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.
From a control perspective, the fundamental building blocks for automatic racing can be grouped into three categories: drift control, reference tracking, and path planning. Research associated with the first group focuses on gaining a better understanding of the behavior of the car near the friction limit for designing safety control systems that try to prevent loss-of-control accidents. By analyzing the nonlinear car model, it can be shown that steady state motions corresponding to drifting can be generated, see e.g. @cite_8 and @cite_13 . As these approaches are not designed for trajectory tracking, the controlled car drifts in a circle, which represents a steady state drift equilibrium.
@cite_13 @cite_8
1578293866 1974358072 2018461753 2335306738
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 paper presents simple analytical techniques that are used to understand and control high sideslip drift manoeuvres of road vehicles. These are manoeuvres in which a skilled driver stabilises a vehicle beyond its limits of handling, an operating regime responsible for major safety concerns in everyday driving. An analysis of the equilibria of a bicycle model with nonlinear tyres reveals the existence of unstable 'drift equilibria' corresponding to cornering at high sideslip angle in a countersteer configuration. Equipped with this information, linearisation about a desired drift equilibrium is used to design a controller that stabilises the vehicle at the equilibrium. The controller is subsequently implemented on a steer- and drive-by-wire testbed and successfully used to achieve autonomous drifts. 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. The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal control problem is typically computationally expensive and infeasible for real-time trajectory planning. This paper presents an iterative algorithm that divides the path generation task into two sequential subproblems that are significantly easier to solve. Given an initial path through the race track, the algorithm runs a forward-backward integration scheme to determine the minimum-time longitudinal speed profile, subject to tire friction constraints. With this fixed speed profile, the algorithm updates the vehicle's path by solving a convex optimization problem that minimizes the resulting path curvature while staying within track boundaries and obeying affine, time-varying vehicle dynamics constraints. This two-step process is repeated iteratively until the predicted lap time no longer improves. While providing no guarantees of convergence or a globally optimal solution, the approach performs very well when validated on the Thunderhill Raceway course in Willows, CA. The predicted lap time converges after four to five iterations, with each iteration over the full 4.5 km race course requiring only thirty seconds of computation time on a laptop computer. The resulting trajectory is experimentally driven at the race circuit with an autonomous Audi TTS test vehicle, and the resulting lap time and racing line is comparable to both a nonlinear gradient descent solution and a trajectory recorded from a professional racecar driver. The experimental results indicate that the proposed method is a viable option for online trajectory planning in the near future.