Efficient Spatiotemporal Graph Search for Local Trajectory Planning on Oval Race Tracks

Abstract

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.

TUM autonomous motorsport: An autonomous racing software for the Indy Autonomous Challenge

“…In this case, we select the—at this stage—cheapest available path through the graph that satisfies the planning horizon and still obtain a suboptimal solution. A detailed description of the graph‐search and the following cost function is provided in Rowold at el., 2022.…”

Smooth Trajectory Planning at the Handling Limits for Oval Racing

“…Since the computing time must be reduced for the online application, the racing line is not generated for the entire race track but only for a limited horizon, as in [8]. While the aforementioned approach assumes a 2D race track, Rowold et al [9] perform an online racing line generation considering the effects of a 3D race track. The 3D effects are considered by constraining the combined lateral and longitudinal acceleration by diamond-shaped gg-diagrams that depend on both velocity and vertical acceleration.…”

“…While variational methods that solve an optimal control problem by numerical optimization usually find a local optimum depending on the initialization, approaches exist that select the overtaking direction prior to optimization and perform optimization within a constrained sector [10], [11]. Other approaches, such as [3], [12], are based on spatio-temporal graphs built along the race track. By performing a graph search, the global discrete-optimal solution can be found.…”

“…⊺ and can be derived from the derivatives of the Euler angles [9]. Given the width between the reference line and the left and right track boundaries n l (s) and n r (s), the race track surface S can now be defined as:…”

“…This acceleration depends on the vehicle's movement along the 3D track and may, therefore, deviate from the gravitational acceleration g = 9.81 m/s 2 . For the generation of the gg-diagrams, we follow the method introduced in [9], in which a computationally advantageous diamond-shaped underapproximation of the actual diagram shape is derived. As in [20], the actual shape is obtained based on a doubletrack model and a Pacejka tire model.…”