Linear Time-varying Model Predictive Control Research Articles

Relative navigation control of articulated vehicle based on LTV-MPC

The automation of the articulated vehicle is an important trend of the intelligent transportation system in the mining industry. And the relative navigation is a key technology to automatic vehicles. One of the challenges in the relative navigation of the articulated vehicle is that the system constraints may cause the actuator saturation and other problems. In order to solve these problems, this paper presents a relative navigation control method based on linear time varying model predictive control (LTV-MPC). This control method can explicitly take the system constraints into account. The performance of the controller is verified by simulation and experiment. The results show that the articulated vehicle with the LTV-MPC controller can track the target heading direction, the steady-state error is less than 0.3 rad. The relative navigation controller based on LTV-MPC can be used to improve the automatic driving performance of the articulated vehicle.

Fault-Tolerant Control for Intelligent Electrified Vehicles Against Front Wheel Steering Angle Sensor Faults During Trajectory Tracking

Steer-by-Wire (SBW) systems are an integral and essential component of intelligent electrified vehicles and are critical to ensure safe vehicle operations. In this paper, a fault-tolerant control method for SBW is proposed to mitigate the adverse influence of front wheel steering angle sensor faults based on the Kalman filtering technique. First, a linearized vehicle model is derived based on tire characteristics and is further combined with a steering actuator model to provide the modelling foundation for estimating the front wheel steering angle. Considering multi-source noises and their significant influence on the front wheel steering angle sensor, the Butterworth filter is employed to filter out the high-frequency noises. The front wheel steering angle estimation is realized by incorporating the measurements of the yaw rate and lateral acceleration of vehicle and the current of steering motor. In particular, a dynamic threshold mechanism is adopted to activate the fault diagnosis and fault-tolerant compensation based on the residual theory. Finally, a linear time-varying model predictive controller is presented to execute the trajectory tracking task for an intelligent electrified vehicle. The effectiveness of the proposed scheme is verified under the single lane change and double lane change maneuvers during the trajectory tracking.

Trajectory planning and tracking control of unmanned ground vehicle leading by motion virtual leader on expressway

Formation driving can effectively solve the problem of driving efficiency and safety of unmanned ground vehicles (UGVs) on expressways. This study introduces a trajectory planning and tracking control method from initial position to its motion virtual leader in formation driving. In order to reduce the disturbance to the surrounding UGVs, trajectory planning is divided into two stages: steady speed tracking stage and parameter value matching stage. A tracking controller combined with a trajectory planner is designed to track the reference trajectory accurately. To ensure calculation speed and accuracy, a nonlinear model-predictive control model is used in the trajectory planner, and the tracking controller is based on the linear time-varying model-predictive control (LTV MPC) model. Simulations are carried out with Carsim and MATLAB/Simulink, and the simulation results and comparative analysis show that the planned trajectory is feasible and can effectively avoid static and moving obstacles. Compared with the Stanley controller, the LTV MPC controller has the advantages of faster convergence speed, better stability and accurately tracking.

On the Distributed Path Planning of Multiple Autonomous Vehicles Under Uncertainty Based on Model-Predictive Control and Convex Optimization

In this article, a fully distributed control structure named distributed linear time-varying model predictive controller is proposed for motion control of multiple vehicles in dynamic environments with uncertainty resources based on local communication and local controllers. Efficient operation of this structure in such real-world conditions needs reasoning about the future and the uncertainties over environmental objects; therefore, future evolution of vehicles and environmental objects is accounted as a planning strategy. A general planning framework is proposed, which integrates estimation, prediction, and planning. Simulation results for different dynamic scenarios demonstrate the benefit and applicability of this approach.

Energy Management of the Power-Split Hybrid Electric City Bus Based on the Stochastic Model Predictive Control

The energy management strategy of hybrid electric vehicles is of significant importance to improve the fuel economy. In this regard, two energy management strategies are designed for power-split hybrid electric city bus (HECB), which are based on the linear time-varying stochastic model predictive control (LTV-SMPC) and stochastic model predictive control based on Pontriagin’s minimum principle (PMP-SMPC). In the present study, the Markov chain and long short-term memory (LSTM) forecast demand torque and velocity respectively are applied to establish a combination forecast model. Then several processes, including linear approximation, processing simplified control model, the proposed nonlinear vehicle model is converted into a linear time-varying model. Meanwhile, the energy management problem in a linear quadratic programming problem is solved. Considering linearization error and limitations of the quadratic optimization, Pontriagin’s minimum principle (PMP) is applied to optimize the nonlinear model predictive control. Based on the reference theory, the range of coordinated variables is derived, and the optimal coordination variable is searched by dichotomy to realize the rolling optimization of the model predictive control (MPC). Finally, the effectiveness of the proposed energy management strategy is verified by simulating several case studies. Obtained results show that compared with the rule-based (RB) control strategy, the fuel economy of LTV-SMPC and PMP-SMPC increases by 8.79% and 14.42%, respectively. Meanwhile, it is concluded that the two strategies have real-time computing potential.

Modeling, Simulation, and Vision-/MPC-Based Control of a PowerCube Serial Robot

A model predictive control (MPC) scheme for a Schunk PowerCube robot is derived in a structured step-by-step procedure. Neweul-M2 provides the necessary nonlinear model in symbolical and numerical form. To handle the heavy online computational burden concerning the derived nonlinear model, a linear time-varying MPC scheme is developed based on linearizing the nonlinear system concerning the desired trajectory and the a priori known corresponding feed-forward controller. Camera-based systems allow sensing of the robot on the one hand and monitoring the environments on the other hand. Therefore, a vision-based MPC is realized to show the effects of vision-based control feedback on control performance. A semi-automatic trajectory planning is used to perform two meaningful experimental studies in which the advantages and restrictions of the proposed (vision-based) linear time-varying MPC scheme are pointed out. Everything is implemented on a slim, low-cost control system with a standard laptop PC.

Modeling, simulation, and vision-/MPC-based control of a PowerCube serial robot

A model predictive control (MPC) scheme for a Schunk PowerCube robot is derived in a structured step-by-step procedure. Neweul-M2 provides the necessary nonlinear model in symbolical and numerical form. To handle the heavy online computational burden concerning the derived nonlinear model, a linear time-varying MPC scheme is developed based on linearizing the nonlinear system concerning the desired trajectory and the a priori known corresponding feed-forward controller. Camera-based systems allow sensing of the robot on the one hand and monitoring the environments on the other hand. Therefore, a vision-based MPC is realized to show the effects of vision-based control feedback on control performance. A semi-automatic trajectory planning is used to perform two meaningful experimental studies in which the advantages and restrictions of the proposed (vision-based) linear time-varying MPC scheme are pointed out. Everything is implemented on a slim, low-cost control system with a standard laptop PC.

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.

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.

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.

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).

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.

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.

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.