A Comprehensive Derivation of Quintic Spline Interpolation and Its Applications to 3-D Collision-Free Trajectory Generation

Abstract

For trajectory generation, quintic spline interpolation can ensure the zero velocities and accelerations of both the starting and ending points, presenting advantages not achievable by cubic spline interpolation. Due to the scarcity of quintic spline interpolation in existing research and applications, and considering its relatively intricate implementation process, this article presents a comprehensive derivation for its solution. Moreover, a three-dimensional (3-D) collision-free smooth trajectory scheme using quintic spline interpolation is proposed to generate collision-free and sufficiently smooth trajectories. Finally, two case studies are conducted to validate the effectiveness of quintic spline interpolation and the trajectory generation scheme in planning motion trajectories for robotic agents in a 3-D map with several obstacles.