Abstract: The autonomous racing car(ARC) is supposed to plan path and speed simultaneously to meet the requirement of the fastest driving strategy. However, the spatiotemporal coupling relationship between path and speed makes the optimization problem difficult to formulate and solve. To deal with this problem, a simultaneous path and speed planning(SP²) approach for autonomous racing car is proposed in this paper to achieve rapid cooperative trajectory planning. First, a trajectory planning problem considering track boundaries and vehicle dynamics constraints is formulated. Second, the steady action space and action-state space including spatiotemporal information of the ARC is built, and the available action-state transition relationship is determined via offline traversal. After that, we transform the time optimal trajectory optimization problem into an optimization problem with the objective of achieving the longest distance per time step and apply multi-step recursive optimization scheme to render a trajectory with the fastest lap time. Last but not least, simulations and experiments in a small scaled platform is conducted. Results show that the proposed SP² approach can efficiently provide global path and speed for the ARC, with a faster lap times compared with the traditional approach of following the center line of track.

Key words: autonomous racing car(ARC), trajectory planning, discrete operating point, spatiotemporal coupling, time optimization