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.
Research in motion planning and control at the handling limits was influenced by research in the racing community. Through the use of nonlinear programming, @cite_28 were able to compute the time-optimal speed profile and racing line for an entire race track, although computational limits required the trajectories to be computed offline. Kapania and Gerdes @cite_34 presented an experimentally validated algorithm that reduced computational expense by breaking down the combined lateral longitudinal vehicle control problem into two sequential subproblems that were solved iteratively.
@cite_28 @cite_34
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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. 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. The minimum-lap-time optimal control problem for a Formula One race car is solved using direct transcription and nonlinear programming. Features of this work include significantly reduced full-lap solution times and the simultaneous optimisation of the driven line, the driver controls and multiple car set-up parameters. It is shown that significant reductions in the driven lap time can be obtained from track-specific set-up parameter optimisation. Reduced computing times are achieved using a combination of a track description based on curvilinear coordinates, analytical derivatives and model non-dimensionalisation. The curvature of the track centre line is found by solving an auxiliary optimal control problem that negates the difficulties associated with integration drift and trajectory closure. 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.