Computationally Efficient Minimum-Time Motion Primitives for Vehicle Trajectory Planning

In the context of vehicle trajectory planning, motion primitives are trajectories connecting pairs of boundary conditions. In autonomous racing, motion primitives have been used as computationally faster alternatives to model predictive control, for online obstacle avoidance. However, the existing motion primitive formulations are either simplified and suboptimal, or computationally expensive for accurate collision avoidance. This paper introduces new motion primitives for autonomous racing, aiming to accurately approximate the minimum-time vehicle trajectories while ensuring computational efficiency. We present a novel neural network, named PathPoly-NN, whose internal architecture is designed to learn the minimum-time vehicle path. Our motion primitives combine PathPoly-NN with a fast forward-backward method to compute the minimum-time speed profile. Compared to existing neural networks, PathPoly-NN generalizes better with small training sets, and it has better accuracy in approximating the minimum-time path. Additionally, our motion primitives have lower computational burden and higher accuracy than existing methods based on cubic polynomials and $G^{2}$ clothoid curves. Finally, the motion primitives of this paper achieve similar maneuver times as minimum-time economic nonlinear model predictive control (E-NMPC), but with significantly lower computational load (two orders of magnitude). The results open promising perspectives of applications in graph-based trajectory planners for autonomous racing.