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.
Safe autonomous driving at moderate speeds has been demonstrated for example in the context of Autonomous Highway Systems (AHS) in 1997 @cite_18 within the Californian PATH programme, or in contests such as the DARPA Grand Challenge in 2005 @cite_11 and the Urban Challenge in 2007 @cite_2 by numerous research groups. In these projects, the main goal was do develop autonomous driving systems for public traffic situations. Autonomous racing has received less attention, but impressive advances have been made recently also in this discipline. For instance, a fully autonomous Audi TTS has been reported to race at high speeds in @cite_15 using a trajectory tracking controller, which follows a pre-computed trajectory. However, to the best knowledge of the authors, fully automatic racing including obstacle avoidance in dynamic racing situations has not been demonstrated yet in practice.
@cite_15 @cite_18 @cite_2 @cite_11
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Automated driving within a lane is a fascinating experience already. However, more exiting but also technically more challenging is to dare the next step of automating tactical behavior decisions for lane changes, as well. In this paper, we present our approach for situation assessment in tactical behavior planning for lane changes, whether lane changes are beneficial and or possible. We present a way to tackle perception uncertainties and how to monitor the system's abilities and current skills. This is achieved by a dynamic Bayesian network and an unscented variance transform. Our approach is evaluated not only in a simulation, but also in real traffic. Our implementation has recently been demonstrated to the public in the Audi A7 piloted driving concept vehicle, driving 550 miles from Stanford to Las Vegas to the Consumer Electronics Show (CES) 2015. 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. Recently, automated driving has more and more been transformed from an exciting vision into hands on reality by prototypes. While drivers are used to assistance and maybe even automation for driving within a lane, it is exciting to dare a step ahead: Deciding and executing tactical maneuvers like lane changes in automated vehicles without any human interaction. In this paper, we present our approach for tactical behavior planning for lane changes. We present a way to tackle perception uncertainties and how to achieve provident, prediction-based behavior planning. For this, we introduce a novel framework to plan in high-dimensional, mixed-integer state spaces in real-time. Our approach is evaluated not only in simulation, but also in real traffic. The implementation has recently been demonstrated to the public in the Audi A7 piloted driving concept vehicle, driving from Stanford to the Consumer Electronics Show (CES) 2015 in Las Vegas. 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.