal forces provided by the Chassis Manager, maximizing energy efficiency through optimized torque mixing between the electric motor and friction brake, and preventing wheel lock or over-spin through slip control. The Corner Manager uses an inverse tire model to determine reference data for MPC-based optimization. Depending on the drive configuration, the references can be wheel torque, slip, rotational speed, and even steering angle references. A Pacejka tire model in vector form is used to calculate all of this reference data, although a reference rotational speed and a reference steering angle are not mandatory in the motion control concept described here. Please note that a single wheel is considered below and therefore all vectors have two components unless otherwise stated.The Pacejka model determines the wheel forces using a known nonlinear function with the slip vector s as input and with F max and the tire parameters B and C, . F x F y = F max sin C arctan B s 1 s s x s y , s = s x 2 + s y 2

[0094] The inverse tire model, ie a determination of the longitudinal and lateral slip from the wheel forces is given by s x s y = 1 B tan 1 C arcsin F F max 1 F F x F y , F = F x 2 + F y 2

[0095] To avoid division by zero, the tire models require a non-zero absolute slip or force. In our application, we set the slip to zero when the absolute force is zero. Note that the slip in the inverse tire model is only uniquely defined for F < F max.

[0096] Using the slip calculated from the inverse tire model, a steering angle at the wheel can be determined, provided the wheel speeds are given and v wx is not zero, δ = arctan s y v w + v wy s x v w + v wx , v w = v wx 2 + v wy 2

[0097] When stationary, the steering angle δ > 0 from the previous step and kept constant. In addition, if necessary, the wheel speed from ω w = 1 r w s x v w + v wx 2 + s y v w + v wy 2 be determined.

[0098] It is worth noting that in all equations based on the inverse tire model, no coordinate system has been specified so far, meaning that the coordinates can be specified either in the chassis or wheel corner system. To decide on the most suitable coordinates, a closer look at the wheel vectors is helpful, see Figure 5 .

[0099] Figure 5 shows a moving wheel in a curve situation. The rotation of the wheel with the speed ω w generates a circumferential speed vc, which is given in the chassis corner system as v c c = − ω w r w cos δ sin δ .

[0100] The vector sum of the circumferential speed and the translational speed results in the so-called slip or sliding speed vs . It is assumed that the corner force always points in the opposite direction to the sliding speed. The wheel slip is then simply the sliding speed normalized by the absolute wheel speed, i.e. s = s x s y = − 1 v w v s = − 1 v w v c + v w

[0101] The slip reads differently in the respective chassis or wheel cover systems, as can be seen from the following variants s c = − 1 v w − ω w r w cos δ + v wx c − ω w r w sin δ + v wy c , s w = − 1 v w − ω w r w + v wx w v wy w .

[0102] In the following, we prefer the wheel-corner-based description of slip. For slip control, a model of the slip dynamics is derived from a quarter-car model, which describes the wheel rotational dynamics with the wheel rotational speed and the quarter-car translational dynamics with the wheel longitudinal speed v wx . The input to the quarter-car model is the wheel torque T w . The required parameters are the wheel moment of inertia J w , the quarter-car mass mq =m / 4 and the wheel radius rw . The tire force F x couples the translational and rotational parts together. The model is simplified because all resistances are neglected. The quarter-car model is nonlinear because the longitudinal force is a nonlinear function of the slip, as seen above. The state-space form of the quarter-car model is given by v ˙ wx ω ˙ w = 1 m q F x s x − r w J w F x s x + 0 1 J w T w

[0103] The prediction model of the longitudinal slip results from the differentiation of the longitudinal slip with respect to time and the onset of the accelerations from the quarter-car model, where the upper index w of the coordinate system has been omitted and the lateral wheel speed is assumed to be zero, s x = ω w r w − v wx v w , s ˙ x ≈ r w v wx ω ˙ w − ω w r w v wx 2 v ˙ wx = − 1 v wx r w 2 J w + ω w r w v wx m q F x s x + r w J w v wx T w

[0104] The slip model can be further simplified by neglecting the angular velocity term and approximating the longitudinal force F x linearly, ie with ω w r w v wx m q ≪ r w 2 J w , F x s x ≈ k Fx s x , k Fx = F max s x , thr , s x < s x , thr F max s x , s x ≥ s x , thr

[0105] The slip threshold sx,thr is either given individually for the traction and braking control or can be calculated from the inverse tire model above. Note that the force approximation is absolute and does not describe a deviation from the operating point. The result of these simplifications is a linear time-variant slip model in state-space form. x s = s x , u s = T w , y s = s x , A s = − r w 2 k Fx J w v wx , B s = r w J w v wx , C s = 1 , D s = 0

[0106] The corner manager is also responsible for the torque distribution between the electric motor and the friction brake. This task of dynamic control allocation is performed by the Corner-MPC. For each wheel, there is a corner manager that requires the current measurement of the electric motor torque T m , the friction brake torque T b , and the wheel longitudinal slip sx . The motor and brake actuators are modeled using simple first-order dynamics with the time constant T 1 . The output of the actuator model is the sum of the motor and brake torque, i.e., the wheel torque T w . The state-space model of the actuators is linearly time-invariant and given by x a = T m T b , u a = T md , MPC T bd , MPC , y a = T w A a = − 1 T 1 m 0 0 − 1 T 1 b , B a + 1 T 1 m 0 0 1 T 1 b , C a = 1 1 , D a = 0

[0107] The models of the actuators and the slip are discretized using the Tustin method and then combined to form the discrete overall model of the corner used in the MPC x k = x a x s , u k = u a , y k = y a y s = T w s x , A k = A ak 0 B sk C ak A sk , B k = B ak B sk D ak , C k = C ak 0 D sk C ak C sk , D k = D ak D sk D ak

[0108] The reference values ​​for the MPC optimization result from the reference corner forces in chassis coordinates, y dk = T wd s xd = r w F xd c cos δ + F yd c sin δ s xd , u dk = T md T bd = T wd 0

[0109] To optimize energy efficiency, the electric motor is the preferred actuator over the friction brake. Unlike the chassis manager, the static corner control assignment for providing reference control actions in the corner manager is essentially a rule-based assignment without the need for a pseudo-inverse.

[0110] Equality conditions of the MPC of the curve manager are the state dynamics and a torque sum condition, which compares the control effect with the target wheel torque, w k = T wd , C wk = 0 , D wk = 1 1 , V w = 1

[0111] The inequality constraints are the upper and lower limits of the electric motor and the friction brake. Other constraints are not considered.

[0112] The task of the curve observer is to provide the actual wheel slip data in the longitudinal direction. For this, the translational velocities at each wheel must be determined. The eight velocities in the wheel corner coordinate systems are given by transforming the measured vehicle state using the transformation matrices defined in the Chassis Manager section as v w w = T wc G T v x v y ω T

[0113] Another task of the curve observer is to monitor the temperature of the friction brake disc. A temperature profile model is used for this purpose.

[0114] The temperature model includes the surface temperature ϑ 1 and the window temperature ϑ2 as state variables. The input of the model is the friction brake power P b and the ambient air temperature ϑ u . The output is the brake disc temperature ϑ 2 .The parameters of the model are the heat capacities c b1 , c b2 , the thermal conductivity value λ b and convection α b . The state space form of the temperature model is ϑ ˙ 1 ϑ ˙ 2 = − λ b c b 1 λ b c b 1 λ b c b 2 − λ b + α b c b 2 ϑ 1 ϑ 2 + 1 c b 1 0 0 α b c b 2 P b ϑ u ϑ 2 = 0 1 ϑ 1 ϑ 2

[0115] The temperature model is used to monitor the disc temperature and initiate an alarm event when the temperature exceeds a certain threshold. When this event occurs, the vehicle speed must be reduced to no more than 30 km / h. For this purpose, a PID cruise controller designed using the so-called Model Free Control (MFC) method is used. The cruise controller overrides the driver's acceleration request. The temperature model is linear and can therefore potentially be integrated into the Corner Manager MPC along with disc temperature restrictions. It is worth noting that limiting waste heat at the friction brake is accompanied by a reduction in brake particulate emissions.

[0116] The simulation results demonstrate the validity of the motion control concept, which is explained and illustrated using the requested and actual vehicle dynamics data. For each of the high-level motion control objectives specified above, a representative maneuver is selected to evaluate the feasibility and performance of the proposed control concept. In all simulations, the chassis MPC sampling time is Ts=10 ms, and the prediction and control horizons are N=4 and M=2, respectively. The curve MPC sampling times are 2 ms, and the horizon lengths are identical to the chassis MPC.

[0117] The first maneuver shown in the diagrams of the Figure 6The figure shown is a straight-line braking test to visualize the front-to-rear torque vectoring by the Chassis Manager MPC and a braking torque overlay by the two corner MPCs on the front axle. In the final phase of the maneuver, the two rear corner MPCs perform slip control to prevent wheel locking.

[0118] Figure 6 shows a simulation of a straight-line braking maneuver with energy prioritization, d) and e) torque vectoring between front and rear axle, g) torque blending on the front axle with a maximum braking torque limit of -500 Nm assumed to be constant, k) slip control on the rear axle.

[0119] The second test case is the same as before, but with a failure of the front left friction brake actuator, see Figure 7This dangerous situation would generate a disruptive yaw moment, leading to immediate, uncontrolled spinning of the vehicle. With motion control, the situation is manageable for the driver at all times. The strategy is to reduce the maximum force limits on the remaining healthy curves to ensure stability. The amount of reduction was determined empirically. With this simple measure, the chassis MPC is able to redistribute the braking forces in such a way that the disruptive yaw moment is counteracted while simultaneously meeting the driver's braking request, albeit at a lower level than in the error-free case.

[0120] Figure 7shows a simulation of an actuator failure, g) failure of the front left friction brake, f) and i) vehicle stability ensured by reducing the maximum force requirements on the rear axle by 80% and on the right front wheel by 60%, b) and j) loss of the deceleration considered in the reference speed due to disturbance estimation, i) trajectory deviation is controllable by the driver.

[0121] The final test case is a spirited step steering maneuver that illustrates the ability of lateral torque vectoring to improve agility while maintaining stability, see Figure 8In the first phase, the chassis MPC assigns negative force to the inside front wheel and positive force to the outside wheel. The fast electric motors follow the requests quickly, and the yaw rate tracking is quite impressive. In the following phase, the inside front wheel force reaches saturation and thus also the yaw rate, so the chassis MPC reduces the requested force accordingly. At the same time, the chassis MPC allocates a small portion of the braking force to the right rear outside corner to ensure stability. The amount of speed reduction during cornering is very small due to the torque vectoring capabilities of the electric motors.

[0122] Figure 8 shows a simulation of a step steering maneuver with agility and stabilization, d) and e) torque vectoring on the front axle between left and right and on the right side between front and rear.

Claims

1. Method for controlling actuators acting on vehicle wheels of a motor vehicle (1), wherein the method comprises the following steps: - ascertaining a force (Fxd, Fyd, Mzd) to be brought about on a reference point of the motor vehicle on the basis of driver specifications (axd, δfd), - ascertaining wheel forces (Fxid, Fyid) to be brought about on the vehicle wheels to implement the force (Fxd, Fyd, Mzd) to be brought about on the reference point of the motor vehicle by means of a first dynamic allocation by model-based predictive control (MPC), - ascertaining setpoint values for wheel parameters (Tmjd, Tbjd) from the ascertained wheel forces (Fxid, Fyid), and - actuating the actuators of the motor vehicle so as to implement the setpoint values of the wheel parameters (Tmjd, Tbjd), characterized in that, in an intermediate step, kinematic setpoint motion variables (v, β, ω) are adapted by way of a virtually controlled single-track model (STM) and are taken into account in the dynamic allocation (MPC) of the wheel forces.

2. Method according to one of the preceding claims, characterized in that the driver specifications (axd, δfd) are made available by a virtual driver and / or an assistance system.

3. Method according to one of the preceding claims, characterized in that the driver specifications (axd, δfd) are an acceleration and / or at least one steering angle.

4. Method according to one of the preceding claims, characterized in that the setpoint values for the wheel parameters (Tmjd, Tbjd) are torques respectively acting on the wheels, slip values of the wheels, rotational speeds of the wheels and / or steering angles of the wheels.

5. Method according to one of the preceding claims, characterized in that, for implementing a setpoint value for a torque acting on a vehicle wheel, the method also has a second dynamic allocation (MPC), which includes slip control.

6. Method according to one of the preceding claims, characterized in that the actuators are electric motors and / or friction brakes.

7. Method according to one of the preceding claims, characterized in that the dynamic allocation (MPC) of the wheel forces (Fxid, Fyid) includes driving dynamics control.

8. Method according to one of the preceding claims, characterized in that wheel forces (Fxid, CA, Fyd,CA) are ascertained by means of a static allocation (CA) and these are fed to the dynamic allocation (MPC) as input values, wherein in particular an arbitration is carried out from the ascertained wheel forces of the static and dynamic allocation.

9. Method according to one of the preceding claims, characterized in that the dynamic allocation (MPC) comprises a saturation of an assigned actuator, a reconfiguration to ensure the error tolerance in the event of failure of the actuator, an increase in the energy efficiency and a minimization of wear.

10. Method according to one of the preceding claims, characterized in that the ascertained wheel forces (Fxid, Fyid) are converted by an inverse tyre-force model into setpoint variables for torques, wheel slips, rotational speeds and steering angles of the wheels.