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. I. INTRODUCTIONAutonomous car racing is a challenging task for automatic control systems due to the need for handling the vehicle close to its stability limits and in highly nonlinear operating regimes. In addition, dynamically changing racing situations require advanced path planning mechanisms with obstacle avoidance executed in real-time. Fast dynamics constrain the sampling time to be in the range of a few tens of milliseconds at most, which severely limits the admissible computational complexity of the algorithms. This situation is even more challenging if the autonomous algorithms shall be executed on simple, low-power embedded computing platforms.In this paper, we investigate optimization-based control strategies for the task of racing an autonomous vehicle around a given track. We focus on methods that can be implemented to run in real-time on embedded control platforms, and present experimental results using 1:43 scale Kyosho dnano RC race cars that achieve top speeds of more than 3 m/s, which corresponds to an upscaled speed of about 465 km/h. For high performance, the proposed controllers operate the car at its friction limits, far beyond the linear region of what is typically used in other autonomous driving systems. This challenging task is generally mastered only by expert drivers with lots of training. In contrast, our approach requires merely a map of the track a...

In this paper, we present a learning-based control approach for autonomous racing with an application to the AMZ Driverless race car gotthard. One major issue in autonomous racing is that accurate vehicle models that cover the entire performance envelope of a race car are highly nonlinear, complex and complicated to identify, rendering them impractical for control. To address this issue, we employ a relatively simple nominal vehicle model, which is improved based on measurement data and tools from machine learning. The resulting formulation is an online learning data-driven Model Predictive Controller, which uses Gaussian Processes regression to take residual model uncertainty into account and achieve safe driving behavior. To improve the vehicle model online, we select from a constant inflow of data points according to a criterion reflecting the information gain, and maintain a small dictionary of 300 data points. The framework is tested on the full-size AMZ Driverless race car, where it is able to improve the vehicle model and reduce lap times by 10% while maintaining safety of the vehicle.

This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid obstacles while moving in an n-dimensional space. The proposed reformulation does not introduce approximations, and applies to general obstacles and controlled objects that can be represented as the union of convex sets. We connect our results with the notion of signed distance, which is widely used in traditional trajectory generation algorithms. Our method can be applied to generic navigation and trajectory planning tasks, and the smoothness property allows the use of general-purpose gradient-and Hessian-based optimization algorithms. Finally, in case a collision cannot be avoided, our framework allows us to find "leastintrusive" trajectories, measured in terms of penetration. We demonstrate the efficacy of our framework on a quadcopter navigation and automated parking problem, and our numerical experiments suggest that the proposed methods enable real-time optimization-based trajectory planning problems in tight environments.Source code of our implementation is provided at https://github.com/XiaojingGeorgeZhang/OBCA.

This paper presents an adaptive high performance control method for autonomous miniature race cars. Racing dynamics are notoriously hard to model from first principles, which is addressed by means of a cautious nonlinear model predictive control (NMPC) approach that learns to improve its dynamics model from data and safely increases racing performance. The approach makes use of a Gaussian Process (GP) and takes residual model uncertainty into account through a chance constrained formulation. We present a sparse GP approximation with dynamically adjusting inducing inputs, enabling a real-time implementable controller. The formulation is demonstrated in simulations, which show significant improvement with respect to both lap time and constraint satisfaction compared to an NMPC without model learning.

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