Time-varying Model Predictive Control Research Articles

Human-Like Obstacle Avoidance Trajectory Planning and Tracking Model for Autonomous Vehicles That Considers the River's Operation Characteristics.

Developing a human-like autonomous driving system has gained increasing amounts of attention from both technology companies and academic institutions, as it can improve the interpretability and acceptance of the autonomous system. Planning a safe and human-like obstacle avoidance trajectory is one of the critical issues for the development of autonomous vehicles (AVs). However, when designing automatic obstacle avoidance systems, few studies have focused on the obstacle avoidance characteristics of human drivers. This paper aims to develop an obstacle avoidance trajectory planning and trajectory tracking model for AVs that is consistent with the characteristics of human drivers’ obstacle avoidance trajectory. Therefore, a modified artificial potential field (APF) model was established by adding a road boundary repulsive potential field and ameliorating the obstacle repulsive potential field based on the traditional APF model. The model predictive control (MPC) algorithm was combined with the APF model to make the planning model satisfy the kinematic constraints of the vehicle. In addition, a human driver’s obstacle avoidance experiment was implemented based on a six-degree-of-freedom driving simulator equipped with multiple sensors to obtain the drivers’ operation characteristics and provide a basis for parameter confirmation of the planning model. Then, a linear time-varying MPC algorithm was employed to construct the trajectory tracking model. Finally, a co-simulation model based on CarSim/Simulink was established for off-line simulation testing, and the results indicated that the proposed trajectory planning controller and the trajectory tracking controller were more human-like under the premise of ensuring the safety and comfort of the obstacle avoidance operation, providing a foundation for the development of AVs.

Fault-Tolerant Model Predictive Control Algorithm for Path Tracking of Autonomous Vehicle.

The fault detection and isolation are very important for the driving safety of autonomous vehicles. At present, scholars have conducted extensive research on model-based fault detection and isolation algorithms in vehicle systems, but few of them have been applied for path tracking control. This paper determines the conditions for model establishment of a single-track 3-DOF vehicle dynamics model and then performs Taylor expansion for modeling linearization. On the basis of that, a novel fault-tolerant model predictive control algorithm (FTMPC) is proposed for robust path tracking control of autonomous vehicle. First, the linear time-varying model predictive control algorithm for lateral motion control of vehicle is designed by constructing the objective function and considering the front wheel declination and dynamic constraint of tire cornering. Then, the motion state information obtained by multi-sensory perception systems of vision, GPS, and LIDAR is fused by using an improved weighted fusion algorithm based on the output error variance. A novel fault signal detection algorithm based on Kalman filtering and Chi-square detector is also designed in our work. The output of the fault signal detector is a fault detection matrix. Finally, the fault signals are isolated by multiplication of signal matrix, fault detection matrix, and weight matrix in the process of data fusion. The effectiveness of the proposed method is validated with simulation experiment of lane changing path tracking control. The comparative analysis of simulation results shows that the proposed method can achieve the expected fault-tolerant performance and much better path tracking control performance in case of sensor failure.

Decision Making, Planning, and Control Strategies for Intelligent Vehicles

The intelligent vehicle will play a crucial and essential role in the development of the future intelligent transportation system, which is developing toward the connected driving environment, ultimate driving safety, and comforts, as well as green efficiency. While the decision making, planning, and control are extremely vital components of the intelligent vehicle, these modules act as a bridge, connecting the subsystem of the environmental perception and the bottom-level control execution of the vehicle as well. This short book covers various strategies of designing the decision making, trajectory planning, and tracking control, as well as share driving, of the human-automation to adapt to different levels of the automated driving system. More specifically, we introduce an end-to-end decision-making module based on the deep Q-learning, and improved path-planning methods based on artificial potentials and elastic bands which are designed for obstacle avoidance. Then, the optimal method based on the convex optimization and the natural cubic spline is presented. As for the speed planning, planning methods based on the multi-object optimization and high-order polynomials, and a method with convex optimization and natural cubic splines, are proposed for the non-vehicle-following scenario (e.g., free driving, lane change, obstacle avoidance), while the planning method based on vehicle-following kinematics and the model predictive control (MPC) is adopted for the car-following scenario. We introduce two robust tracking methods for the trajectory following. The first one, based on nonlinear vehicle longitudinal or path-preview dynamic systems, utilizes the adaptive sliding mode control (SMC) law which can compensate for uncertainties to follow the speed or path profiles. The second one is based on the five-degrees-of-freedom nonlinear vehicle dynamical system that utilizes the linearized time-varying MPC to track the speed and path profile simultaneously. Toward human-automation cooperative driving systems, we introduce two control strategies to address the control authority and conflict management problems between the human driver and the automated driving systems. Driving safety field and game theory are utilized to propose a game-based strategy, which is used to deal with path conflicts during obstacle avoidance. Driver's driving intention, situation assessment, and performance index are employed for the development of the fuzzy-based strategy. Multiple case studies and demos are included in each chapter to show the effectiveness of the proposed approach. We sincerely hope the contents of this short book provide certain theoretical guidance and technical supports for the development of intelligent vehicle technology.

Autonomous Vehicle Trajectory Following: A Flatness Model Predictive Control Approach With Hardware-in-the-Loop Verification

Trajectory following of autonomous vehicle is a challenging task because of the multiple constraints imposed on the plant. Therefore, Model Predictive Control (MPC) is becoming prevail in vehicle motion control as it can explicitly handle system constraints. However, MPC, grounded in real-time iterative optimization, entails a considerable computational burden for current electronic control units. To mitigate the MPC execution load, a popular strategy is to linearize the original (nonlinear) system around the current working point and then design a Linear Time-Varying MPC (LTVMPC). Nevertheless, the successive linearization introduces extra modeling errors, which may impair the control performance. Indeed, if the plant model satisfies the `differential flatness' condition, it can be exactly linearized to the Brunovsky's canonical form. In contrast to the LTV model, this newly appeared linear form reserves all the nonlinear features of the native plant model. Based on this equivalent linear system, a Flatness Model Predictive Controller (FMPC) can be formulated. FMPC on the one hand, improves the control performance over an LTVMPC because it avoids extra modeling errors from the local linearization. On the other hand, it entails a much lighter computational load versus a nonlinear MPC thanks to its linear nature. Real-time simulations conducted on a hardware-in-the-loop system indicate the advantages of the proposed FMPC in autonomous vehicle trajectory following.

Degradation-conscious control for enhanced lifetime of automotive polymer electrolyte membrane fuel cells

A linear time varying model predictive control (LTV-MPC) framework is developed for degradation-conscious control of automotive polymer electrolyte membrane (PEM) fuel cell systems. A reduced-order nonlinear model of the entire system is derived first, including the reactant and coolant supply subsystems and the fuel cell stack. This nonlinear model is then successively linearized about the current operating point to obtain a linear model. The linear model is utilized to formulate the control problem using a rate-based MPC formulation. The controller objective is to ensure offset-free tracking of the power demand, while maximizing the overall system efficiency and enhancing its durability. To this end, the fuel consumption and the power loss due to auxiliary equipment are minimized. Moreover, the internal states of the fuel cell stack are constrained to avoid harmful conditions that are known stressors of the fuel cell components. Membrane dry-out, rapid changes in the membrane hydration, and reactant starvation are among the stressors considered in this work. However, the framework can accommodate further lifetime indicators as needed. Simulation-based studies showcase the utility of the proposed control framework in meeting the outlined objectives.

Vehicle Yaw Stability Control at the Handling Limits Based on Model Predictive Control

This study proposes a double linear model predictive control (DLMPC) structure to improve the tyre force utilization of active front steering (AFS) vehicle at the handing limits. The DLMPC structure consists of a linear model predictive control (LMPC) and a linear time-varying model predictive control (LTV-MPC). During normal driving conditions, the AFS adopts LMPC to control the vehicle. When vehicle running at the handing limits, the tyre force is near saturation, LTV-MPC is activated to prevent tyre force from entering unstable region. The proposed DLMPC controller can reflect the nonlinear dynamic characteristic of tyres by the expression design of tyre force. Double lane change and sine with dwell maneuver tests are provided to demonstrate the effectiveness and feasibility of the DLMPC controller. Results corroborate that the proposed DLMPC controller can fully exploit the potential of AFS and maintain the yaw stability of the vehicle at the handling limits.

Quaternion based linear time-varying model predictive attitude control for satellites with two reaction wheels

Attitude control of a satellite having only two reaction wheels is a challenging issue. To address this problem, previously published researches considered some simplifying assumptions on the satellites such as diagonality of the moment of the inertia matrix. On the other hand, in some works, the total angular momentum of the satellite is assumed to be zero. In this paper, a linear time-variant model predictive control (LTV MPC) is designed to control a satellite with two reaction wheels. This control method can be applied to a satellite with a non-diagonal inertial matrix in the presence of external torques, to rotate the satellite toward the desired directions in the space and orbit. The simulations results show that this method has a small amount of computational cost and enables an under-actuated satellite to perform large real-time maneuvers with acceptable accuracy.

Model Predictive Control with Time Varying Parameters for Plasma Shape and Current in a Tokamak

Synthesis and modeling of the advanced time-varying magnetic control system for plasma shape and current on the base of the Model Predictive Control principle in a tokamak is considered. The study was done for the Globus-M2 tokamak (Ioffe Institute, St. Petersburg, RF). The system presented has a hierarchical structure with a time-varying Model Predictive Controller at the top level and robust time-invariant controllers at the low level. The approach of adaptation of the plasma magnetic axis position to the shape parameters is used to resolve the contradiction between plasma position and shape. Numerical modeling of the control system synthesized has shown the efficiency of the proposed approach and a possibility to apply it in physical experiments.

Trajectory Tracking Control Algorithm for Autonomous Vehicle Considering Cornering Characteristics

Trajectory tracking control is a key technology in the research and development of autonomous vehicles. With the aim of addressing problems such as low control accuracy and poor real-time performance, which can occur easily when an autonomous vehicle avoids obstacles, this research focuses on the trajectory tracking control algorithm for autonomous vehicle considering cornering characteristics. First, the vehicle dynamics model and tire model are established through appropriate simplification. Then, based on the basic principle of model predictive control, a linear time-varying model predictive controller (LTV MPC) that considers the cornering characteristics is designed and optimized. Finally, using CarSim and MATLAB/Simulink software, a joint simulation model is established and the trajectory tracking performance of the controlled vehicle under different vehicle speeds and road adhesion conditions are tested through simulation experiments in combination with the double-shift line reference trajectory. The simulation results show the LTV MPC controller that considers cornering characteristics has good self-adaptability under complicated and severe working conditions, and no cases, such as car sideslip or track departure, were observed. Compared with other controllers and algorithms, the designed trajectory tracking controller has remarkable comprehensive performance, exhibits superior robustness and anti-interference ability, and significant improvements in the trajectory tracking control accuracy and real-time performance. The proposed control algorithm is of great importance in improving the tracking stability and driving safety of autonomous vehicles under complex extreme conditions and conducive to the further development and improvement of the technological level of intelligent vehicle driving assistance.

Model Predictive Trajectory Tracking Control of Electro-Hydraulic Actuator in Legged Robot With Multi-Scale Online Estimator

This paper addresses the trajectory tracking problem for constrained high dynamic electro-hydraulic actuator in the presence of time-varying parameters, high frequency external load interference, measurement noise and some unmeasurable states. An adaptive robust optimal control scheme is proposed for the electro-hydraulic actuator in legged robot. The framework of our presented scheme is based on a linear time-varying model predictive controller (LTV-MPC) embedded with a multi-scale online estimator (MEKF). With fast- varying and slow- varying time scales, the MEKF part is used not only for measurable states filtering and unmeasurable states estimation, but also for time-varying parameters and external load interference estimation, which will be integrated into the mpc model in real time. The LTV-MPC part is a trajectory tracking controller designed by constrained MPC with an approximate high-precision real-time model and a rapidly solved cost function, which guarantees that the input and output constraints are satisfied during the receding horizon and optimal control process. Finally, with a series of highly dynamic conditions, the comparison experiment results show that the proposed controller has a simple design process, strong adaptive robust performance and trajectory tracking performance, which verifies the effectiveness of the control scheme.

Trajectory Tracking Control for Four-Wheel Independent Drive Intelligent Vehicle Based on Model Predictive Control

For four-wheel independent drive intelligent vehicle, the Model Predictive Control (MPC) is adopted to design the trajectory tracking controller through active steering and four-wheel independent drive/brake. The control objective is to follow a desired trajectory while taking into account the control actuator constraints and vehicle dynamic stability constraints. To reduce the computational complexity, a linear time-varying model predictive controller is designed to linearize the nonlinear vehicle model locally at each sampling point. The co-simulation of CarSim/Simulink shows that the designed controller has high tracking accuracy on the basis of ensuring vehicle stability and strong robustness to vehicle velocity and road adhesion coefficient. The trajectory tracking accuracy based on MPC is better than that of the preview driver model (PDM).

Path Tracking Control Based on the Prediction of Tire State Stiffness Using the Optimized Steering Sequence

This study proposes a linear time-varying model predictive control method based on tire state stiffness prediction for the path tracking using a steering decision sequence in a prediction horizon. A nonlinear UniTire model is employed to represent the nonlinear features of vehicle dynamics in critical situations. And the changing trend of tire state stiffness over the prediction horizon is constructed based on the steering decision sequence, which is the optimized solution of the previous execution step by the controller. Moreover, a method of adjusting the tire state stiffness is proposed to address the jittering in the process of linearization. Meanwhile, a nonlinear model predictive controller and a traditional linear time-varying model predictive controller are designed to verify the effectiveness of the proposed linearization method. Experimental results clearly show that this linearization method can considerably improve vehicle stability under extreme conditions.

Linear Time-Varying Model Predictive Control for Automated Vehicles: Feasibility and Stability under Emergency Lane Change

In this work, we present a novel approach based on linear matrix inequalities to design a linear-time varying model predictive controller for a nonlinear system with guaranteed stability. The proposed method utilizes a multi-model description to model the nonlinear system where the dynamics is represented by a group of linear-time invariant plants, which makes the resulting optimization problem easy to solve in real-time. In addition, we apply the control invariant set designed as the final stage constraint to bound the additive disturbance introduced to the plant by other subsystems interfacing with the controller. We show that the persistent feasibility is ensured with the presence of such constraint on the disturbance of the specified kind. The proposed method is then put into the context of emergency lane change for steering control of automated vehicles and its performance is verified via numerical evaluation.

Time-Varying Model Predictive Control of a Reversible-SOC Energy-Storage Plant Based on the Linear Parameter-Varying Method

Hydrogen conversion plants based on reversible solid oxide cells (rSOCs) provide a potential solution for large-scale energy storage to facilitate renewable integration. When operating an rSOC plant, the security and performance should be monitored at all times, including the steady-state periods and the transient processes connecting them. Model predictive control (MPC) is an appropriate method for this problem. This paper presents a comprehensive rSOC plant model to describe the multiscale dynamics (such as temperature and mass flows) under both fuel cell and electrolysis modes. Then, a time-varying MPC strategy based on a linear parameter-varying prediction model is proposed to provide fast control to the nonlinear rSOC plant. A numerical case is simulated to validate the effects of the proposed MPC strategy. The results suggest that the automatic coordination of actuators ensures consistent stack security, improves both short-term tracking and long-term production performance, and ultimately benefits the plant economically in practical operation.

Active steering control for autonomous vehicles based on a driver-in-the-loop platform: A case study of collision avoidance

Leveraging the advancements in sensor and mapping technologies, the collision-free autonomous vehicle becomes possible in the future. In this article, a case study of collision avoidance by active steering control is presented and verified by a driver-in-the-loop platform. The proposed control system integrates a risk assessment algorithm and a hierarchical model predictive control approach to ensure a safe driving. First, a fuzzy logic is used to estimate the potential conflict. Besides, a nonlinear model predictive control is introduced in the upper layer of the model predictive controller to generate a collision-free trajectory. Furthermore, the lower layer determines the optimal steering angle based on the linear time-variant model predictive control to follow the replanning path. The performance of the controller has been evaluated in the real-time driver-in-the-loop test. The results show that the autonomous vehicle is able to avoid the collision with the surrounding vehicle that is operated by a real driver, and the performance of collision avoidance is improved by means of the risk assessment.

Trajectory Tracking of Autonomous Vehicle with the Fusion of DYC and Longitudinal\u2013Lateral Control

The current research of autonomous vehicle motion control mainly focuses on trajectory tracking and velocity tracking. However, numerous studies deal with trajectory tracking and velocity tracking separately, and the yaw stability is seldom considered during trajectory tracking. In this research, a combination of the longitudinal–lateral control method with the yaw stability in the trajectory tracking for autonomous vehicles is studied. Based on the vehicle dynamics, considering the longitudinal and lateral motion of the vehicle, the velocity tracking and trajectory tracking problems can be attributed to the longitudinal and lateral control. A sliding mode variable structure control method is used in the longitudinal control. The total driving force is obtained from the velocity error in order to carry out velocity tracking. A linear time-varying model predictive control method is used in the lateral control to predict the required front wheel angle for trajectory tracking. Furthermore, a combined control framework is established to control the longitudinal and lateral motions and improve the reliability of the longitudinal and lateral direction control. On this basis, the driving force of a tire is allocated reasonably by using the direct yaw moment control, which ensures good yaw stability of the vehicle when tracking the trajectory. Simulation results indicate that the proposed control strategy is good in tracking the reference velocity and trajectory and improves the performance of the stability of the vehicle.

Vehicle Stability Control Based on Model Predictive Control Considering the Changing Trend of Tire Force Over the Prediction Horizon

This paper proposes a vehicle stability control approach based on time-varying model predictive control to enhance the handling and stability of active front steering vehicle at the vehicle dynamics limits. The prediction equation of the proposed controller is designed based on the changing trend of tire force over the prediction horizon. Therefore, the prediction equation can represent the nonlinear characteristics in the process of prediction. To verify the effectiveness of the proposed control strategy, nonlinear model predictive controller, and previous linear time-varying model predictive controller are designed and used for comparison. Simulation experiments are performed based on the cosimulation environment of MATLAB and CarSim. At the handling limits, the control performance of the proposed controller exhibited significant improvement compared with the previous one. Moreover, its performance was close to that of the nonlinear controller, whereas its calculation speed is much faster than that of the nonlinear model predictive controller.

Tire State Stiffness Prediction for Improving Path Tracking Control During Emergency Collision Avoidance

In this study, a model predictive path tracking control method based on the prediction of tire state stiffness is proposed to improve the path tracking performance at the limit of vehicle dynamics. Considering the influence of the nonlinear properties of tire force on vehicle dynamics, a nonlinear UniTire model is established, based on which a state stiffness 3D look-up table is designed to linearize the nonlinear tire model. The tire state stiffness in the prediction horizon is predicted by the vehicle motion model using the reference path information. A new linear time-varying path tracking control model in the prediction horizon is designed based on the predicted tire state stiffness. A nonlinear model predictive controller and a traditional linear time-varying model predictive controller are also designed and compared with the proposed method to verify the effectiveness and advantage of the latter. Results clearly show an improved control performance of the proposed method compared with the traditional method under the limit condition. Moreover, the calculation speed of the proposed method is faster than that of the nonlinear model predictive control method.

Experimental validation of model predictive control stability for autonomous driving

This paper addresses the design of time-varying model predictive control of an autonomous vehicle in the presence of input rate constraints such that closed-loop stability is guaranteed. Stability is proved via Lyapunov techniques by adding a terminal state constraint and a terminal cost to the controller formulation. The terminal set is the maximum positive invariant set of a multi-plant description of the vehicle linear time-varying model. The terminal cost is an upper-bound on the infinite cost-to-go incurred by applying a linear–quadratic regulator control law. The proposed control design is experimentally tested and successfully stabilizes an autonomous Scania construction truck in an obstacle avoidance scenario.

An optimal hierarchical framework of the trajectory following by convex optimisation for highly automated driving vehicles

ABSTRACTThis paper presents a hierarchical trajectory following framework for SAE-level 2/3 automatic driving by convex optimisation, which aims for daily common driving manoeuvres with low traffics on the highway, such as free driving, adaptively following and overtaking. More specifically, it includes several combined functionalities of lane keeping, adaptive following, active obstacle avoidance and speed adaptation. The trajectory-planning module would generate the optimal path and speed profiles for the structure road (e.g. highway) with different geometric shapes, by using the natural cubic spline and convex optimisation approach. While modules of trajectory following or adaptive following are realised by a linearised time-varying model predictive control method. It is expected that the proposed framework could improve the driving safety, as well as the driving efficiency and driving comforts simultaneously. Thus, typical scenarios are designed to verify the effectiveness of the proposed trajectory following framework. Simulation results demonstrate that it could successfully deal with daily manoeuvres on a straight or curved highway without human driver's interventions.