Path Planning of Slender Tensegrities Based on the Artificial Potential Field Method

Abstract

Focusing on the constraints of obstacle avoidance and compliance of structural geometry, a path planning method is proposed for slender morphing tensegrities in this paper based on the artificial potential field method. An analytical kinematic equation is established for tensegrities under member length actuation. The expressions of the elongations of active members are derived for the specified motion with elastic and rigid-body deformations, respectively. The mathematical models of the repulsive fields induced by obstacles and the attractive fields generated by target points are given to define the artificial potential field. For any configuration on the kinematic path, the nodes in the repulsive fields and the guide nodes in the attractive fields are forced to move in the steepest descent directions of their potential energies. The motion directions of nodes are then adjusted for the compliance of structural geometry. A numerical strategy is proposed to trace the kinematic path of a tensegrity step by step in the artificial potential field. The path plannings are performed on an illustrative slender tensegrity consisting of stacked modules by considering the motions with elastic and rigid-body deformations, respectively; and the validity of the proposed method is verified by investigating the obstacle avoidance, the compliance of structural geometry, the slack prevention of cables, and the structural stability for the obtained kinematic paths.