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In motion planning for autonomous racing, the challenge arises in planning smooth trajectories close to the handling limits of the vehicle with a sufficient planning horizon. Graph-based trajectory planning methods can find the global discrete-optimal solution, but they suffer from the curse of dimensionality. Therefore, to achieve low computation times despite a long planning horizon, coarse discretization and simple edges that are efficient to generate must be used. However, the resulting rough trajectories cannot reach the handling limits of the vehicle and are also difficult to track by the controller, which can lead to unstable driving behavior. In this paper, we show that the initial edges connecting the vehicle’s estimated state with the actual graph are crucial for vehicle stability and race performance. We therefore propose a sampling-based approach that relies on jerk-optimal curves to generate these initial edges. The concept is introduced using a layer-based graph, but it can be applied to other graph structures as well. We describe the integration of the curves within the graph and the required adaptation to racing scenarios. Our approach enables stable driving at the handling limits and fully autonomous operation on the race track. While simulations show the comparison of our concept with an alternative approach based on uniform acceleration, we also present experimental results of a dynamic overtake with speeds up to 74 m/s on a full-size vehicle.

Autonomous racing has increasingly become a research subject as it provides insights into dynamic, high-speed situations. One crucial aspect of handling these situations, especially in the presence of dynamic obstacles, is the generation of a collision-free trajectory that represents a safe behavior and is also competitive in the case of racing. We propose a local planning approach that generates such trajectories for a racing car on an oval race track by searching a spatiotemporal graph. A considerable challenge of search-based methods in a spatiotemporal domain is the curse of dimensionality. Therefore, we propose how a previously presented graph structure that is based on intervals instead of discrete values can be searched more efficiently without losing optimality by using a uniform-cost search strategy. We extend the search method to make it anytime-capable so that it can provide a suboptimal trajectory even if the search has to be terminated early. The graph-based planning approach allows us to apply a flexible cost function so that our approach can operate fully autonomously on an oval race track, including the pit lane. We present a cost function for oval racing and explain how the terms contribute to the desired behaviors. This is supported by results with a full-scale prototype.