Locally Minimized Jerk Energy Based RRT*: A Fast Algorithm for Generating Paths With $G^{2}$ Continuity and Low Curvature Variation

Abstract

This work proposes an algorithm based on RRT* that generates $G^{2}$-continuous path from a start position to a goal position. Additionally, the generated paths satisfy initial heading constraints, bounded absolute curvature, and reduced variation of curvature. The proposed algorithm employs cubic Bézier curves for tree extension and quintic Bézier curves for rewiring, with their control points computed under the minimum jerk energy criterion. The cubic curves admit closed form solutions enabling fast tree growth, while quintic curves enable rewiring which preserves curvature continuity across the path. Results show that the proposed planner produces paths with lower curvature variation than comparable planners at competitive planning times. Additionally, the curvature and curvature rate profiles confirm that the proposed planner remains well below the allowable bound with fewer abrupt transitions. The resulting paths turn gradually around obstacles, producing natural motion suited for passenger vehicles, wheelchairs, and transport of delicate materials.