Autonomous Trajectory Planning Based on Bézier Curve with Curvature Constraints and Piecewise-Jerk Speed-Time Optimization

Abstract

In this paper, we propose an efficient trajectory planning algorithm with path smoothing based on the Bézier curve with curvature constraints and piecewise-jerk speed-time optimization. We use hybrid A* to generate a rough path and construct a safe corridor by inflating the path. After that, we formulate the smooth problem as a nonlinear programming(NLP) with piecewise Bézier curves. Since the curvature constraints for Bézier curves are difficult, we employ quartic Bézier Curves with special forms and compute the closed-form solution for the maximum curvature to simplify the representation of the maximum curvature. By using the special Bézier curves, we realize the gear shifts and easily guarantee the security, continuity, and feasibility of the path. Meanwhile, we add time variables based on PJSO, improving the quality of trajectory within an acceptable increase in time, making the allocation of time and speed better. Simulation and real-world experiments with a car-like robot in various environments confirm that our algorithm can generate a smooth, feasible, and high-quality trajectory for robots.