A system for adaptive control of vehicle dynamics.

Abstract

The vehicle dynamics control system receives feedback state signals including roll rate and roll angle values ​​of the vehicle's motion and updates parameters of a roll dynamics model by incorporating the received values ​​into a model of the vehicle's roll dynamics. The roll dynamics model describes the evolution of the roll rate and roll angle based on parameters including a Center of Gravity (CoG) parameter that models a location of the vehicle's CoG, a spring constant, and a damping coefficient that models the suspension dynamics of the vehicle. The system determines control commands for controlling at least one actuator of the vehicle using a motion model including the updated CoG parameters and sends the control commands to a vehicle controller to control the vehicle's motion.

Description

[Technical field]

[0001] The present invention relates generally to vehicle control, and more particularly to a system for adaptive control of vehicle dynamics, such as vehicle rollover control. To Regarding. [Background technology]

[0002] To design roll dynamics control methods such as differential braking systems or rollover avoidance systems based on Active Front Steering (AFS), it is mandatory to have at least a basic knowledge of the inertial parameters such as mass and inertia, as well as the location of the mass, i.e. the Center of Gravity (CoG). Vehicle manufacturers can provide values ​​of the inertial parameters and CoG. However, they are generally values ​​for some nominal (usually empty) loaded conditions, whereas in reality the loaded conditions, and therefore the CoG, will vary significantly depending on the driving.

[0003] Rollover accidents, although relatively rare, account for the majority of serious and fatal accidents. Therefore, the development of improved control principles to avoid such accidents is important. Automotive manufacturers typically utilize robust active road handling control strategies that take into account the unknown and changing CoG by designing for the worst-case scenario. Another common approach in the case of Sport Utility Vehicles (SUVs) is to intentionally design the vehicle heavier than usual by adding ballast to the undercarriage, aiming to lower the CoG position while suppressing the CoG position variation by reducing the percentage margin of load variation. Such approaches are successful to a certain extent, but they also have drawbacks such as reduced performance under normal driving conditions and reduced efficiency due to the added weight.

[0004] To avoid designing a conservative control strategy assuming worst-case scenarios, and because the CoG position is the most prominent factor in the occurrence of endogenous rollover, the control performance benefits from a real-time CoG position estimation function. Such an estimator can be used as a warning system for the driver or can be well integrated into active road handling or rollover prevention controllers, thus improving the overall safety of the vehicle and its occupants.

[0005] Due to its importance, the CoG estimation problem has been studied in parallel with the rollover avoidance control problem, with methods ranging from Recursive Linear Least-Squares (RLS) type methods to multiple model estimation and Extended Kalman Filter (EKF). However, RLS and EKF methods require the use of models that are linear or nearly linear in parameters, which is not the case for the CoG estimation problem. Thus, the assumption of linearity in such parameters can lead to poor estimator performance and ultimately hinder safety in vehicle rollover prevention systems.

[0006] Conversely, some vehicle rollover prevention systems assume that the CoG height is known when designing the controller in charge of avoiding rollovers, which is unrealistic since the CoG position varies with the loading conditions and the type of maneuver being performed. Such an assumption makes the control system suboptimal, since to be as safe as possible, the control system must necessarily be designed assuming the worst-case scenario, i.e. the worst possible CoG position.

[0007] Therefore, there remains a need for a vehicle dynamics control system, such as roll dynamics control suitable for rollover prevention based on real-time estimation of CoG position. Summary of the Invention

[0008] An object of some embodiments is to provide a system and method for a vehicle dynamics control system suitable for preventing vehicle rollover. Another object of some embodiments is to provide a system and method that adapts its control actuation according to the center of gravity (CoG) position by adapting the CoG position in real time. Additionally or alternatively, another object of some embodiments is to adapt the CoG estimation in real time simultaneously with the controller. Additionally or alternatively, another object of some embodiments is to adapt the CoG estimation simultaneously with the vehicle state when measurements do not explicitly measure the CoG position.

[0009] Additionally or alternatively, another object of some embodiments is to estimate the suspension parameters of the system using the CoG position. Additionally or alternatively, another object of some embodiments is to provide such an estimator in the form of a Bayes filter. Additionally or alternatively, another object of some embodiments is to design such an estimator using a model of the vehicle that accurately represents the CoG estimation while reducing the computational complexity. The CoG in this specification includes a CoG height that defines the distance from the CoG position to the ground. The vehicle state in this specification includes a vehicle roll angle and a vehicle roll rate.

[0010] Some embodiments are based on the realization that the CoG position can be estimated based only on a model of vehicle roll dynamics, which is simpler than also having a model of vehicle planar dynamics. This realization is based on the fact that while including a planar vehicle dynamics model slightly improves accuracy, the complexity of the algorithms required to include such a model increases exponentially. Thus, including only vehicle roll dynamics results in a slight loss of accuracy while significantly reducing computational and algorithmic complexity.

[0011] However, such a reduction in the computational complexity of CoG estimation based solely on a model of vehicle roll dynamics requires a separation of the estimation of CoG and the dynamics control based on the estimated CoG, since a simple model of vehicle roll dynamics may lead to inaccurate actual control. To that end, some embodiments separate the estimation of CoG and the control of vehicle dynamics by performing these tasks using different models. Specifically, the CoG is estimated based on a vehicle roll dynamics model, whereas the control is performed based on a motion model that may or may not include the vehicle roll dynamics model. For example, the motion model may include a planar model of the vehicle dynamics.

[0012] One embodiment is based on the realization that vehicle roll dynamics can be represented as a torsion spring-damper model with three unknown parameters: CoG position and spring and damping coefficients. Another embodiment is based on the understanding that while CoG position is the main parameter of interest for rollover prevention systems, the suspension dynamics of the vehicle greatly influence the behavior of the CoG position. As a result, for accurate CoG estimation, it is essential to also estimate the parameters of the suspension dynamics.

[0013] Some embodiments are based on the understanding that the output of the roll dynamics is the roll rate and roll angle which are inputted linearly into the motion model, whereas the unknown CoG position and spring and damping coefficients are inputted nonlinearly into the motion model. In one embodiment, this realization is used to exploit a linear substructure in the roll dynamics, which enables an efficient implementation of analytically estimating the roll rate and roll angle while numerically estimating the CoG position and spring and damping coefficients based on analytical estimates of the roll rate and roll angle.

[0014] In one embodiment, the estimation of the CoG position and the spring and damping coefficients is done using a Bayes filter, which generates not only estimates of the parameters of interest, but also a probability distribution of the uncertainty of said parameters, which in one embodiment is used to control the vehicle to avoid rollover.

[0015] Some embodiments implement a Bayes filter using a particle filter, where the particles include samples of the CoG positions and spring and damping coefficients, estimates of the vehicle state based on the samples, and probability weights for the samples. The use of a particle filter eliminates the need for linear or near-linear assumptions of the dynamics.

[0016] Some embodiments take advantage of the fact that as more data (i.e., measurements) are collected, the probability distribution of the parameter uncertainty shrinks because more data means more information is at hand to generate estimates. Confidence intervals for the parameter uncertainty can be inferred from the estimates of the probability distribution, and in one embodiment, an uncertainty-aware controller uses the estimate of the CoG position and the confidence in the estimate of the CoG position to determine control commands to avoid rollover. In some embodiments, the likelihood of rollover is determined using the associated CoG confidence.

[0017] Some embodiments are based on the recognition that rollover prevention can be formulated in terms of constraints on vehicle states and parameters that must be satisfied to avoid rollover. Such constraints depend on the CoG position and vehicle states.

[0018] Some embodiments disclose a parameter adaptation controller that can satisfy constraints on vehicle maneuvering while avoiding vehicle rollover. In one embodiment, such constraint enforcement is done by so-called constraint admissible sets, which guarantee a certain probability that a constraint will be satisfied.

[0019] Some embodiments provide a sampling-based approach to generate features and labels offline and iteratively update a robust constrained admissible set online as more data becomes available and confidence in the parameter estimates improves. To construct a robust constrained admissible set, some embodiments use not only the parameter point estimates themselves, but also regions in the parameter space where the true parameters lie with high confidence, ascertained by probability. To this end, some embodiments use a Bayes filter to determine the confidence.

[0020] In some vehicle control applications, there are usually existing controllers that are not easy to replace or redesign for various purposes. In such cases, a reference governor is useful. A reference governor is a lightweight constraint enforcement controller that can be used as an add-on scheme to an already deployed controller. One embodiment discloses a parameter-adaptive reference governor that learns the constraint admissible set online by leveraging parameter information from a Bayes filter.

[0021] Some embodiments of the present disclosure are based on the recognition that a reference governor provides an effective way to ensure safety through constraint enforcement in a closed-loop control system. When the parameters of the underlying system are unknown, such as in the case of the CoG position, a robust formulation of the reference governor that takes into account only the worst-case effects may be overly conservative and exhibit poor performance. To that end, some embodiments disclose a parameter-adaptive reference governor architecture that can generate safe control commands that are less conservative than the robust reference governor, despite the CoG uncertainties. Some embodiments use a Bayes filter to generate confidence bounds around the parameter estimates, which are fed into a supervised machine learning machine to approximate the robust constraint tolerance set utilized by the parameter-adaptive reference governor. Initially, due to the lack of online data, the parameter-adaptive reference governor may be as conservative as the robust reference governor, but as more data is collected and the confidence bounds become tighter, the conservativeness decreases.

[0022] Accordingly, one embodiment discloses a vehicle dynamics control system comprising at least one processor and a memory having instructions stored thereon, the instructions, when executed by the at least one processor, causing the vehicle dynamics control system to receive feedback state signals indicative of a measurement of a state of motion of a vehicle controlled by a vehicle controller, the state comprising roll rate and roll angle values ​​for the vehicle, the instructions, when executed by the at least one processor, further causing the vehicle dynamics control system to update one or more parameters of the roll dynamics model by incorporating the received roll rate and roll angle values ​​into a model of roll dynamics of the vehicle, the roll dynamics model being a spring-damper model describing the evolution of the roll rate and roll angle based on the parameters, the parameters being relative to a Center of Gravity (CoG) of the vehicle. and a vehicle dynamics control system that, when executed by the at least one processor, determines a control command for controlling at least one actuator of the vehicle using a motion model including the updated CoG parameters based on the state of the vehicle, and transmits the control command to the vehicle controller to control the motion of the vehicle based on the control command.

[0023] Some other embodiments disclose a vehicle rollover prevention method executed by at least one processor connected to a vehicle. The method uses a Bayes filter to estimate one or more internal states of a vehicle roll dynamics model including a vehicle CoG position. Using the estimated CoG position, the method determines a control command to reduce the likelihood of rollover and transmits the control command to at least one component of the vehicle. [Brief description of the drawings]

[0024] [Figure 1A] FIG. 2 is a schematic diagram of a model of vehicle planar dynamics. [Figure 1B] FIG. 1 shows a model in which four wheels are modeled, as well as the dynamics for roll and pitch. [Figure 1C] FIG. 13 is an alternative schematic diagram of a model including only vehicle roll dynamics. [Figure 1D] FIG. 2 illustrates an example of the interaction of different vehicle models according to some embodiments. [Figure 1E] FIG. 2 illustrates the interaction of various vehicle dynamics models according to one embodiment. [Figure 2A] FIG. 2 illustrates the interaction of the vehicle dynamics control system with other system components of a vehicle according to some embodiments. [Figure 2B] 1 shows a general structure of a vehicle dynamics control system according to an embodiment of the present invention; [Figure 3A] FIG. 1 is a block diagram of a method for controlling vehicle dynamics including CoG parameters of a vehicle according to some embodiments. [Figure 3B] FIG. 13 is a schematic diagram of incorporating received roll rate and roll angle values ​​into a roll dynamics model to update one or more parameters of a model of roll dynamics of a vehicle, according to some embodiments. [Figure 4A] FIG. 1 illustrates a flowchart of a method for estimating one or more parameters, including CoG parameters, of a vehicle by incorporating measurements of at least one or a combination of roll rate and roll angle into vehicle roll dynamics using a Bayes filter in accordance with some embodiments. [Figure 4B] FIG. 2 illustrates a flowchart of a method for determining initial parameters for an estimator, according to some embodiments. [Figure 4C] FIG. 2 illustrates a flowchart of one iteration of a method for estimating CoG parameters using a particle filter, according to one embodiment. [Figure 4D] FIG. 1 illustrates a flowchart of an exemplary implementation of updating the probability distribution of CoG parameters, according to one embodiment. [Figure 4E] FIG. 1 is a simplified schematic diagram of the results of three iterations of the steps where five particles are generated for each iteration. [Figure 4F] FIG. 4C illustrates possible assigned probabilities for five different CoG parameters in the first iteration in FIG. 4E. [Figure 5A] FIG. 1 illustrates an example of a vehicle controlled by a pre-designed legacy controller capable of following desired criteria according to some embodiments. [Figure 5B] FIG. 1 is a schematic diagram of components of a vehicle dynamics control system interfaced with a vehicle controlled by a legacy control system. [Figure 5C] FIG. 1 is a block diagram of a CAIS learner. [Figure 5D] FIG. 1 illustrates a flowchart of a method for offline generation of features and labels for use in CAIS, according to some embodiments. [Figure 6A] FIG. 2 is a schematic diagram of a reference generation module in the adaptive reference governor. [Figure 7] FIG. 13 shows an example of an updated CAIS based on a gradually shrinking boundary around a point estimate. [Figure 8A] 2 is another example of a schematic diagram of components of a vehicle dynamics control system according to some embodiments. [Figure 8B] FIG. 1 is a block diagram of an example implementation of a two-level optimization procedure for solving a nonlinear dynamic optimization problem with inequality constrains at each control step of an SMPC. [Figure 9A] FIG. 1 is a block diagram for implementing SMPC using a control model including a motion model including CoG parameters. [Figure 9B] FIG. 1 is a block diagram of an SNMPC that solves a constrained optimal control structure nonlinear programming problem (OCP-NLP) to compute the control signal at each control time step. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025] FIG. 1A is a schematic diagram of a model of vehicle planar dynamics used by some embodiments. The vehicle planar dynamics model describes the time evolution of the vehicle's longitudinal motion, lateral motion and heading. That is, the vehicle planar dynamics model is a specific example of a vehicle motion model. The heading ψ represents the rotation of the vehicle around an axis perpendicular to the vehicle's forward axis x and lateral axis y. In the case of FIG. 1A, the vehicle model, i.e., the vehicle planar dynamics, combines two wheels on the same axle into one, effectively making it a bicycle model. However, the same description applies to a four-wheeled vehicle model. The model in FIG. 1A shows a model that is widely used in vehicle control. However, it is not useful as a stand-alone model for a vehicle dynamics control system aiming to control a vehicle under non-negligible roll motion of the vehicle, for example, a sports utility vehicle (SUV) with aggressive steering maneuvers, since it does not capture the roll dynamics of the vehicle.

[0026] Figure 1B shows a more complex model in which four wheels are modeled, as well as the dynamics for roll φ and pitch θ. The mathematical equations underlying the schematic in Figure 1B include the roll dynamics and can therefore be used to estimate the CoG height in a recursive manner, for example using a Kalman filter type method or a recursive least squares type method or any other recursive method applicable to the particular estimation problem.

[0027] FIG. 1C is an alternative schematic of a model including only vehicle roll dynamics, where the model governing the roll motion is a torsion spring-damper system that models the CoG height h, spring constant K, and damping coefficient D. Roll motion as used herein is described by vehicle states including vehicle roll rate and vehicle roll angle. In the model in FIG. 1C, the parameters of primary interest for control of vehicle roll dynamics, e.g., to avoid vehicle rollover, are a total of three, namely, the CoG height h, the spring constant K, and the damping coefficient D.

[0028] The model in Figure 1C is substantially simplified compared to Figure 1B. For example, the model shown by Figure 1B requires modeling the interaction of the vehicle tires with the road, since tire forces are essentially what dominate the planar dynamics. Thus, if pitch dynamics are excluded, the number of parameters that need to be estimated increases to at least seven, compared to three in the model shown in Figure 1C.

[0029] Different vehicle dynamics models capture different aspects of vehicle dynamics and are therefore suitable for different purposes. For example, if the vehicle's heading rate is controlled and the vehicle is assumed to be aligned with the road, the planar dynamics model is sufficient to control the vehicle. However, the assumption that the vehicle is aligned with the road is sometimes difficult to verify a priori. For example, when driving on dry asphalt, the friction between the tires and the road is large, so that steering maneuvers intended to control the vehicle's heading rate lead to large roll angles, and as a result, using only the vehicle planar dynamics model as a motion model when controlling the vehicle may be insufficient.

[0030] If the roll angle is large enough that the vehicle's CoG position changes more than slightly, it is beneficial for the control system that controls the vehicle's dynamics, i.e., the vehicle dynamics control system, to also include parameters that model the vehicle's CoG position.

[0031] Moreover, different vehicle models may have different objectives. Figure 1D illustrates an example of the interaction of different vehicle models and how they may be incorporated into a vehicle dynamics control system for controlling vehicle 200, according to some embodiments.

[0032] For example, some embodiments recognize that while a complex vehicle model such as that shown in FIG. 1B necessarily leads to accurate modeling of the vehicle, such a model increases complexity without necessarily providing a significant improvement in modeling. For example, when controlling 120d the vehicle 200 using a controller, an embodiment uses a kinetic model of vehicle dynamics that includes the roll dynamics of the vehicle and the planar dynamics of the vehicle, where the roll dynamics model is a spring-damper model with CoG position as a parameter. However, when updating 110d the CoG position 111d for control 120d, an embodiment uses only a model of roll dynamics that describes the evolution of the roll rate and roll angle based on parameters, where these parameters include CoG parameters that model the position of the CoG of the vehicle, spring constants, and damping coefficients that model the suspension dynamics of the vehicle. In other words, updating of one or more parameters of the model of the roll dynamics of the vehicle may be done using the simple roll dynamics model, and the updated parameters may be transmitted 111d to the vehicle controller 120d, which may use such parameters to determine control commands 121d to the vehicle.

[0033] Different models can be used for different purposes, and different models may require different information from the sensor that measures aspects of the vehicle's motion. For example, to update the CoG parameters, some embodiments use lateral acceleration measurements, roll rate measurements, and roll angle measurements sensed by sensors mounted on the vehicle 200, and these measurements 201d are used in updating the CoG parameters. However, for purposes of controlling the vehicle (120d), some embodiments use measurements 202d that include other aspects of the vehicle dynamics, such as measurements of heading rate, vehicle speed, wheel speed, and vehicle position.

[0034] Other embodiments are based on the recognition that not only are there interactions between various models related to the estimation of CoG parameters and the control of the vehicle, but different models are used for different aspects of the estimation.

[0035] For example, a vehicle sensor setup can measure relevant conditions required for control. For example, a gyroscope included in an Inertial Measurement Unit (IMU) can measure the vehicle's heading rate, and a Global Positioning System (GPS) receiver can measure the vehicle position. However, GPS can only measure vehicle position within an accuracy of a few meters, and automotive-grade IMUs are imprecise. Therefore, some embodiments utilize different estimators to estimate different aspects of the vehicle operation.

[0036] FIG. 1E illustrates the interaction of various vehicle motion models, according to one embodiment. For example, the controller 120d that determines the vehicle commands 121d may include a combination of a vehicle planar dynamics model 121e and a model of the vehicle's roll dynamics 122e. Although shown as two different vehicle models in FIG. 1E, the vehicle model shown in FIG. 1B, including joint modeling of planar dynamics and vehicle roll dynamics, including CoG parameters, may also be included in the controller 120d. The determination of the CoG parameters (110d) may include the vehicle roll dynamics model as a spring-damper model, where the CoG parameters include CoG position, spring constant, and damping coefficient. At the same time, vehicle states such as vehicle speed, vehicle position, vehicle heading, and vehicle heading rate can be estimated (130d) using the vehicle dynamics planar model 121e.

[0037] FIG. 2A illustrates the interaction of a vehicle dynamics control system 199 with other system components of a vehicle 200, according to some embodiments. The vehicle may be any type of mobile vehicle, such as a four-wheeled passenger car or a mobile robot. The vehicle may be fully human-operated, semi-autonomous, or fully autonomous. For example, the vehicle may receive external inputs 210 from a vehicle driver generating reference steering and / or brake / throttle commands to the vehicle. For example, the vehicle may receive external inputs 210 from an automated driving system of the vehicle generating reference steering and / or brake / throttle commands to the vehicle. The vehicle dynamics control system 199 may be connected to a sensing system 230 that outputs various sensor measurements 231, such as sensing of lateral acceleration, steering commands, speed, or the suspension system of the vehicle. The sensing system 230 may include a GPS and / or an IMU. For example, the IMU may comprise a three-axis accelerometer, a three-axis gyroscope, and / or a magnetometer. The IMU may provide speed, orientation and / or other position related information to other components of the vehicle dynamics control system 199. For example, the sensing system 230 may include sensors for measuring or estimating the vehicle's roll angle and the vehicle's roll rate.

[0038] The vehicle dynamics control system 199 determines control commands 241 to the vehicle's lower level actuators and controller 260. The vehicle dynamics control system can drive various actuators of the vehicle. The control commands 241 can be modified steering commands that modify the driver's reference input 210 so as not to violate the vehicle's constraints, or can be braking commands for individual tires. The commands 241 are used as inputs or references to the vehicle controller 260 to calculate vehicle commands such as steering, braking and throttle. Those commands are sent to the vehicle's actuators to move the vehicle according to the commands 241.

[0039] If the vehicle motion model included in the vehicle dynamics control system 199 uses the same control inputs as the actual vehicle, the vehicle can be directly controlled using the calculated inputs. For example, if the vehicle 200 is controlled by applying steering and engine torques, and if the control model used in the vehicle dynamics control system 199 also uses steering and engine torques as control inputs, these can be applied directly to the vehicle, thereby overriding the vehicle control system 260. However, since the mathematical description of the vehicle 200 used in the vehicle dynamics control system 199, such as the mathematical description corresponding to the model in FIG. 1B, is often a simplification of the true motion of the vehicle, the control inputs 241 may instead be used as feedforward or nominal control signals with a reference as inputs to the vehicle control system 260. For example, accelerations may be modeled to be proportional to engine torque. Thus, if accelerations are used as inputs in the vehicle motion model utilized in the vehicle dynamics control system 199, these accelerations can be used as scaled feedforward inputs to the vehicle control system 260.

[0040] In some implementations, the vehicle dynamics control system 260 may include a steering controller, a brake controller, and a throttle controller, where the steering controller takes the steering angle as an input, the brake controller takes a reference deceleration or wheel slip as an input, the engine controller takes a nominal speed or acceleration as an input, and all controllers output torque, and the vehicle dynamics control system 199 includes all of these entities. And the torque calculated by the vehicle dynamics control system 199 may bypass the vehicle controller 260, or the torque 241 may be used as a zero level value for the vehicle controller 260, and the steering angle, the reference deceleration or wheel slip, and the nominal speed or acceleration may be used as references 241 to the vehicle controller 260.

[0041] Some embodiments use a motion model of the vehicle to control the vehicle, which does not include the spring constants and damping coefficients of the roll dynamics model, because the CoG position is a key parameter for controlling the vehicle to avoid rollover, and a motion model that controls the roll of the vehicle must include the CoG position.

[0042] In other embodiments, the motion model used in controlling the vehicle includes the vehicle's planar dynamics. For example, if rollover is the only control objective, a vehicle roll dynamics model is sufficient for control, so some embodiments include roll dynamics in the motion model. However, if other states of the vehicle, such as position, heading rate, or speed, are controlled, other models are included. For example, in one embodiment, the motion model used in controlling the vehicle includes the vehicle's planar dynamics model.

[0043] Some embodiments are based on the understanding that sensor measurements are noisy and that such noise is probabilistic, i.e., can be explained by statistics. To this end, some embodiments use a probabilistic, i.e., Bayesian, filter to update one or more parameters of a model of the roll dynamics of the vehicle. The use of a Bayesian filter allows extraction of various moments, e.g., first and second moments, of the determined probability distribution, which can be used in determining the control commands. For example, the second moment, i.e., the variance, of the updated CoG position can be used to determine the control commands such that the vehicle is behaving safely at a CoG position within the range of possible CoG position variations.

[0044] 2B illustrates a general structure of a vehicle dynamics control system 199 according to one embodiment. The vehicle dynamics control system 199 includes at least one processor 270 for executing instructions of the vehicle dynamics control system 199 stored in a memory 280. The processor 270 is coupled (271) to the memory 280 for storing a Bayes filter 281 that uses the sensed information 231 and a model of the vehicle roll dynamics. The memory also stores an initial guess 282 of the distribution of one or more parameters of the vehicle roll dynamics, including, for example, the dynamics' spring stiffness constants, damping coefficients, and the vehicle's CoG position, and a motion model 283 that includes the CoG parameters. The memory also stores vehicle constraints 284 and a controller having a component 285 for determining control commands that satisfy such constraints. For example, the memory may store a constraint-tolerant invariant set 285 that, when used by the controller, can guarantee that the constraints are satisfied. In one embodiment, the vehicle dynamics control system determines such a set based on estimates from a Bayes filter according to various embodiments of the present invention.

[0045] FIG. 3A is a block diagram of a method for controlling vehicle dynamics including CoG parameters of the vehicle according to some embodiments, the method being executed by at least one processor 270 of the vehicle. The method estimates 310a one or more parameters of a vehicle roll dynamics model 350a including CoG parameters that model the position of the vehicle's CoG, spring constants, and damping coefficients that model the suspension dynamics of the vehicle by incorporating measurements of at least one of roll rate and roll angle or a combination thereof into the vehicle roll dynamics model. In some embodiments, the method uses a Bayes filter that also estimates confidence intervals of the parameters. In other embodiments, the Bayes filter also estimates probability distributions of the uncertainty of the parameters. Using the estimated parameters 312a and the estimated uncertainty 311a of the internal state, the method determines 320a a control command 321a for controlling at least one actuator of the vehicle using a motion model 360a including the updated CoG parameters, and transmits 330a the control command 321a to the vehicle via a control signal 331a. Finally, using the vehicle controller 260, the method controls 340a the motion of the vehicle according to the control commands. In some embodiments, the objective of the control is to reduce the likelihood of rollover of the vehicle having the estimated CoG.

[0046] In other embodiments, the Bayes filter estimates not only the CoG parameters, but also estimates of the uncertainty of the CoG parameters. In some embodiments, the estimates of the CoG parameters are general probability distributions, while in other embodiments, the estimates of the CoG parameters are made by assuming that the CoG parameter uncertainties follow a Gaussian distribution. In other embodiments, the Bayes filter uses measurements of the roll rate and roll angle of the vehicle using the sensing system 230.

[0047] Some embodiments are based on the realization that parameters including CoG parameters that model the position of the vehicle's CoG, spring constants, and damping coefficients that model the vehicle's suspension dynamics can be estimated based only on a model of vehicle roll dynamics, which is simpler than also having a model of vehicle planar dynamics. This realization is based on the understanding that there is a slight increase in accuracy while including a planar vehicle dynamics model. However, the complexity of the algorithms required to include such a model increases exponentially. Therefore, by including only vehicle roll dynamics, there is a slight decrease in accuracy while significantly reducing the computational complexity and algorithmic complexity.

[0048] One embodiment is based on the realization that vehicle roll dynamics can be represented as a torsion spring-damper model with three unknown parameters: CoG position and spring and damping coefficients. Another embodiment is based on the understanding that while CoG position is the primary parameter of interest for vehicle dynamics control systems focused on rollover prevention, the suspension dynamics of the vehicle greatly influence the behavior of the CoG position. As a result, for accurate CoG estimation, it is essential to also estimate the parameters of the suspension dynamics.

[0049] FIG. 3B is a schematic diagram of incorporating received roll rate and roll angle values ​​into a roll dynamics model to update one or more parameters of a model of roll dynamics of a vehicle, according to some embodiments. The roll dynamics model includes parameters 310b and a relationship 320b connecting the parameters 310b with an output of roll dynamics. In various embodiments, the parameters 310b include one or a combination of CoG parameters that model the position of the vehicle's CoG, a spring constant, and a damping coefficient that model the suspension dynamics of the vehicle. The output of roll dynamics in the roll dynamics model includes the roll rate and roll angle of the vehicle. Thus, knowing the parameters 310b of the roll dynamics model, the values ​​340b of the roll rate and roll angle can be estimated according to the relationship 320b. An example of the relationship 320b is a roll dynamics model with the parameters inserted into the model, and these values ​​are the output of the roll dynamics model with the parameters inserted into the model.

[0050] To that end, updates 370b to parameters 310b result in various values ​​340b of estimated roll rate and roll angle, which can be compared to values ​​360b of roll rate and roll angle received in the form of feedback signals to determine a difference 350b between the estimated values ​​340b and the received values ​​360b of roll rate and roll angle. Knowing this difference 350b, various embodiments update 370b one or more of parameters 310b to reduce the difference 350b. Various techniques can be used to estimate the direction and magnitude of the updates 370b. For example, some embodiments use a Bayes filter to determine the parameter updates 370b by incorporating measurements of at least one or a combination of roll rate and roll angle into the vehicle roll dynamics. Other embodiments use optimization-based techniques, such as gradient descent, to minimize the error between the output of the roll dynamics model and the measurements of roll rate and roll angle.

[0051] FIG. 4A illustrates a flowchart of a method for estimating one or more parameters including CoG parameters of a vehicle by incorporating measurements of at least one or a combination of roll rate and roll angle into vehicle roll dynamics using a Bayes filter, where the CoG parameters are probabilistically estimated as probability distributions using the Bayes filter, and the motion model includes first and second moments of the probability distribution of the CoG parameters incorporating the uncertainty of the CoG parameter estimation such that control commands are determined based on the uncertainty of the CoG estimation. In a first time step, the method initializes estimates of the parameters using input data acquired according to other embodiments. Then, using measurements from the sensing system, the method updates estimates of the one or more parameters by incorporating the measurements into a vehicle roll dynamics model that connects the measurements and the parameters. Using the updated estimates of the parameters, the method predicts the parameters until the next time step and transmits the predicted parameters. Further, the method outputs (431a) these parameters for use in determining control commands for controlling the vehicle.

[0052] Initialization of parameter estimates can be done in a variety of ways. For example, if the vehicle dynamics control system is to be used with a particular vehicle model or type of vehicle, the range of possible values ​​of the parameters may be determined and bounded in advance, and initialization may be done by sampling values ​​from these ranges, e.g., from a probability distribution that models the a priori range. However, there are two problems with such an approach. First, the range of values ​​may be so large that it is not possible to test all values ​​for computational reasons. Second, although one can sample a finite set of values ​​by modeling a probability distribution over the possible range of values, it is difficult how to model such a distribution that captures the true uncertainty of the underlying parameters.

[0053] One embodiment recognizes that if prior measurements are available, e.g., collected on the same type of vehicle using a vehicle driven by a human operator, these measurements can be used in combination with a model of the vehicle's roll dynamics, and various values ​​of the internal states can be tested and compared for fit with the measurements.

[0054] Some embodiments use a model of the vehicle's roll dynamics with internal state hypotheses to determine an initial guess by optimizing a cost function that minimizes the difference between the sequence of measurements and a set of estimated measurements.

[0055] 4B illustrates a flowchart of a method 410a for determining initial parameters for the estimator 310a, according to some embodiments. aUsing a model 408b of vehicle roll dynamics having these measurements as model outputs, and a range 407b of possible parameter values, the method determines 410b a predicted measurement sequence as an output of the model of vehicle roll dynamics using a set of parameter values ​​determined from the range 407b. Using the predicted measurements 411b, the method determines 420b a value of a cost function reflecting a difference between the measurement sequence and the predicted measurement sequence. The method then updates 430b the parameters using a history of combinations of parameter values ​​and cost function values ​​obtained from the set of parameter values. If a termination threshold 440b is met, the updated set of parameters is used to determine 450b a probability distribution of possible parameter sets from which an initial set of parameters is determined. If a termination threshold 450b is not met, the method uses the updated parameters to determine a new set of predicted measurements.

[0056]

number

[0057] Determining the updated CoG parameters (430b) is based on a surrogate cost function, in one embodiment, this is done by implementing an acquisition function designed to obtain CoG parameters within a range of possible values ​​where the best CoG parameters (optimal solution) are likely to be located.

[0058]

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[0059] In some embodiments, not only one CoG parameter but several different possible values ​​of the CoG parameter are determined by sampling the probability distribution determined by 410a.

[0060] Another embodiment of the invention implements a Bayes filter using a particle filter, which maintains a set of particles, each particle representing a weighted estimate of a probability distribution of a CoG parameter, and the set of particles may collectively represent first and second moments of the estimated probability distribution of the CoG parameters. The particle filter particles also include estimates of the vehicle state based on the CoG parameters for the particles, and probability weights of combinations of the CoG parameters and the vehicle state. The use of a particle filter eliminates the need for linear or near-linear assumptions of the model of vehicle dynamics and dependence on the unknown parameters estimated by the particle filter.

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[0066] FIG. 4C illustrates a flowchart of one iteration of a method for estimating CoG parameters using a particle filter (420a), according to an embodiment, executed by a processor of the vehicle. The particle filter estimates the probability distribution of the CoG parameters by a set of weighted particles, each particle representing a weighted estimate of the probability distribution of the CoG parameters, and the set of particles collectively representing the first and second moments of the estimated probability distribution of the CoG parameters, with the weights being determined according to the fit of the measurements to the predicted measurements using the measurement model. Thus, the particle filter determines (410c) a relationship between the roll angle and roll rate estimated using the roll dynamics model with the uncertainty of the CoG parameters and the roll angle and roll rate received (409c). Using the determined relationship 411c, the particle filter updates (420c) the probability distribution of the CoG parameters based on the determined relationship to reduce the difference between the roll angle and roll rate and the received roll angle and roll rate values ​​409c.

[0067] 4D illustrates a flowchart of one example implementation of updating the probability distribution of the CoG parameters (420c), according to one embodiment. Using the determined relationship 411c, the method determines weights (410d) by determining the fit of the measurements to the roll angle and roll rate estimated using a roll dynamics model with the uncertainty of the CoG parameters for the particle. These weights are then normalized to 1 to ensure that the sum of the weights reflects the probability distribution.

[0068] Using the determined weights, the most likely or best particles are resampled 420d to remove less likely particles. The resampled particles 421d are used to determine 430d a probability distribution for the CoG parameters based on these weights.

[0069] FIG. 4E is a simplified schematic diagram of the results of three iterations of steps 420a and 430a when five particles are generated for each iteration. An initial state 410e is predicted 411e forward in time using a model of roll dynamics and five sampled CoG parameters (one for each particle) to generate five next states 421e, 422e, 423e, 424e and 425e. Probabilities are determined as a function of the fit of measurements 426e and a probabilistic measurement model 427e of measurements 426e according to the relationship between the roll angles and roll rates estimated using the roll dynamics model with uncertainties in the CoG parameters and the received roll angles and roll rates. At each time step, i.e. at each iteration, the ensemble of probabilities is used to generate 420e the first and second moments of the CoG parameters.

[0070] FIG. 4F illustrates the possible assigned probabilities of the five different CoG parameters in the first iteration in FIG. 4E. Those probabilities 421f, 422f, 423f, 424f, and 425f are reflected in selecting the size of the dots representing CoG parameters 421e, 422e, 423e, 424e, and 425e. Referring again to FIG. 4E, the most likely particle becomes the initial CoG parameter for the next iteration, which again generates the five sampled CoG parameters.

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[0072] Some embodiments are based on the understanding that particle filters are computationally heavy Bayesian filters, and an efficient implementation is necessary for implementation in time-sensitive tasks such as vehicle control. Another embodiment recognizes that roll angles and roll rates are input linearly to a model of the vehicle's roll dynamics, whereas CoG parameters are input nonlinearly. Thus, roll angle and roll rate updates can be made efficiently and analytically using Kalman filter updates for each particle. Doing so guarantees reduced computational complexity.

[0073] In some embodiments, the estimates of the CoG parameters and the confidence in the estimates of the CoG parameters are used to control the vehicle to reduce the likelihood of the vehicle rolling over. Any control method for controlling the vehicle based on a probabilistic estimation of the CoG parameters can be used in a vehicle dynamics control system to control the vehicle using a motion model that includes the CoG parameters.

[0074] In some embodiments, the control command determined to reduce the likelihood of rollover is a control command determined by a legacy controller of the vehicle, such as an adjustment of a steering angle criterion or a braking behavior criterion. In other embodiments, the control command determined to reduce the likelihood of rollover is an adjustment of a steering behavior of a driver of the vehicle. In yet other embodiments, the control command determined to reduce the likelihood of rollover is made autonomously without the driver manipulating the nominal behavior of the vehicle.

[0075] 5A illustrates an example of a vehicle 501a controlled by a pre-designed legacy controller that can track a desired criterion 509a, according to some embodiments. In some implementations, to enforce constraint satisfaction, an Adaptive Reference Governor (ARG) 503a uses measurements 505a to adjust the desired criterion 509a to a constraint tolerance criterion 507a.

[0076] 5B is a schematic diagram of components of a vehicle dynamics control system 199 connected with a vehicle controlled by a legacy control system 501b. The desired reference signal 509b may be a steering profile generated by a human operator of the vehicle, or an automatic steering or braking profile generated by a legacy controller. In some embodiments, the vehicle dynamics control system 199 has the following modules: a Bayes filter 531b, a Constraint-Admissible Invariant Set (CAIS) learning module 521b, and a reference generation module 511b.

[0077] The Bayes filter 531b estimates the CoG parameters and associated uncertainties, e.g., expressed as second moments, according to some other embodiments. The vehicle 501b and control system are designed to satisfy constraints 527b arising from safety considerations, physical limitations and / or specifications, which limit the range in which the outputs, inputs and possibly even vehicle states are allowed to function. For example, a constraint may be the maximum roll angle of the vehicle, or the maximum allowable load transfer of the vehicle, beyond which there is a risk of the vehicle rolling over. The constraints 528b are defined in a continuous space. For example, the state constraints are defined in a continuous state space of the vehicle, and the reference input constraints are defined in a continuous reference input space. The CAIS learning module 521b takes the estimates of the CoG parameters from the Bayes filter 531b together with the features and labels stored in the memory 523b, and generates a constraint allowable set using the CPU / GPU or for use in the reference generator module 511b.

[0078] Given a desired reference input 509b from the vehicle driver, such as a commanded steering profile, the reference generator unit 511b uses the CAIS generated by the CAIS learner 521b to adjust this desired reference input r to an adjusted reference input v. This adjusted reference input belongs to a set of allowable references 517b, such as the vehicle's steering angle limits. The reference generator accesses its memory 513b to find the adjusted reference at the previous time instant and updates it to calculate the new adjusted reference. The adjusted reference input is connected to the vehicle via an interface 507b to ensure that the constraints 527b are enforced without changing the behavior or structure of the legacy control system or the driver's behavior in case of a fully human-operated vehicle.

[0079] FIG. 5C is a block diagram of a CAIS learner 521c that leverages CoG parameter estimate boundaries 513c from a Bayes filter and stored state features and constraint tolerance labels 527c to train an updated CAIS 531b given constraints 528c, in accordance with some embodiments.

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[0082] To generate parameter-robust constraint admissible set estimates, some embodiments utilize an offline sampling-driven approach to collect data for learning these sets online as measurements become available.

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[0086] In one embodiment, sample x i Set the corresponding labels of as follows:

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[0089] 6A is a schematic diagram of a criteria generation module 630a in an adaptive reference governor. The updated CAIS 610a and the set of acceptable criteria 620a obtained from the learning module are used to calculate adjusted criteria that satisfy the output constraints.

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[0091] As a result, one embodiment rewrites problem (8) as a grid search as follows:

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[0093] 7 illustrates an example of an updated CAIS based on a gradually shrinking boundary 725 around the CoG parameter estimates 723, e.g., first moments, of the CoG parameters at increasing times 740, 742, 744. The uncertainty around time 740 is high (large interval), so the corresponding invariant set is tight (741), but as the boundary shrinks from 740 to 742, 744, the corresponding CAIS expands from 741 to 743, 745. In some embodiments, this expansion may completely change the shape of the CAIS, such as from 743 to 745.

[0094] A variety of different controllers may be used by various embodiments of the vehicle dynamics control system to reduce the likelihood of vehicle rollover, so long as the controller takes into account aspects of the probability distribution of the CoG parameters, such as the second moment.

[0095] FIG. 8A illustrates another example of a schematic diagram of components of a vehicle dynamics control system 199, according to some embodiments. In this example, a Bayesian filter 830 including a CoG estimator 831 using a model of roll dynamics 850 is connected (821) to a Stochastic Model-Predictive Controller (SMPC) 810 to control the vehicle. The SMPC uses a motion model 860 including CoG parameters in its control model to control the vehicle. The SMPC may include constraints 842 representing the physical and operational limits of the vehicle. For example, a rollover avoidance constraint is included in the constraints 842. For example, a maximum limit on the steering angle, i.e., the maximum allowable lateral deviation on the road, is included in the constraints 842. In operation, the SMPC 810 receives commands, e.g., steering commands 801, indicating the desired behavior of the system. In response to receiving the commands 801, the SMPC generates a control signal 811, which serves as an input to the vehicle 820 via an interface 812.

[0096] In some embodiments, the control model 840 for the SMPC 810 may include one or more probabilistic chance constraints 843. A chance constraint, as used herein, is a constraint that defines physical or geometric limitations of the vehicle taking into account uncertainties in various aspects of the control model. For example, a chance constraint may define a constraint on the lateral displacement of the vehicle on a road or may include a rollover avoidance constraint. Various embodiments may formulate one or more of any of the vehicle's physical limitations and specification constraints as one or more probabilistic chance constraints 843, which seek to enforce that the probability of violating the corresponding constraint is below a certain probability threshold.

[0097] In various embodiments, the control model 840 of the system includes a vehicle motion model including CoG parameters with first and second moments of the estimated probability distribution of the CoG parameters, for example, the first and second moments of the estimated probability distribution of the uncertainty of the CoG parameters are included in the control model.

[0098] 8B is a block diagram of an exemplary implementation of a two-level optimization procedure for solving an inequality-constrained nonlinear dynamic optimization problem at each control step of the SMPC 810, which includes a probabilistic chance constraint representing the uncertainty of the CoG parameters to generate control commands that reduce the possibility of rollover. The two-level optimization procedure alternates between propagation of the second moment extracted from the probability distribution of the uncertainty of the CoG parameters of the probabilistic chance constraint within the forecast range of fixed values ​​of the state, i.e., covariance matrix 850b and the control variables 865b, and optimization of the state and control variables 860b within the forecast range of fixed values ​​of the CoG parameter covariance matrix 855b. When the termination condition of the two-level optimization procedure is met, the control signal 811 is calculated.

[0099] In some embodiments of the invention, the two-level optimization procedure 810 consists of three main computational steps. The first step is to prepare a linear quadratic objective function and to calculate the Jacobian matrix to prepare linearization equality and inequality constraints, which propagate 850b the trajectory of the covariance matrix by evaluating a nonlinear covariance propagation equation for the current trajectories of the states, CoG parameters and control values ​​865b, this covariance matrix representing the uncertainty of the predicted state values ​​over the control range affected by the second moment of the CoG parameters. The second step is to solve the resulting block-structured QP subproblem with one or more tight inequality constraints to approximate each of the chance constraints 870b. The third and final step involves a Newton-type update 875b to the current trajectories of the optimal states and control values.

[0100] In some embodiments, adjoint gradient calculations are used to correct inaccurate Jacobian information in the SMPC, and the resulting two-level optimization procedure consists of three main computational steps. The first step is to prepare a linear quadratic objective function, to prepare linearization equality and inequality constraints by computing Jacobian matrices with respect to the state and control variables, to compute adjoint-based gradient estimates, and to numerically eliminate the covariance matrix from each of the objective and constraint functions by propagating 850b the covariance matrix, i.e., the second moment trajectory, for the current trajectories of predicted state and control values ​​865b using a motion model including the CoG parameters. The second step is composed of solving the resulting block-structured QP subproblem with one or more tight inequality constraints to approximate each of the chance constraints 870b. The third and final step involves Newton-type updates 875b to the optimal state and control value trajectories and the corresponding update extensions of the Lagrange multipliers.

[0101] 9A is a block diagram for implementing SMPC using a control model 840 including a motion model 860 including CoG parameters. Specifically, SMPC calculates a control solution, e.g., a solution vector 965a, by solving a constrained optimization problem 950a at each control time step, where the control solution includes a sequence of future optimal or near-optimal control inputs over a forecast time horizon of the system 960a. The objective function, equality and inequality constraint data 945a in this optimization problem 950a depend on the control model and system constraints 940a, which are determined from the current state estimates of the system, the estimated CoG parameters, and the control commands.

[0102] Embodiments of the present invention use direct optimal control methods to formulate the continuous-time SMPC problem as an inequality-constrained nonlinear dynamic optimization problem. Some embodiments of the present invention use derivative-based optimization algorithms to solve the inequality-constrained optimization problem 950a exactly or approximately using an iterative procedure based on Newton-type methods and successive linearization of the feasibility and optimality conditions of the optimization problem. Examples of such Newton-type optimization algorithms include the Interior Point Method (IPM) and Sequential Quadratic Programming (SQP). Some embodiments of the present invention are based on the recognition that the inequality-constrained optimization problem 950a has the form of an optimal control structure optimization problem (OCP), and thus a structure that exploits an implementation of a derivative-based optimization algorithm can be used to calculate the solution vector 965a at each control time step.

[0103] In some embodiments of the present invention, solving the inequality constrained optimization problem (950a) uses exact or approximate state and / or control values ​​910a over a forecast time range from a previous control time step that can be read from memory as solution guesses to reduce the computational effort of solving the inequality constrained optimization problem (950a) in the current control time step. This concept of calculating a solution guess from solution information 910a in a previous control time step is called a warm start or hot start of the optimization algorithm, which can reduce the required computational effort of the SNMPC in some embodiments of the present invention. Similarly, the corresponding solution vector 965a can be used to update and store a sequence of exact or approximate state and / or control values ​​for the next control time step 960a.

[0104] 9B is a block diagram of an SNMPC that solves a constrained optimal control structure nonlinear programming problem (OCP-NLP) 950a to compute control signals 811 at each control time step given the current state estimate of the system, the estimated CoG parameters providing the inserted updated model 509a, and the commands 801. The OCP-NLP 950a considers the state variables x=[x0, x1, ..., x N ] and the state covariance matrix variables P=[P0,P1,...,P N ] and the control input variables u=[u0,u1,...,u N-1 ] is included.

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[0106] In some embodiments, one or more of the inequality constraints 955a can be defined as probabilistic chance constraints, where the probability of violating the corresponding inequality constraint is below a certain probability threshold, i.e., a backoff factor value α i >0, and for standard deterministic inequality constraints, α i = 0. Note that the deterministic inequality constraints aim to ensure that the corresponding inequality constraints on the expected values ​​of the state and control value trajectories are satisfied.

[0107] Using an approximate formulation of the stochastic chance constraints 955a based on an individual tightening for each inequality constraint, the resulting inequality-constrained nonlinear dynamic optimization problem can be solved using a Newton-type optimization algorithm based on successive linearization of optimality and feasibility conditions. Examples of such Newton-type optimization algorithms include the interior point method (IPM) and sequential quadratic programming (SQP). Some embodiments of the present invention are based on the recognition that the SQP algorithm solves a quadratic program (QP) approximation for the stochastic nonlinear OCP at each iteration of the SQP optimization algorithm based on a linear quadratic approximation of the objective function, a linearization-based approximation for the discretized system dynamics and discrete-time covariance propagation equations, and a linearization-based approximation for each of the inequality constraints and each of the tight stochastic chance constraints.

Claims

1. 1. A vehicle dynamics control system comprising: at least one processor; and a memory having instructions stored thereon, the instructions, when executed by the at least one processor, causing the vehicle dynamics control system to: and receiving feedback state signals indicative of measurements of states of motion of a vehicle controlled by a vehicle controller, the states including values ​​of roll rate and roll angle for the vehicle, the instructions, when executed by the at least one processor, further comprising: updating one or more parameters of a roll dynamics model of the vehicle by incorporating the received roll rate and roll angle values ​​into the roll dynamics model, the roll dynamics model being a spring-damper model that describes the evolution of the roll rate and the roll angle based on the parameters, the parameters including a Center of Gravity (CoG) parameter that models a position of the vehicle's Center of Gravity; a spring constant and a damping coefficient that models suspension dynamics of the vehicle, and the updated parameters include the CoG parameters, and the instructions when executed by the at least one processor further cause the vehicle dynamics control system to: determining a control command for controlling at least one actuator of the vehicle based on the state of the vehicle using a motion model including the updated CoG parameters; A vehicle dynamics control system that transmits the control commands to the vehicle controller to control the motion of the vehicle based on the control commands.

2. The vehicle dynamics control system of claim 1 , wherein the updated parameters of the roll dynamics model include the spring constant and the damping coefficient.

3. The vehicle dynamics control system of claim 2 , wherein the motion model does not include the spring constants and the damping coefficients of the roll dynamics model.

4. The vehicle dynamics control system of claim 1 , wherein the motion model includes planar dynamics of the vehicle.

5. The vehicle dynamics control system of claim 4 , wherein the motion model includes roll dynamics of the vehicle.

6. 2. The vehicle dynamics control system of claim 1, wherein the CoG parameters are probabilistically estimated as a probability distribution using a Bayes filter, and the motion model includes first and second moments of the probability distribution of the CoG parameters that capture the uncertainty in the estimation of the vehicle's CoG, such that the control commands are determined based on the uncertainty in the estimation of the CoG parameters.

7. The vehicle dynamics control system of claim 6 , wherein the Bayes filter is a Kalman filter that assumes that the probability distribution of the CoG parameters is Gaussian.

8. The vehicle dynamics control system of claim 6 , wherein the Bayes filter is a particle filter.

9. The particle filter maintains a set of particles, each particle representing a weighted estimate of the probability distribution of the CoG parameters, the set of particles collectively representing the first and second moments of the estimated probability distribution of the CoG parameters, and to update the particles, the at least one processor performs: determining a relationship between the roll angle and the roll rate estimated using the roll dynamics model having the uncertainty of the CoG parameters and the received roll angle and roll rate; 10. The vehicle dynamics control system of claim 8, further configured to update the probability distribution of the CoG parameters based on the determined relationship between the roll angle and the roll rate and to reduce the received values ​​of the roll angle and the roll rate.

10. 2. The vehicle dynamics control system of claim 1, wherein the vehicle dynamics control system iteratively updates the CoG parameters from initial values ​​of the parameters of the roll dynamics model, the initial values ​​being determined by minimizing a cost function of a difference between a sequence of historical values ​​of the roll rate and the roll angle and a sequence of estimated values ​​of the roll rate and the roll angle, the sequence of estimated values ​​of the roll rate and the roll angle being estimated based on values ​​of the parameters of the roll dynamics model selected from a range of possible values ​​for the parameters.

11. The vehicle dynamics control system of claim 10 , wherein the cost function is a Gaussian process regressor optimized by Bayesian optimization.

12. The vehicle dynamics control system of claim 1 , wherein the control command is sent to override a control signal generated by the vehicle controller.

13. The vehicle dynamics control system of claim 6 , wherein the control commands are sent as feedforward inputs to the vehicle controller.

14. The vehicle dynamics control system of claim 13 , wherein the control commands are determined to reduce a likelihood of the vehicle rolling over.

15. 15. The vehicle dynamics control system of claim 14, wherein the vehicle controller includes a reference trajectory adjusted from a desired reference signal by an Adaptive Reference Governor (ARG) for the state of the vehicle according to the motion model having the updated CoG parameters.

16. 15. The vehicle dynamics control system of claim 14, wherein the vehicle controller is a Stochastic Model-Predictive Controller (SMPC), the SMPC performing optimization under constraints including rollover avoidance constraints, and the SMPC determining the control commands using the second moment of the estimated probability distribution of the CoG parameters.

17. 16. The vehicle dynamics control system of claim 15, wherein the ARG is configured to update the reference trajectory and calculate a CoG parameter robust constraint allowable set based on the updated reference trajectory and a state of the system, and the ARG generates and transmits a reference trajectory to the system based on the CoG parameter robust constraint allowable set.

18. 20. The vehicle dynamics control system of claim 17, wherein the ARG includes a Constraint-Admissible Invariant Set (CAIS) learner configured to generate a constraint-admissible set using the estimated probability distributions of the CoG parameters.

19. The vehicle dynamics control system of claim 18 , wherein the CAIS learner is configured to utilize CoG parameter estimates and stored state features and constraint tolerance labels to learn an updated CAIS.

20. 2. The vehicle dynamics control system of claim 1, wherein the CoG parameters are numerically estimated using a particle filter, and the roll rate and roll angle of the vehicle are analytically estimated based on the numerical estimates of the CoG parameters.

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