Smooth and collision-free trajectory generation in cluttered environments using cubic B-spline form

Abstract This paper presents an effective trajectory generation algorithm to shorten and smooth the jerky paths obtained from the sampling-based planners in cluttered environments. We utilize the cubic smoothing B-spline curves to represent the final trajectories that are collision-free, strict C 2 continuity and respect velocity and acceleration constraints. Our algorithm mainly contains two core parts: a two-layer local adjustment strategy to avoid collisions and a fast trajectory pruning algorithm by introducing the Douglas-Peucker algorithm into the Path pruning technique to remove unnecessary and jerky motions. The two-layer local adjustment strategy takes advantage of B-splines’ local support properties and geometry operations, adaptively selecting the trajectory adjustment method according to the complexity of the environment. We emphasize that our trajectory adjustment strategy only needs to adjust the segments around the colliding sections, and it is even feasible for environments with narrow passages. Furthermore, the pruning algorithm decimates the initial path with fewer dominant points, significantly accelerating the pruning speed. Simulation and actual experimental results show that our algorithm can rapidly generate smooth, collision-free, and natural-looking trajectories.