Summary This paper describes autonomous racing of RC race cars based on mathematical optimization. Using a dynamical model of the vehicle, control inputs are computed by receding horizon based controllers, where the objective is to maximize progress on the track subject to the requirement of staying on the track and avoiding opponents. Two different control formulations are presented. The first controller employs a two-level structure, consisting of a path planner and a nonlinear model predictive controller (NMPC) for tracking. The second controller combines both tasks in one nonlinear optimization problem (NLP) following the ideas of contouring control. Linear time varying models obtained by linearization are used to build local approximations of the control NLPs in the form of convex quadratic programs (QPs) at each sampling time. The resulting QPs have a typical MPC structure and can be solved in the range of milliseconds by recent structure exploiting solvers, which is key to the real-time feasibility of the overall control scheme. Obstacle avoidance is incorporated by means of a high-level corridor planner based on dynamic programming, which generates convex constraints for the controllers according to the current position of opponents and the track layout. The control performance is investigated experimentally using 1:43 scale RC race cars, driven at speeds of more than 3 m s and in operating regions with saturated rear tire forces (drifting). The algorithms run at 50 Hz sampling rate on embedded computing platforms, demonstrating the real-time feasibility and high performance of optimization-based approaches for autonomous racing. Copyright © 2014 John Wiley & Sons, Ltd.
Reference tracking controllers usually are designed to operate the vehicle within the linear tire force region for maximum safety and robustness. Approaches based on NMPC, which allows one to incorporate the latter constraint in a systematic manner, deal with the nonlinearities of the model either directly by a nonlinear programming (NLP) solver @cite_5 , or use LTV @cite_16 or piece-wise affine (PWA) approximations @cite_9 , resulting in a convex quadratic program (QP) or a mixed-integer QP, respectively. Approaches without optimization in real-time include nonlinear robust control @cite_32 and flatness-based control @cite_24 , which however lack the ability to incorporate constraints. One approach that is explicitly designed for operating with saturated tire forces is @cite_15 , where the center of percussion (CoP) is used to design a state feedback steering controller for reference tracking. At the CoP, the rear tire forces do not influence the dynamics by definition, which allows for a simple linear steering controller.
@cite_9 @cite_32 @cite_24 @cite_5 @cite_15 @cite_16
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Summary This paper describes autonomous racing of RC race cars based on mathematical optimization. Using a dynamical model of the vehicle, control inputs are computed by receding horizon based controllers, where the objective is to maximize progress on the track subject to the requirement of staying on the track and avoiding opponents. Two different control formulations are presented. The first controller employs a two-level structure, consisting of a path planner and a nonlinear model predictive controller (NMPC) for tracking. The second controller combines both tasks in one nonlinear optimization problem (NLP) following the ideas of contouring control. Linear time varying models obtained by linearization are used to build local approximations of the control NLPs in the form of convex quadratic programs (QPs) at each sampling time. The resulting QPs have a typical MPC structure and can be solved in the range of milliseconds by recent structure exploiting solvers, which is key to the real-time feasibility of the overall control scheme. Obstacle avoidance is incorporated by means of a high-level corridor planner based on dynamic programming, which generates convex constraints for the controllers according to the current position of opponents and the track layout. The control performance is investigated experimentally using 1:43 scale RC race cars, driven at speeds of more than 3 m s and in operating regions with saturated rear tire forces (drifting). The algorithms run at 50 Hz sampling rate on embedded computing platforms, demonstrating the real-time feasibility and high performance of optimization-based approaches for autonomous racing. Copyright © 2014 John Wiley & Sons, Ltd. This article presents a new kind of navigation system for agricultural machines. The focus is on trajectory control where a Nonlinear Model Predictive path tracking for tractor and trailer system is presented. The experiments of the proposed method are carried out by using real agricultural machines in real environments. The agricultural objective is to drive so that swaths are exactly side-by-side, without overlapping or gaps. Hence, the objective of this research was to control the lateral position of the towed implement and to keep it close to the adjacent driving line. The adjacent driving line was recognized locally by using a 2D laser scanner. The local measurement and global position information was merged with the help of an Extended Kalman Filter (EKF). The measurement of the heading by GPS was improved by using an inertial measurement unit and a separate EKF filter. The position of the implement was controlled by steering the tractor and by the use of a hydraulically controlled joint. Because there were two actuators which affected the position of the implement, the problem was a multivariable control problem. Nonlinear Model Predictive Control (NMPC) was used to accomplish the navigation task. The goal was to build a system, which is able to have at least the same accuracy as a human driver. The sufficient accuracy requirement was at most 10cm lateral error at a speed of 12km h. The results presented in the article show that the goal was met and NMPC is a feasible method for accurate path tracking. Further investigation is, however, needed to adapt the method to other kinds of agricultural machines. This paper presents a Robust Constrained Learning-based Nonlinear Model Predictive Control RC-LB-NMPC algorithm for path-tracking in off-road terrain. For mobile robots, constraints may represent solid obstacles or localization limits. As a result, constraint satisfaction is required for safety. Constraint satisfaction is typically guaranteed through the use of accurate, a priori models or robust control. However, accurate models are generally not available for off-road operation. Furthermore, robust controllers are often conservative, since model uncertainty is not updated online. In this work our goal is to use learning to generate low-uncertainty, non-parametric models in situ. Based on these models, the predictive controller computes both linear and angular velocities in real-time, such that the robot drives at or near its capabilities while respecting path and localization constraints. Localization for the controller is provided by an on-board, vision-based mapping and navigation system enabling operation in large-scale, off-road environments. The paper presents experimental results, including over 5 km of travel by a 900 kg skid-steered robot at speeds of up to 2.0 m s. The result is a robust, learning controller that provides safe, conservative control during initial trials when model uncertainty is high and converges to high-performance, optimal control during later trials when model uncertainty is reduced with experience. Understanding how a race car driver controls a vehicle at its friction limits can provide insights into the development of vehicle safety systems. In this paper, a race car driver's behaviour inspires the design of an autonomous racing controller. The resulting controller uses the vehicle's centre of percussion (COP) to design feedforward and feedback steering. At the COP, the effects of rotation and translation from the rear tire force cancel each other out; consequently, the feedforward steering command is robust to the disturbances from the rear tire force. Using the COP also simplifies the equations of motion, as the vehicle's lateral motion is decoupled from the vehicle's yaw motion and highlights the challenge of controlling a vehicle when the rear tires are highly saturated. The resulting dynamics can be controlled with a linear state feedback based on a lane-keeping system with additional yaw damping. Utilising Lyapunov theory, the closed-loop system is shown to remain stable even when the rear tires are highly saturated. The experimental results demonstrate that an autonomous vehicle can operate at its limits while maintaining a minimal lateral error.