Nonlinear MPC-Based Formation Control for Autonomous Ground Vehicles with Dynamic Geometric Patterns

The article studies the trajectory tracking control problem of underactuated marine vehicles via the nonlinear model predictive control (NMPC) strategy, where practical control and state constraints present. It is a well-known challenging issue that the conventional NMPC is not applicable for underactuated marine vehicles, due to the fact that there does not exist a local static continuous state-feedback controller to stabilize the underactuated dynamics. To resolve this issue, this article proposes to construct an auxiliary time-varying tracking controller to aid terminal constraint design in the NMPC framework, where the time-varying tracking controller borrows the ideas from Lyapunov's direct method and backstepping approach. Based on this, a novel NMPC algorithm is designed to ensure trajectory tracking control of underactuated marine vehicles. Furthermore, a systematic parameter design approach is developed. Under the designed parameters, we show that the tracking error system is input-to-state stable (ISS). Finally, the effectiveness of the designed algorithm is verified by thorough simulation and hardware experiments.

Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

This paper develops and experimentally demonstrates an automatic parallel parking control algorithm for autonomous ground vehicles (AGVs). The automatic parallel parking problem is described and fuzzy logic controllers are designed for each step of the parking process. Detailed membership functions and fuzzy reasoning rules are given for each fuzzy logic controller. The parking algorithm is tested by simulation and experimental implementation based on the model of a skid steering autonomous ground vehicle. Both results demonstrate the ability of the developed algorithm to parallel park AGVs in tight spaces.

In this article, we present a quasi-infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable. For such systems, we provide a reference generic offline procedure to compute an incrementally stabilizing feedback with a continuously parameterized quadratic quasi-infinite horizon terminal cost. As a result, we get a nonlinear reference tracking MPC scheme with a valid terminal cost for general reachable reference trajectories without increasing the online computational complexity. The practicality of this approach is demonstrated with a benchmark example.

This paper combines the interval analysis tools with the nonlinear model predictive control (NMPC). The NMPC strategy is formulated based on an uncertain dynamic model expressed as nonlinear ordinary differential equations (ODEs). All the dynamic parameters are identified in a guaranteed way considering the various uncertainties on the embedded sensors and the system’s design. The NMPC problem is solved at each time step using validated simulation and interval analysis methods to compute the optimal and safe control inputs over a finite prediction horizon. This approach considers several constraints which are crucial for the system’s safety and stability, namely the state and the control limits. The proposed controller consists of two steps: filtering and branching procedures enabling to find the input intervals that fulfill the state constraints and ensure the convergence to the reference set. Then, the optimization procedure allows for computing the optimal and punctual control input that must be sent to the system’s actuators for the pendulum stabilization. The validated NMPC capabilities are illustrated through several simulations under the DynIbex library and experiments using an inverted pendulum.

Designing non-linear model predictive control (NMPC) laws for controlling multiple autonomous surface vessels in arbitrary formations in environments containing obstacles are reported in this paper. Two leader-follower decentralized geometrical control schemes that are required for defining a unique two-dimensional formation are considered. A three-degree-of-freedom dynamic model of surface vessels has been used for the controller design. It is assumed that the surface vessels are under-actuated and obstacles are present in the vessels' work environment. The real-time optimization abilities of the NMPC method has been used to improve the response of the unactuated DOF of the vessels and to directly incorporate the local obstacle avoidance into the formation control eliminating the need for an external local obstacle avoidance algorithm. This leads to more effective obstacle avoidance decisions based on the dynamics of the vehicle. The effectiveness the developed control law, even in the presence of model uncertainty and external disturbances are demonstrated via computer simulations.

This paper deals with the application of interval arithmetic to non linear model predictive control (NMPC) problem. The NMPC problem is expressed as a constraints satisfaction problem (CSP) which can be solved by interval analysis techniques. We present the classical interval techniques to build a nonlinear model predictive control law and propose some improvements in order to adapt interval tools to the context of control. Moreover, in order to reduce the pessimism introduced by interval state estimation, we propose a spatial discretisation of the input. These methods are illustrated on a inverted pendulum model.

Reinforcement learning (RL) and approximate dynamic programming (ADP) have been recently studied to solve nonlinear optimal control problems (OCPs) of continuous‐time (CT) systems. However, online learning efficiency and reliability are two major concerns to be further improved. Motivated by the above issues, in this paper we propose a receding‐horizon reinforcement learning (RHRL) algorithm for near‐optimal control of CT systems under control constraints. Different from classic RL and ADP, in the proposed approach, the infinite‐horizon OCP is decomposed as a series of finite‐horizon ones solved with an actor‐critic structure according to the receding horizon strategy, which can improve the online learning efficiency and reliability. The unknown dynamics of the system are identified offline using a sparse kernel‐based neural network structure whose weights are also updated online in the RHRL framework to improve the control performance. Moreover, the convergence of the modeling error is proven. To verify the effectiveness of our approach, we apply the RHRL algorithm to the autonomous ground vehicle for realizing near‐optimal path‐tracking control. Compared with CT model predictive control using a nominal model and other model‐free tracking controllers such as pure pursuit, heuristic dual programming, and the soft actor‐critic algorithm, RHRL performs better in terms of control performance.

In order to decrease computation loads for path following control of autonomous ground vehicles (AGVs), in this article, we aim to design an output-feedback path following controller by using a learning-based least squares support vector machine (LS-SVM) model. The signal transmission delay, which would deteriorates the control performance, is considered as well. First, the LS-SVM model for vehicle path following system is trained. Then, the output-feedback controller subject to stochastic communication delay, which meets the stability condition, is designed for the LS-SVM model. The modeling error and bias terms of LS-SVM model are regarded as the disturbance term. In order to attenuate the effect of disturbance, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> controller is designed for the AGVs to track the target path. Grey wolf optimizer is employed to solve the controller design problem with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance and transform stability condition from bilinear matrix inequality to linear matrix inequality (LMI). Then, we employ efficient LMI toolbox to solve the LMI. To guarantee the effectiveness of proposed controller, characteristics of steering wheel in a hardware-in-loop platform are studied and rate of steering angle is regarded as the actuator constraints for designing controller. Experimental results based on the hardware-in-loop platform have verified the effectiveness of the proposed control strategy.

Velocity-based robust fault tolerant automatic steering control of autonomous ground vehicles via adaptive event triggered network communication

In this paper, we propose a real-time nonlinear model predictive control (NMPC) strategy for stabilization of a vehicle near the limit of lateral acceleration using the rear axle electric torque vectoring configuration of an electric vehicle. A nonlinear four-wheel vehicle model that neglects the wheel dynamics is coupled with a nonlinear tire model to design three MPC strategies of different levels of complexity that are implementable online: one that uses a linearized version of the vehicle model and then solves the resulting quadratic program problem to compute the necessary longitudinal slips on the rear wheels, a second one that employs the real-time iteration scheme on the NMPC problem, and a third one that applies the primal dual interior point method on the NMPC problem instead until convergence. Then, a sliding mode slip controller is used to compute the necessary torques on the rear wheels based on the requested longitudinal slips. After analyzing the relative tradeoffs in performance and computational cost between the three MPC strategies by comparing them against the optimal solution in a series of simulation studies, we test the most promising solution in a high-fidelity environment.

Uncertain characteristics along with unknown exterior disturbances are fundamental issues in the path‐following control of autonomous ground vehicles (AGVs). Here, a novel robust non‐singular terminal sliding mode (NTSM) control method based on a recurrent neural network (RNN) structure is proposed to enhance the path‐following performance of AGVs. First, based on the dynamic model and path‐following model of AGVs, the robust NTSM steering controller is proposed to ensure that the lateral offset converges to zero within a limited time, and concurrently suppresses the chattering phenomenon that occurs in the regular sliding mode control (SMC) strategy. Then, the RNN is applied to approximate the unknown dynamics section of the system online. With an implied feedback loop, its study ability precedes the regular neural network to catch up with the dynamic response. In addition, the adaptive learning algorithms of the parameters in the RNN are derived using the Lyapunov stability theorem and Taylor linearisation technique to ensure the stability of the closed‐loop system. Finally, the robustness and effectiveness of the proposed control approach against parametric uncertainties and unknown external disturbances are verified in the Simulink‐CarSim simulation platform by comparison with selected reported control methods.

This article investigates the problem of event-triggered secure path tracking control of autonomous ground vehicles (AGVs) under deception attacks. To relieve the burden of the shareable vehicle communication network and to improve the tracking performance in the presence of deception attacks, a learning-based event-triggered mechanism (ETM) is proposed. Different from existing ETMs, the triggering threshold of the proposed mechanism can be dynamically adjusted with conditions of the latest vehicle state. Each vehicle in this study is deemed as an agent, under which a novel control strategy is developed for these autonomous agents with deception attacks. With the assistance of Lyapunov stability theory, sufficient conditions are obtained to guarantee the stability and stabilization of the overall system. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed theoretical results.

In this paper, we provide a method for a quadrotor to track a ground moving target (GMT). The least squares method is used to obtain a series of reference trajectories generated by the GMT. The tracking is accomplished by applying a novel nonlinear model predictive control (MPC) scheme. The nonlinear MPC scheme applied can deal with the dynamic trajectory tracking problem of nonlinear systems by using reference generic terminal ingredients. After obtaining the reachable reference trajectories and calculating the terminal ingredients of the nonlinear MPC problem, the nonlinear MPC problem can be solved online to obtain the control inputs that enable the quadrotor to accurately track the GMT. A simulation experiment is conducted to verify the efficacy of this method.

NONLINEAR MODEL PREDICTIVE CONTROL BASED ON SEQUENTIAL MONTE CARLO STATE ESTIMATION