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.
@cite_9: In this paper the concept of Hybrid Parameter-Varying Model Predictive Control (HPV-MPC) is applied for autonomous vehicle steering. Parameter-varying in the MPC context means that a prediction model with non-constant, parameter-varying system matrices is employed. In the investigated scenarios, the displacement of a car on an icy road due to a side wind gust shall be mitigated, and a double lane-change maneuver shall be performed autonomously. In order to explore a possible reduction of online computations and the inherent degradation of control performance, the nonlinear model of the lateral dynamics is approximated in various ways. A comparison between controllers using prediction models varying from the full nonlinear model, as an indication for the maximal achievable performance, to a linear model was performed. Particular emphasis was put on the hybrid parameter-varying prediction model, to investigate their potential in terms of computational effort and control performance.
@cite_32: For an automatic steering problem of a city bus the reference maneuvers and specifications are introduced. The robustness problem arises from large variations in velocity, mass, and road-tire contact. Two controller structures, both with feedback of the lateral displacement and the yaw rate, are introduced: a linear controller and a nonlinear controller. The controller parameters are first hand-tuned and then refined by performance vector optimization. Both controllers meet all specifications. Their relative merits are analyzed in simulations for four typical driving maneuvers. >
@cite_24: The central issue of this contribution is the discussion of the differential flatness of the planar holonomic bicycle model. The components of a flat output are given as the lateral and the longitudinal velocity component of a distinguished point located on the longitudinal axis of the vehicle. This property is shown for the front-, rear- and all-wheel driven vehicle, without referring to particular representatives of the functions modelling the lateral tire forces. The clear physical meaning of the flat output is regarded as particularly useful for the control design task. The vehicle dynamics control design is accomplished following the flatness based control theory.
@cite_5: In this paper a novel approach to autonomous steering systems is presented. A model predictive control (MPC) scheme is designed in order to stabilize a vehicle along a desired path while fulfilling its physical constraints. Simulation results show the benefits of the systematic control methodology used. In particular we show how very effective steering manoeuvres are obtained as a result of the MPC feedback policy. Moreover, we highlight the trade off between the vehicle speed and the required preview on the desired path in order to stabilize the vehicle. The paper concludes with highlights on future research and on the necessary steps for experimental validation of the approach.
@cite_15: 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.
@cite_16: In this paper, a model predictive control (MPC) approach for controlling an active front steering system in an autonomous vehicle is presented. At each time step, a trajectory is assumed to be known over a finite horizon, and an MPC controller computes the front steering angle in order to follow the trajectory on slippery roads at the highest possible entry speed. We present two approaches with different computational complexities. In the first approach, we formulate the MPC problem by using a nonlinear vehicle model. The second approach is based on successive online linearization of the vehicle model. Discussions on computational complexity and performance of the two schemes are presented. The effectiveness of the proposed MPC formulation is demonstrated by simulation and experimental tests up to 21 m s on icy roads
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.