Vehicle yaw rate

Abstract

Processing circuitry for a vehicle configured to: obtain for at least two wheels a slip ratio 202 and a slip angle 204. Obtain for each wheel, a wheel longitudinal force 206 and a wheel lateral force

Description

The present disclosure relates to determining a vehicle yaw rate and to using the determined vehicle yaw rate in the control of a vehicle. BACKGROUND In general, when a vehicle is being controlled determining the vehicle yaw rate may be used to determine part of the performance, or operation, or the vehicle, and alternatively or additionally may be used to control the vehicle. SUMMARY OF THE INVENTION Examples herein relate to determining a target yaw rate of a vehicle. The yaw rate of the vehicle may be the rate of change of the vehicle’s heading about the yaw axis, which may be synonymous with the rate of change of the heading of the vehicle. As such, the yaw rate can be an indication of whether the vehicle is being oversteered or understeered, and as such whether the vehicle is deviating from a desired path. The present disclosure relates to determining an accurate target yaw rate of a vehicle which can be used to control the operation of the vehicle (e.g. so that the vehicle avoids a condition of oversteer or understeer) and which alternatively or additionally may be used to determine whether the vehicle is being oversteered or understeered by comparing the target yaw rate to the vehicle’s actual, or current, yaw rate. According to this disclosure there is provided processing circuitry for a vehicle. The processing circuitry is configured to obtain, for at least two wheels of the vehicle, a slip ratio and a slip angle, the slip ratio having a non-linear relationship to the wheel rotational speed and the wheel centre point velocity, and the slip angle having a non-linear relationship to the wheel centre point velocity. The processing circuitry is configured to determine a target yaw rate of the vehicle based on the slip ratio and the slip angle. Optionally, the processing circuitry may be configured to obtain, for each wheel, a wheel longitudinal force and a wheel lateral force, the wheel longitudinal force having a linear dependence on the slip ratio, the wheel lateral force having a linear dependence on the slip angle. In this example the processing circuitry is configured to determine the target yaw rate of the vehicle based on the slip ratio, the slip angle, the wheel longitudinal force, and the wheel lateral force for each wheel. The processing circuitry may be configured to obtain a set of information pertaining to a trip of the vehicle, and to determine at least one vehicle parameter for the vehicle based on the target yaw rate. The at least one vehicle parameter may comprise a predicted yaw rate of the vehicle. The set of information pertaining to the trip of the vehicle may comprise at least one of: the curvature for an upcoming section of road and a future speed of the vehicle, and wherein the vehicle parameter comprises at least one of: a wheel torque and a steering wheel angle. The processing circuitry may be configured to obtain a yaw rate for the vehicle from an onboard system, such as an inertial measurement unit (“IMU”), determine a difference between the target yaw rate and the IMU yaw rate, and, if the difference exceeds a predetermined threshold, cause a fail-safe action to be triggered. The slip ratio, for a given wheel, may be based on the centre point velocity of the wheel in a first axis, the rotational speed of the wheel, and an effective wheel radius. The slip angle, for a given wheel, may be based on the centre point velocity of the wheel in the first axis and the centre point velocity of the wheel in a second axis, the second axis being perpendicular to the first axis. The processing circuitry may be configured to obtain a loading force for each wheel and to to determine the target yaw rate based on the loading force for each wheel. The processing circuitry may be configured to obtain a static loading force for each wheel, obtain a dynamic loading force for each wheel. The loading force, for each wheel, may be based on the static loading force and the dynamic loading force for the respective wheel. The static loading force, for a given wheel, may be based on the wheel base, the distance between the centre of gravity and the wheel, the distance between the centre of gravity to the road, the vehicle mass, and the road grade. The dynamic loading force, for a given wheel, may be based on at least one of the spring stiffness, the spring damping coefficient, the spring displacement change, the spring displacement speed, and the vehicle pitch angle. The processing circuitry may be configured to obtain, for each wheel, the static part of the wheel longitudinal force based on the slip ratio and the loading force and to obtain, for each wheel, the static part of the wheel lateral force based on the slip angle and the loading force. The target yaw rate may be based the static part of the wheel longitudinal force and the static part of the wheel lateral force. The processing circuitry may be configured to determine the target yaw rate based on a dynamic model of the force lag for each tire. The processing circuitry may be configured to obtain a first-order system of non-linear differential equations including a differential equation for the target yaw rate; and wherein the processing circuitry is configured to determine the target yaw rate by solving the system of non-linear differential equations for the target yaw rate. The processing circuitry may be configured to determine the target yaw rate by solving the following system of first-order non-linear differential equations for the target yaw rate, ip. where vy is vehicle body lateral velocity, m is the vehicle mass, Fiy ith wheel force in the y axis direction, F, = (Flx,Fiy), Fix is the ith wheel force in the x axis direction, vx is the vehicle body longitudinal velocity (input to the yaw rate calculator), lz is the vehicle body moment of inertia along the yaw axis, ly is the vehicle body moment of inertia along the pitch axis, rt is the ith wheel position vector with respect to the vehicle centre of gravity, and d is the vehicle body pitch rate. The processing circuitry may be configured to determine the target yaw rate by solving a system of first-order non-linear differential equations for the target yaw rate, the system of first-order non-linear differential equations being: e = e, where vy is vehicle body lateral velocity, m is the vehicle mass, Fiy ith wheel force in the y axis direction, Ft = {Flx,Fly), Flx is the ith wheel force in the x axis direction, vx is the vehicle body longitudinal velocity (input to the yaw rate calculator), Iz is the vehicle body moment of inertia along the yaw axis, Iy is the vehicle body moment of inertia along the pitch axis, rf is the ith wheel position vector with respect to the vehicle centre of gravity, and 0 is the vehicle body pitch rate; The processing circuitry may be configured to determine the target yaw rate by solving a system of first-order non-linear differential equations for the target yaw rate, ip. 1 pxf = (F^f - Fxf), T p F x 1 *y 1 p =___(pstat _ p A x,r v x,r 1 x,rb TF* 1 p —___(pstat _ p A r y,r t \yr ry,rJ> where vy is vehicle body lateral velocity, m is the vehicle mass, Fly ith wheel force in the y axis direction, F\ = (Flx,Fly), Flx is the wheel force in the x axis direction, vx is the vehicle body longitudinal velocity (input to the yaw rate calculator), Iz is the vehicle body moment of inertia along the yaw axis, rt is the ith wheel position vector with respect to the vehicle centre of gravity, tFx and xFy are longitudinal and lateral force lag time constants, Fxf and Fyj are the final forces acting on the vehicle body generated by the front wheels in the x and y axis direction (e.g. the longitudinal and lateral directions), e.g. the final longitudinal and lateral forces respectively, Fxr and Fyr are the final forces acting on the vehicle body generated by the rear wheels, F^f is the static part of the front wheel longitudinal force, F^ is the static part of the rear wheel longitudinal force, Fy f is the static part of the front wheel lateral force, and Fy™ is the static part of the rear wheel lateral force. It will be appreciated that the above ‘force equations’ are for two wheels, one front wheel and one rear wheel, the equations being for the longitudinal (e.g. x direction) and lateral (e.g. y direction) forces for the front and rear wheel. The processing circuitry may be configured to determine the target yaw rate by solving the following system of first-order non-linear differential equations for the target yaw rate, ip. e = e, i FX.f = — (fx.f* _ px,f)’ 1 F r =--(Fst^ - F ry,f T \ry,f ry,fJ’ Tpy 1 p =___(pstat p A 1 x,r v x>r 1 x>rj> ?x 1 r ____( nstat_ p A ry,r~ — V y,r ry,rJ> Fy where vy is vehicle body lateral velocity, m is the vehicle mass, Fiy ith wheel force in the y axis direction, Ft = (Fix,Fiy\ Fix is the wheel force in the x axis direction, vx is the vehicle body longitudinal velocity (input to the yaw rate calculator), l7 is the vehicle body moment of inertia along the yaw axis, Iy is the vehicle body moment of inertia along the pitch axis, r, is the ith wheel position vector with respect to the vehicle centre of gravity, 0 is the vehicle body pitch rate, tFx and xFy are longitudinal and lateral force lag time constants, F^ and Fy f are the final forces acting on the vehicle body generated by the front wheels, Fxri and Fy r are the final forces acting on the vehicle body generated by the rear wheels, F^ is the static part of the front wheel longitudinal force, F^ is the static part of the rear wheel longitudinal force, is the static part of the front wheel lateral force, and F^ is the static part of the rear wheel lateral force. The present disclosure provides a process and processing circuitry to implement the process to calculate a vehicle yaw rate target for nominal conditions. Herein “nominal conditions” may relate to conditions where the vehicle is not sliding. Hence, the “target” yaw rate as determined according to this disclosure may be a yaw rate as if the vehicle is not sliding and, if the actual yaw rate was approximately the target yaw rate, may indicate that the vehicle is not sliding. The vehicle not sliding may be considered synonymous with no oversteering and / or understeering occurring. Therefore, the processes herein determine a target yaw rate as if the vehicle is not sliding, meaning that no oversteering and / or understeering is occurring. Nominal conditions may comprise at least one of the following: a dry road (e.g. tarmac) surface, a current vehicle weight (e.g. a real-time mass estimate), a nominal vehicle weight, a nominal vehicle moment of inertia, a nominal tire cornering stiffness coefficient, and a nominal tire longitudinal stiffness coefficient. The target yaw rate may be used in a vehicle electronic control unit (“ECU”). Put another way, the processing circuitry described herein may be implemented in a controller (e.g. for a vehicle), for example an ECU. The present disclosure allows a yaw rate to be determined accurately, assuming that the vehicle is not sliding, which, in turn, allows vehicle controllers that use the target yaw rate to both determine whether the vehicle is sliding, to monitor the current or future performance of the vehicle, and to more accurately mitigate the vehicle being driven in a potentially dangerous way. BRIEF DESCRIPTION OF THE DRAWINGS Examples of the present disclosure will be described in detail with reference to the accompanying drawings, which should not be considered limiting, in which: Figure 1 shows a schematic diagram of a vehicle operating according to a desired path, oversteer, and understeer, and an associated graph of yaw rate gain; Figures 2-5 show flowcharts of example processes; and Figure 6 shows a schematic diagram to illustrate the process of Figure 5. DETAILED DESCRIPTION These drawings should not be considered limiting, rather they are used for explaining and understanding the present disclosure. Some of the figures relate to flowcharts / processes; it should be understood that the steps may be performed in any order, the order in which they are described being purely exemplary and illustrative. Figure 1 shows a schematic diagram of a vehicle being “saturated” (e.g. oversteered or understeered” compared to the vehicle following a desired path (synonymous with a “neutral steer” of the vehicle). The right-hand side shows the relationship between the vehicle lateral acceleration and steering wheel angle 3 for a constant yaw rate. For a vehicle travelling on a constant radius curve, as the vehicle speed increases the circumferential (lateral) acceleration increases. Therefore, to keep the vehicle on track (with the constant yaw rate) either the steering wheel angle is increased (for understeering vehicle) or decrease (for oversteering vehicle). For small speeds, a vehicle operating in the linear region is controllable (although it may be exhibiting a modest amount of controllable slide), however after a certain point the vehicle reaches a “saturation” state corresponding to uncontrollable sliding of the vehicle, either in an understeering manner or in an oversteering manner. As the vehicle yaw rate is proportional to the steering wheel angle, it will be appreciated that determining the vehicle yaw rate accurately can, in turn, lead to an accurate determination of whether the vehicle is oversteering or understeering and can further allow for more accurate control of the vehicle. In some examples oversteering or understeering can be synonymous with the vehicle uncontrollably sliding and therefore in some examples determining an accurate target yaw rate can lead to a reliable determination as to whether the vehicle is sliding. Figure 2 shows a flowchart of a process 200 for determining a target yaw rate of a vehicle. At block 202, the process comprises obtaining a slip ratio and at block 204 the process comprises obtaining a slip angle. As will be described below, the slip ratio has a non-linear relationship to the wheel rotational speed and the wheel centre point velocity and the slip angle has a non-linear relationship to the wheel centre point velocity. According to the disclosure, the slip ratio and the slip angle are obtained for at least two wheels of the vehicle (e.g. a front wheel and a rear wheel. In one example the slip ratio and the slip angle are obtained for all four wheels of the vehicle (two front and two rear). At block 206 the process comprises obtaining a wheel longitudinal force and at block 208 the process comprises obtaining a wheel lateral force. As above, these may be obtained for each wheel for which the slip ratio and slip angle were obtained. The wheel longitudinal force has a linear dependence on the slip ratio and the wheel lateral force has a linear dependence on the slip angle. As will be described below, this may be considered a constraint, or condition, to ensure that the determined target yaw rate is a nominal target yaw rate (meaning one for which there is no oversteer or understeer). At block 210 the process comprises determining a target yaw rate of the vehicle based on the slip ratio, the slip angle, the wheel longitudinal force, and the wheel lateral force for each wheel. With reference to blocks 202 and 204, the slip ratio and the slip angle (which together may be referred to as the “slip variables”) may be used to parameterise the tire forces generated by a tire-to-road interface. The slip ratio, A is a longitudinal slip ratio and may be referred to as such, being a difference (e.g. a normalized difference) between the vehicle’s longitudinal speed and the wheel longitudinal speed. As stated above, the slip variables are defined for single wheel, e.g. for each wheel. In other words, each wheel has its own slip ratio A and slip angle a. According to the disclosure, the slip variables may be obtained for at least two wheels and the target yaw rate may therefore be calculated based on a plurality of slip variables; those obtained for the at least two wheels. Herein, when “at least two wheels” are referred to with reference to the processes described here it should be understood that any vehicle front wheel and rear wheel may be used in the processes disclosed herein (e.g. frontright and rear-right, front-left and rear-left, front-right and rear-left, front-left and rear-right and that at least two wheels may comprise four wheels of the vehicle (e.g. two front, two rear) or all wheels of the vehicle (some vehicles may comprise more than four wheels). Indeed, the vehicle may compare any number of wheels depending on the type of vehicle and “vehicle” as used herein should be understood to comprise any suitable vehicle including but not limited to cars, truck cabs, vans etc.) The slip variables may be defined in a wheel coordinate system, which may be a fixed coordinate system. In an example fixed wheel coordinate system, x may denote a first direction in which the wheel is pointing, and y may denote a second direction that is perpendicular to the wheel disc plane. Let v denote the velocity of the wheel center point, being defined as the velocity of the point where the wheel is mounted to the chassis. This is different from the wheel circumferential velocity (in particular, the two may be different when the vehicle is sliding). In one example, the slip ratio is defined, or determined, as follows: o)r - vx max(|vx|, (or)’ where vx is the x-ordinate vale of the wheel center point velocity vector (e.g. the wheel center point velocity in the x direction), a) is wheel rotational speed along the y axis, i.e., the wheel rpm, and r is the wheel radius. However, the slip ratio may be defined according to another nonlinear relationship. In one example, the slip angle is defined, or determined, as a = —arctan—, where vy is the wheel center point velocity in the y direction. However, the slip angle may be defined according to another nonlinear relationship. In this example, it will therefore be appreciated that the slip ratio has a non-linear relationship to the wheel rotational speed and the wheel centre point velocity, and further that the slip angle has a non-linear relationship to the wheel centre point velocity. This leads to a more accurate determination of a target yaw rate than in examples where the slip variables are linearized, e.g. in approaches that calculate the solution of a linearized single-track model assuming small angles (e.g. small slip angles, steering wheel angles). In other words, such models may use a steady state value of yaw rate for a given steering wheel input and vehicle velocity using a linearized single-track model (where the nonlinear relationship for A and slip angle a are linearized). By using the nonlinear relationship, the determined target yaw rate is more accurate, hence the present disclosure provides a more accurate target yaw rate. As stated above, the determined target yaw rate is based on a wheel longitudinal force and a wheel lateral force which are linearly dependent on the slip ratio and the slip angle, respectively, in other words (for each wheel): Fx = cU, Fy = c2a, where Fx is the wheel longitudinal force (e.g. the component of the wheel force in the longitudinal, or x, direction), Fy is the wheel lateral force (e.g. the component of the wheel force in the lateral, or y, direction), and c1, and c2 are constants. The constant c1 may be the longitudinal stiffness. Alternatively or additionally the constant c2 may be the cornering stiffness. As above, this linearized relationship may be referred to as a “tire-to-road interface” because it describes the forces generated by thewheel (or tire, for the purposes of this disclosure the two should be considered synonymous) in the x and y directions (as defined above) which should be considered synonymous with the vehicle longitudinal and lateral directions. This linear dependence of the wheel longitudinal and lateral forces on A and a means that it is assumed that the tire(s) is / are not uncontrollably sliding or uncontrollably deforming, meaning that the above equations are effectively constraints imposing that the wheel(s) and therefore the vehicle is / are not uncontrollably sliding, meaning that the vehicle is not understeering or oversteering (it will be appreciated that some deformation and sliding behavior is inherent in the vehicle tires when being operated “normally” and at which point the deformation / slide is controllable, but that deformation and sliding may become uncontrollable if the wheel and tires reach a “saturation point” as shown in Figure 1 at which point the vehicle may be oversteering or understeering). As the target yaw rate is determined based on these constraints (e.g. the above described linear relationship) this imposes the constraint that the target yaw rate is determined as if the wheel(s) and therefore the vehicle is / are not uncontrollably sliding and hence as if there is no understeer or oversteer. It will be apparent that this means that when an actual (or current) yaw rate is determined for the vehicle and compared to the target yaw rate, an actual yaw rate that is greater than (or less than) the target yaw rate by an amount that is greater than (or less than) a respective predetermined threshold can be a reliable indication that the vehicle is understeering or oversteering. Figure 3 shows a flowchart of a process 300 for controlling a vehicle. The process may be considered a predictive control process for the vehicle. The process may be implemented by a controller for a vehicle. At block 302 the process comprises obtaining a set of information pertaining to a trip of the vehicle. At block 304 the process comprises determining the target yaw rate for the vehicle, e.g. according to any of the processes described herein. At block 306 the process comprises determining at least one vehicle parameter for the vehicle based on the target yaw rate. In one example, the at least one vehicle parameter comprises a predicted yaw rate of the vehicle. In another example, the set of information pertaining to the trip of the vehicle comprises at least one of: the curvature for an upcoming section of road and a future speed of the vehicle. The vehicle parameter may comprise at least one of: a wheel torque and a steering wheel angle. The set of information pertaining to the trip of the vehicle may alternatively or additionally comprise information relating to a state of the vehicle (e.g. at least one of the vehicle speed, the steering wheel angle, and the wheel speeds (any wheel speed)). Alternatively or additionally, the set of information pertaining to the trip of the vehicle may comprises at least one of a speed limit of the vehicle (e.g. a velocity limit). Together, road curvature information and speed limit information may be referred to as “road preview information.” Any of the previous information may be determined and / or calculated and / or estimated. Therefore, in some examples the information pertaining to the trip of the vehicle may comprise vehicle state information (e.g. at least one of vehicle speed, steering wheel angle, wheel speeds) and / or road preview information (at least one of road curvature and velocity limit information). The information pertaining to a trip of the vehicle may comprise upcoming information (e.g. at a future, or later, time) or current information (e.g. at a current time). Such future / preview information may allow the yaw rate of the vehicle to be predicted. For example, the information obtained at block 302 may be used in the equations discussed above with respect to Figure 2 to determine the target yaw rate (e.g. an upcoming vehicle speed limit or current vehicle speed may be used to determine the wheel center-point velocities, the road curvature information may be used to determine the steering wheel angle etc.). The determined target yaw rate according to this example may therefore be considered a future, or predicted, or preview target yaw rate. Put another way, the process 300 may obtain vehicle trip information and then determine a target yaw rate for the vehicle performing the trip. In other words, information is obtained based on the journey the vehicle is expected to perform and so the target yaw rate for the vehicle can be predicted. The vehicle can then be controlled to take this predicted yaw rate into account. For example, block 306 comprises determine at least one vehicle control parameter based on the target yaw rate. The vehicle parameter may comprise at least one of: a wheel torque and a steering wheel angle. In some examples, the vehicle control parameter may be a parameter relating to the control of the vehicle (e.g. a predicted value of the wheel torque or steering wheel angle for example) to enable a determination as to how the vehicle is predicted to be controlled, but in some examples the vehicle control parameter may be a parameter according to which the vehicle is to be controlled (e.g. a wheel torque or steering wheel angle that the vehicle is to achieve). The vehicle control parameter may be a parameter that prevents oversteer or understeer (e.g. in examples where the target yaw rate determined at 304 indicated that the vehicle would oversteer or understeer based on the vehicle trip information). As such, the process may comprise determining whether the vehicle will understeer or oversteer and determining a parameter according to which the vehicle is to be controlled such that the vehicle does not understeer or oversteer. The process 300 may therefore be referred to as a process for predictive control. A software application implementing the process may therefore be referred to as a predictive control model. The process effectively predicts how the vehicle shall behave in the future with regard to the vehicle’s yaw rate state. The process may therefore be a process of determine whether the vehicle is going to be oversteering and / or understeering at a future time. The process 300 may be implemented by a model predictive control (“MPC”) application that is configured to control a vehicle’s lateral dynamics. Such a model may use, as input, any of the information described above in relation to block 302 in addition to the determined target yaw rate according to the present disclosure. This yaw rate is effective a reference yaw rate, or what the vehicle yaw rate is predicted to be at a future time. The process 300 is therefore able to track the performance of a vehicle. Where road preview information is used (e.g. road curvature information) as this may be obtained from a navigation system (e.g. onboard the vehicle or an exterior navigation system). To determine the vehicle control parameter the process may comprise determine a predicted steering wheel angle based on the road curvature information (and therefore the target yaw rate discussed above). Similarly, a predicted vehicle velocity, e.g. the speed limit obtained from road speed information may be used to determine the wheel center point velocities in the calculation of the target yaw rate as discussed above. The speed may be a current speed, a legislative speed (e.g. the speed limit, e.g. obtained from a navigation system), an average traffic speed (e.g. obtained from navigation system) but any speed may be used, which may then be used to determine the wheel centre point velocities. Given that the process 300 determines a target yaw rate at a future time it may receive certain inputs based on which the target yaw rate is calculated. For instance, the process 300 may comprise obtaining at least one of the pitch angle, pitch rate, lateral velocity, and / or lateral acceleration (any one or more of these may be referred to as the “preview information” as discussed above). These inputs may be obtained across a time interval ending at a future time, meaning that these signals may be obtained for a future time window (which may be referred to as a “prediction horizon”). These inputs may be input to a controller (e.g. executing the process) to allow the controller (for controlling a vehicle) to achieve better vehicle control and to be reactive to future events in advance. It refers to the model predictive control algorithm. When the prediction horizon is used, the process may determine a future (for the horizon length) and then update the current inputs to the system, and determine a future state of the vehicle based on these updated inputs. Therefore, the process is able to use at least one “preview information input” such as the vehicle steering wheel angle and vehicle speed to determine a target yaw rate for future time. This determined target yaw rate may then be used by another controller as a preview information parameter and the controller can compute future control actions utilizing the determined target yaw rate. One example of such a controller may be a torque vectoring controller. In this example the target yaw rate may be used to determine the torques for the inner and outer wheels. Another example may be an autonomous driving system, in which the determined target yaw rate may be used to determine the vehicle speed and steering angle. The predictive controller implementing a process such as 300 may, in summary, view the determined target yaw rate as a preview information and it can take it into account when determining a vehicle control parameter. It will then be appreciated that by using such preview information a subsequently computed vehicle control action may be more accurate. Of course, the preview information inputs are not limited to the target yaw rate, and may use at least one of the determined target yaw rate, vehicle lateral acceleration, slip ratios, slip angles etc. for vehicle control such as to limit the slip angle to within a predetermined threshold of a certain value to prevent the oversteering, or to limit the acceleration to within a predetermined threshold to prevent excessive lateral force acting on the passengers. To be able to determine the target yaw rate according to the present disclosure, the process 300 may comprise obtaining at least one of: vehicle speed, steering wheel angle, and wheel speeds. As stated above, the process may comprise obtaining the road grade (or a measure of the road grade). As stated above, in one example the process comprises obtaining the curvature of the road (e.g. from a navigation system or retrieved from a memory) at a first time and deriving the steering wheel angle from the curvature of the road at the first time. In this example the curvature of the road may be determined again at a second, later, time and the steering wheel angle may be determined again corresponding to the later time. This enables a predicted steering wheel angle to be determined across multiple time instances. To determine the steering wheel angle the process may comprise determining how the vehicle’s wheels need to be steered to follow the road curvature (which is obtained as part of the process). Based on the determined wheel angle the steering wheel angle may then be determined (e.g. from a steering system model). The process may comprise obtaining a predicted velocity. This may be obtained from a navigation system (e.g. using a maximal speed limit or average speed) or may be obtained from a prediction model. The velocity may also be assumed to be constant in some examples. The process may comprise obtaining the wheel speeds (e.g. the speed of at least one wheel of the vehicle). The or each wheel speed may be retrieved from a vehicle speed profile (which may be calculated based on the wheel radius). Figure 4 shows a flowchart of a process 400 for determining the operation of a vehicle. The process may be considered a monitoring process, or a control process, for the vehicle. At block 402 the process comprises determining the target yaw rate for the vehicle, e.g. according to any of the processes described herein. At block 404 the process comprises obtaining a current yaw rate for the vehicle. For example, the current yaw rate may be obtained from a system onboard the vehicle such as an inertial measurement system (“IMU”) but the current yaw rate may be obtained by any other methods or from other sources. At block 406 the process comprises determining a difference between the target yaw rate and the IMU yaw rate and at block 408 the process comprises determine whether the difference is greater than or less than a predetermined threshold amount, which may comprise determining whether the IMU yaw rate is greater than (or less than) the determined target yaw rate. Hence, block 408 may comprise determine whether the vehicle is oversteering or understeering. If the difference exceeds the predetermined threshold then the process proceeds to block 410 at which the process comprises causing a fail-safe action to be triggered. This is a closed-loop process in that the vehicle parameters to determine a therefore comprise determining whether the vehicle yaw rate is in a nominal, or safe range and / or determining whether the target yaw rate and IMU yaw rate difference is within a predetermined threshold (e.g. below a predetermined maximum value, which may correspond to a “safe” maximum value), e.g. there is no oversteering or understeering occurring (e.g. as if the vehicle is driving on a dry tarmac, the IMU yaw rate may be continually determined and / or the target yaw rate may be continually determined, e.g. at predetermined time intervals, to monitor the vehicle performance. The process 400 therefore monitors the expected behaviour of the vehicle in that it is determined how the vehicle is behaving (e.g. actually or currently behaving) by means of the IMU yaw rate and in parallel the target yaw rate is determined (representing the vehicle being operated in normal, or nominal, or dry etc. conditions). If the closed loop system behaves differently, e.g., if the vehicle is over / understeering, then the determined target yaw rate value and the IMU yaw rate value will be different, and if this difference is big enough (greater than the predetermined threshold) a detection flag is risen meaning that it is determined that the vehicle is not being operated in an expected and / or safe manner. This detection can be used to trigger any fail-safe action (block 410). The fail-safe action may comprise causing the vehicle to transition to a safe state. One example fail-safe may comprise causing a light internal to the vehicle to be switched on (e.g. causing the indicator to turn on) to inform driver that vehicle behavior is different than nominal one and / or that the vehicle is in a potentially dangerous situation. Alternatively, or additionally, the fail-safe action may comprise causing braking and / or accelerating to be prevented. This may comprise causing the vehicle to be operated such that a risk is avoided (e.g. such that oversteer or understeer is prevented, or such that the vehicle follows a determined, or desired, or nominal path). The predetermined thresholds may be adjustable. The process 400 may be implemented as part of a monitoring and detection algorithm for the vehicle which, as above, may be a closed loop system. Such an algorithm may comprise a vehicle lateral dynamics controller. The lateral dynamics controller may cause the vehicle to be operated as part of the fail-safe action (e.g. block 410) to cause the vehicle to be operated such that there is no oversteer / understeer / slip and / or to prevent oversteer / understeer / slip. In this way the process 400 and therefore a controller implementing the process, can prevent oversteering and / or understeering of the vehicle. A lateral dynamics controller may comprise an electronic stability program (ESP) or an electronic stability control (ESC) system and hence the process 400 may be implemented by an ESP or ESC system of the vehicle. In the Figure 4 process, as different from the process 300 of Figure 3, a “real-time” yaw rate is obtained (e.g. from a vehicle system such as an IMU) and compared to a target yaw rate whereas in the Figure 3 process a future, or predicted, yaw rate is determined to determine whether the vehicle is at risk of being oversteered or understeered at a future time or to determine a reference value for the yaw rate that can be used by a vehicle controller. As such, the processes 300 and 400 may be used together. For example they may be performed concurrently or in sequence. With reference to Figure 2, examples of how the target yaw rate may be determined will now be described with reference to Figure 5. Figure 5 shows a flowchart of a process 500 for determining a target yaw rate of a vehicle. The process 500 may comprise the process 200 as described above with respect to Figure 2 and, as such, blocks 502-510 should be considered analogous to blocks 202-210 as described above and as such their description shall not be repeated here for brevity. The additional parts of the process of Figure 5 (those not in Figure 2) should be regarded as optional depending on the implementation. As indicated by 501 and 503, respectively, the process 500 may comprise obtaining the inputs in which case blocks 502 and 504 may comprise determining (or calculating) the slip ratio and slip angle, respectively, based on the obtained inputs. Accordingly, block 501 may comprise obtaining at least one of: the wheel center point velocity vx, the wheel rotational speed along the y axis and the wheel radius r, and block 502 may comprise determining the slip ratio according to the equation above with respect to Figure 2. Similarly, block 503 may comprise obtaining at least one of: the wheel center point velocities vx and vy and block 504 may comprise determining the slip angle according to the equation above with respect to Figure 2. With reference to blocks 506 and 508, in some examples the wheel longitudinal force is a static wheel longitudinal force and the wheel lateral force is a static lateral force. In these examples, blocks 505 and 507 may comprise obtaining the static wheel longitudinal force and the static wheel lateral force, respectively In these examples, the tire-to-road interface model may be defined as Fxtat = clA, Fy‘" = c2a. where Fsxtat is the static part of the wheel longitudinal force and Fytat is the static part of the wheel lateral force. cA is the longitudinal stiffness and ca is the cornering stiffness. Alternatively or additionally, the tire-to-road interface model may comprise obtaining a loading force, at block 509, and the tire-to-road interface may be based on the loading force. Specifically, the static parts of the wheel longitudinal and lateral forces may be based on the loading force. In these examples, the tire-to-road interface model may be defined as: pstat _ 17 7^0 — &ZC^A, pstat _ p * y 1 z^a^- Here, the constants c^, are the normalized longitudinal and normalized cornering stiffnesses but in some examples they may be other constants. Note that in each of the above examples, the dependence of the longitudinal and lateral forces remains linear (e.g. on the slip ratio and slip angle respectively). In examples using the loading force, the loading force may be based on a static loading force and / or a dynamic loading force. Accordingly, the process may comprise at blocks 511 and 513, respectively, obtaining a static loading force and a dynamic loading force. In these examples, the process may comprise determining the loading force based on the static and / or dynamic loading forces. This may be known as a “suspension model” and hence taking the static and / or dynamic loading forces into account may be referred to as determining the target yaw rate based on a suspension model. According to such suspension model the loading force for a particular wheel may be obtained and then subsequently used to determine the longitudinal and lateral forces generated by the tire (as described above). The static loading force, for a given wheel, may be based on the wheel base, the distance between the centre of gravity and the wheel, the distance between the centre of gravity to the road, the vehicle mass, and the road grade. In one example, the static loading force for a front wheel and for a rear wheel may be defined, or determined, as follows: 1 1 -mgr, ~mgh pstat _ Z-----cos 0 _ --stn 0 ZJ I I 1 1 pstat _ Z --cos 0 + Z— s^n 0 zr I I where F^f1 is the static loading force for the front wheel, F^ is the static loading force for the rear wheel, g is the gravitation constant, I is the wheel base, rf is the distance from the front wheel to the vehicle center of gravity (“CoG”), rr is the distance from the rear wheel to the vehicle center of gravity CoG, h is the distance from the vehicle CoG to the wheel center point, m is the vehicle mass, and 0 is a measure of the road grade. In one example, block 515 may comprise obtaining at least one of the inputs: g, I, rt, h, m, and 0 and block 511 comprises determining the static loading force based on these inputs, e.g. according to the above relationship. The static loading force may therefore be calculated based on the road grade. The dynamic loading force, for a given wheel, may be based on the spring stiffness, the spring displacement change, the suspension damping coefficient, the spring displacement speed, and the vehicle pitch angle. In one example, the dynamic loading force may be defined, or determined, as follows: Fzyn = KsAlz + DsAlz where Ks is the spring stiffness (the stiffness of the wheel suspension spring), Alz is the spring displacement change, Ds is the suspension damping coefficient, Alz is the spring displacement speed, 0 is the vehicle pitch angle, Alz = rtsinO, and Alz = ert. In one example, block 517 may comprise obtaining the inputs Ks, Alz, Ds, Alz, and 9 and block 513 comprises determining the dynamic loading force based on these inputs, e.g. according to the above relationship. In one example, blocks 511 and 513 comprise obtaining the respective static and dynamic loading forces according to the relationships above following which block 509 comprises determining the loading force (for a given wheel). In one example, the loading force for a given wheel is defined, or determined, as follows: Fz = Fzyn + Fztat where Fz is the loading force. The forces described above may be defined in a wheel coordinate system. They may be transformed to a vehicle body coordinate system (e.g. before being used in the above equations). Thus, in some examples, the loading force may be used (and may be defined as above) in the tire-to-road interface constraint as described above. As indicated by block 519, some examples comprise obtaining a force lag model, the target yaw rate being determined based on the force lag model. The force lag model may be any suitable model but in one example the force lag model comprises the following set of dynamic equations: 1 Fx=~(Fsxtat-Fx), tfx 1 Fy=—(Fsytat-Fyy t p where tFx and xFy are longitudinal and lateral force lag time constants, and Fx and Fy are the (longitudinal and lateral, respectively) final forces acting on the vehicle body generated by the wheels (tires generated forces). These “final forces” may be generated by the tires and acting on the tires themselves. They may be described with respect to an arbitrary coordinate system. These forces may be the forces acting on the vehicle body induced by the tire-to-road interface, e.g. the interface between the tire and the road, the forces being generated by the tire which are generated in response to braking or steering etc. to move the vehicle. In these examples the process may comprise at block 521 obtaining the final forces acting on the body based on the wheels and block 519 may comprise determining the force lag model based on these obtained final forces. In these examples, determining the target yaw rate, at block 510, comprises solving the equations that define the force lag model, e.g. above. As indicated by block 523 in some examples determining the target yaw rate comprises obtaining a set of first-order differential equations and the method may comprise, at block 525, solving the set of differential equations. One example set of differential equations according to the present disclosure is as follows (e.g the force lag model equations above). These examples may be based on a vehicle rigid body model having four states - vehicle lateral velocity, yaw rate, pitch rate and pitch. In one example, the following system equations may be solved to obtain the target yaw rate: where is the target yaw rate, vy is the vehicle body lateral velocity, m is the vehicle mass, Fly is the ith wheel force in the y axis (lateral) direction, Ft = (Fix,Fiy), Fix is the ith wheel force in the x axis (longitudinal) direction, vx is the vehicle body longitudinal velocity (input to the yaw rate calculator), Iz is the vehicle body moment of inertia along the yaw axis, and r, is the ith wheel position vector with respect to the vehicle centre of gravity However, in some examples, to increase the accuracy of the determined yaw rate, the set of equations may include a model of the vehicle suspension. In these examples, the following system (of four) equations may be solved to obtain the target yaw rate: where ip is the target yaw rate, vy is the vehicle body lateral velocity, m is the vehicle mass, Fiv is the ith wheel force in the y axis (lateral) direction, F, = (Fix,FlvY Fix is the ith wheel force in the x axis (longitudinal) direction, vx is the vehicle body longitudinal velocity (input to the yaw rate calculator), Iz is the vehicle body moment of inertia along the yaw axis, Iy is the vehicle body moment of inertia along the pitch axis, rf is the ith wheel position vector with respect to the vehicle centre of gravity, and d is the vehicle body pitch rate. Hence, in some examples, the above top two (or four) set of equations may be solved for ip. Alternatively, or additionally, the force lag model may be used for higher fidelity. In these examples, the following system of equations may be solved to obtain the target yaw rate: 1 I F F x 1 F r =--(FSt^ ~F r) ry.f r y,f ry,f)’ Tpy 1 p ____( rjstat _ p A 1 x,r _ x,r 1 x,r)> If r X 1 p =___(pstat p A 1 y>r \ y>r 1 y>rj> Tpy where vy is vehicle body lateral velocity, m is the vehicle mass, Fly ith wheel force in the y axis direction, Ft = (Flx,Fiy), Flx is the wheel force in the x axis direction, vx is the vehicle body longitudinal velocity (input to the yaw rate calculator), Iz is the vehicle body moment of inertia along the yaw axis, rt is the ith wheel position vector with respect to the vehicle centre of gravity, tFx and xFy are longitudinal and lateral force lag time constants, Fxf and Fy f are the final forces acting on the vehicle body generated by the front wheels, Fxr> and Fy r are the final forces acting on the vehicle body generated by the rear wheels, F8*^ is the static part of the front wheel longitudinal force, F^1 is the static part of the rear wheel longitudinal force, Fyf is the static part of the front wheel lateral force, and Fy"1 is the static part of the rear wheel lateral force. It will be appreciated that the x-direction forces are longitudinal forces and the y-direction forces are lateral forces. It will be further appreciated that the above force lag model describes two wheels, one front and one rear, but that more wheels may be taken into account in some implementations. In yet other examples, for increased accuracy and higher fidelity, the following system of differential equations may be solved for the target yaw rate, ip (the system in this example comprising a suspension model and a force lag model): 0 = 0, 1 Fx,f = — - Fx,f)> 1 fy.r=^yT~l,yA I F 1 F =___(pstat _ p A X,r v X,r ‘ X,rJ> 1 p ____(pstat _ p \ r yr - v yr ryrJ’ ^Fy where vy is the vehicle body lateral velocity, m is the vehicle mass, Fiy is the ith wheel force in the y axis direction, F, = (Fix,Fiy), Fix is the ith wheel force in the x axis direction, vx is the vehicle body longitudinal velocity (input to the yaw rate calculator), Iz is the vehicle body moment of inertia along the yaw axis, Iy is the vehicle body moment of inertia along the pitch axis, rt is the ith wheel position vector with respect to the vehicle centre of gravity, 0 is the vehicle body pitch rate, tFx and tFy are longitudinal and lateral force lag time constants, Fxf and Fy f are the final forces acting on the vehicle body generated by the front wheels (for example expressed in a wheel coordinate system) Fxr and Fyr are the final forces acting on the vehicle body generated by the rear wheels, F^ is the static part of the front wheel longitudinal force, F^ is the static part of the rear wheel longitudinal force, Fy^ is the static part of the front wheel lateral force, and Fy^ is the static part of the rear wheel lateral force. In these examples, any suitable technique or method may be used to solve the equations for the target yaw rate. For example, a time discretisation model may be used to solve the differential equations. For example, a Runge-Kutta 4th order discretisation method, a Heun (trapezoidal) method, or an Euler method may be used to solve the differential equations. However, any suitable method may be used. Figure 6 shows a schematic flowchart illustrating the process 500 as described above, indicating the various inputs to the process. It will be appreciated that the processes for determining the target yaw rate as described herein are based on non-linear lateral dynamics single-track model (and in some examples with a suspension dynamic model and / or a force lag model etc. as discussed above). As shown in Figure 6, at least one of the following may be inputs to the process: vehicle longitudinal velocity v*, steering wheel angle S, wheel speed for both front and rear wheels, vehicle mass m and road grade y. The following vehicle states are described (which may be computed using the ordinary differential equations mentioned above, e.g. the states may be the solutions of the equations): vehicle lateral velocity Vy, vehicle yaw rate ip, vehicle pitch rate 0, vehicle pitch angle 0, front wheel longitudinal force Ffx, front wheel lateral force F^y, rear wheel longitudinal force Ffx, and rear wheel lateral force Ff y. “Obtaining” data as used herein may comprise receiving data (e.g. from a sensor), measuring data (e.g. by a sensor), determining or calculating or estimating data (e.g. from data received from a sensor), or retrieving data (e.g. from a memory storing data), depending on the example. The processing circuitry may be implemented according to any suitable hardware and / or software combination sufficient to cause the processes described herein to be executed. For instance the processing circuitry may be implemented on, or on any suitable combination of, a digital signal processor, field programmable gate array, and / or application specific integrated circuit (ASIC). The processing circuitry may be configured to execute instructions, such as processor control code, that, cause a controller to operate according to the processes described herein. Such instructions may be stored on a non-transitory machine-readable medium. Such instructions may be stored in a memory. Such instructions may be stored on any suitable memory medium, e.g. on a volatile or non-volatile medium, programmed memory (e.g. read-only memory such as firmware), or a data carrier. The processing circuitry may comprise such a memory storing the instructions. In other words, a non-transitory machine-readable medium may store instructions that, when executed by processing circuitry, cause the processes herein to be performed. The instructions may comprise code or microcode. The instructions, when executed, may be in any suitable 5 programming language to allow the controller to be dynamically configured and / or reconfigured. The controller and / or processing circuitry may equally comprise, and may be considered synonymous with, and may therefore be referred to as, a processor, microcontroller or microprocessor or electronic control unit or electronic stability program (ESP) or an electronic stability control (ESC) system. 10 The person skilled in the art realizes that the present disclosure by no means is limited to what is explicitly described above. On the contrary, many modifications and variations are possible within the scope of the appended claims. Additionally, variations can be understood and effected by the skilled person in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. 15

Claims

1. Processing circuitry for a vehicle, the processing circuitry configured to: obtain, for at least two wheels of the vehicle, a slip ratio and a slip angle, the slip ratio having a non-linear relationship to the wheel rotational speed and the wheel centre point velocity, and the slip angle having a non-linear relationship to the wheel centre point velocity;obtain, for each wheel, a wheel longitudinal force and a wheel lateral force, the wheel longitudinal force having a linear dependence on the slip ratio, the wheel lateral force having a linear dependence on the slip angle; and todetermine a target yaw rate of the vehicle based on the slip ratio, the slip angle, the wheel longitudinal force, and the wheel lateral force for each wheel.

2. Processing circuitry of claim 1, wherein the processing circuitry is configured to: obtain a set of information pertaining to a trip of the vehicle; and todetermine at least one vehicle parameter for the vehicle based on the target yaw rate.

3. Processing circuitry of claim 2, wherein the at least one vehicle parameter comprises a predicted yaw rate of the vehicle.

4. Processing circuitry of claim 2 or 3, wherein the set of information pertaining to the trip of the vehicle comprises at least one of: the curvature for an upcoming section of road and a future speed of the vehicle, and wherein the vehicle parameter comprises at least one of: a wheel torque and a steering wheel angle.

5. Processing circuitry of any preceding claim, wherein the processing circuitry is configured to:obtain a yaw rate from a system onboard the vehicle;determine a difference between the target yaw rate and the yaw rate obtained from the system onboard the vehicle; and, if the difference exceeds a predetermined threshold, cause a fail-safe action to be triggered.

6. Processing circuitry of any preceding claim, wherein the slip ratio, for a given wheel, is based on the centre point velocity of the wheel in a first axis, the rotational speed of the wheel, and an effective wheel radius; andwherein the slip angle, for a given wheel, is based on the centre point velocity of the wheel in the first axis and the centre point velocity of the wheel in a second axis, the second axis being perpendicular to the first axis.

7. Processing circuitry of any preceding claim, wherein the processing circuitry is configured to:obtain a loading force for each wheel, the processing circuitry being configured to determine the target yaw rate based on the loading force for each wheel.

8. Processing circuitry of claim 7, wherein the processing circuitry is configured to:obtain a static loading force for each wheel; andobtain a dynamic loading force for each wheel, wherein the loading force, for each wheel, is based on the static loading force and the dynamic loading force for the respective wheel.

9. Processing circuitry of claim 8, wherein the processing circuitry is configured to obtain, for each wheel, the static part of the wheel longitudinal force based on the slip ratio and the loading force; andobtain, for each wheel, the static part of the wheel lateral force based on the slip angle and the loading force;wherein the processing circuitry is configured to determine the target yaw rate based the static part of the wheel longitudinal force and the static part of the wheel lateral force.

10. Processing circuitry of claim 9, wherein the processing circuitry is configured to determine the target yaw rate based on a dynamic model of the force lag for each tire.

11. Processing circuitry of any previous claim, wherein the processing circuitry is configured to:obtain a first-order system of non-linear differential equations including a differential equation for the target yaw rate; and wherein the processing circuitry is configured to determine the target yaw rate by solving the system of non-linear differential equations for the target yaw rate.

12. Processing circuitry of claim 11, wherein the processing circuitry is configured to determine the target yaw rate by solving the following system of first-order non-linear differential equations for the target yaw rate, ip:where vy is vehicle body lateral velocity, m is the vehicle mass, Fly ith wheel force in the y axis direction, Ft = iFix,Fiy\ Fix is the ith wheel force in the x axis direction, vx is the vehicle body longitudinal velocity (input to the yaw rate calculator), Iz is the vehicle bodymoment of inertia along the yaw axis, Iy is the vehicle body moment of inertia along the pitch axis, rt is the ith wheel position vector with respect to the vehicle centre of gravity, and 0 is the vehicle body pitch rate.

13. Processing circuitry of claim 11, wherein the processing circuitry is configured to determine the target yaw rate by solving a system of first-order non-linear differential equations for the target yaw rate, ip, the system of first-order non-linear differential equations being:(2 \P iy I -i=l / (2xFt1=1(2 \’ r i x F t I i=l / e = e,where vy is vehicle body lateral velocity, m is the vehicle mass, Fty ith wheel force in the y axis direction, Ft = {Fix,Fiy}, Fix is the ith wheel force in the x axis direction, vx is the vehicle body longitudinal velocity (input to the yaw rate calculator), / z is the vehicle body moment of inertia along the yaw axis, ly is the vehicle body moment of inertia along the pitch axis, rt is the ith wheel position vector with respect to the vehicle centre of gravity, and 0 is the vehicle body pitch rate;14. Processing circuitry of claim 11, wherein the processing circuitry is configured to determine the target yaw rate by solving a system of first-order non-linear differential equations for the target yaw rate, ip.1pxf = (F^f - Fxf), T pF x1*y1p =___(pstat _ p Ax,r v x,r 1 x,rb TF*1 p —___(pstat _ p Ar y,r t \yr ry,rJ>where vy is vehicle body lateral velocity, m is the vehicle mass, Fly ith wheel force in the y axis direction, F\ = (Flx,Fly), Flx is the wheel force in the x axis direction, vx is the vehiclebody longitudinal velocity (input to the yaw rate calculator), Iz is the vehicle body moment of inertia along the yaw axis, rt is the ith wheel position vector with respect to the vehicle centre of gravity, tFx and xFy are longitudinal and lateral force lag time constants, Fxf and Fyj are the final forces acting on the vehicle body generated by the front wheels, Fxr and Fyr are the final forces acting on the vehicle body generated by the rear wheels, F^f* is the static part of the front wheel longitudinal force, F^ is the static part of the rear wheel longitudinal force, Fyf is the static part of the front wheel lateral force, and F^ is the static part of the rear wheel lateral force.

15. Processing circuitry of claim 11, wherein the processing circuitry is configured todetermine the target yaw rate by solving the following system of first-order non-linear differential equations for the target yaw rate, ^).e = d,1 F^-^f-F^, tfx1 Py.fI F *y1 p —___( pstat _ p A1 x,r „ v x,r 1 x,rb TFx1 p =___(pstat p Ayr t k yr 1 yr J’ bp ty5 where vy is vehicle body lateral velocity, m is the vehicle mass, Fly ith wheel force in the y axis direction, Ft = {Flx,Fiy\ Fix is the wheel force in the x axis direction, vx is the vehicle body longitudinal velocity (input to the yaw rate calculator), Iz is the vehicle body moment of inertia along the yaw axis, Iy is the vehicle body moment of inertia along the pitch axis, r, is the ith wheel position vector with respect to the vehicle centre of gravity, 0 is the vehicle10 body pitch rate, tFx and rFy are longitudinal and lateral force lag time constants, Fx fi andFy f are the final forces acting on the vehicle body generated by the front wheels, Fxr andFy r are the final forces acting on the vehicle body generated by the rear wheels, F^1 is the static part of the front wheel longitudinal force, F^ is the static part of the rear wheel longitudinal force, Fy f is the static part of the front wheel lateral force, and Fff is the static 15 part of the rear wheel lateral force.

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