As deployment of automated vehicles increases, so does the rate at which they are exposed to critical traffic situations. Such situations, e.g. a late detected pedestrian in the vehicle path, require operation at the handling limits in order to maximize the capacity to avoid an accident. Also, the physical limitations of the vehicle typically vary in time due to local road and weather conditions. In this paper, we tackle the problem of trajectory planning and control at the limits of handling under time varying constraints, by adapting to local traction limitations. The proposed method is based on Real Time Iteration Sequential Quadratic Programming (RTI-SQP) augmented with state space sampling, which we call Sampling Augmented Adaptive RTI-SQP (SAA-SQP). Through extensive numerical simulations we demonstrate that our method increases the vehicle's capacity to avoid late detected obstacles compared to the traditional planning tracking approaches, as a direct consequence of safe operating constraint adaptation in real time.
Highly automated road vehicles need the capability of stopping safely in a situation that disrupts continued normal operation, e.g. due to internal system faults. Motion planning for safe stop differs from nominal motion planning, since there is not a specific goal location. Rather, the desired behavior is that the vehicle should reach a stopped state, preferably outside of active lanes. Also, the functionality to stop safely needs to be of high integrity. The first contribution of this paper is to formulate the safe stop problem as a benchmark optimal control problem, which can be solved by dynamic programming. However, this solution method cannot be used in real-time. The second contribution is to develop a real-time safe stop trajectory planning algorithm, based on selection from a precomputed set of trajectories. By exploiting the particular properties of the safe stop problem, the cardinality of the set is decreased, making the algorithm computationally efficient. Furthermore, a monitoring based architecture concept is proposed, that ensures dependability of the safe stop function. Finally, a proof of concept simulation using the proposed architecture and the safe stop trajectory planner is presented. 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.