Curvature-Optimal Merging Segment Planning for Autonomous Racing Vehicles

In this article, we propose a path planning algorithm focused on high-speed lane-change scenarios in autonomous racing applications. Specifically, by formulating a quadratic Optimal Control Problem, we design nearly curvature optimal trajectories that can allow for high-speed maneuver execution. The problem formulation includes a convenient approach for the linearization and discretization of the path system dynamics. Unlike most state-of-the-art approaches, the proposed method does not need to constrain the path shape to pre-defined polynomial primitives and does not perform inefficient grid searches over sets of candidate maneuvers. Instead, it can directly optimize path curvature, while fulfilling path smoothness and trajectory constraints. We tested the proposed methods in a racing simulation environment, and compared its results with a benchmark algorithm. The results show the algorithm’s ability to return nearly curvature-optimal solutions while maintaining real-time feasibility. Eventually, such results demonstrate the effectiveness of the proposed solutions.