Path planning of loaded pin-jointed bar mechanisms using Rapidly-exploring Random Tree method

Abstract

Path planning of loaded pin-jointed bar mechanisms, typical of Pantadome, is discussed in this paper. In engineering, the path from the initial configuration to the target configuration generally cannot be determined easily because of the complicated constraint conditions. The basic kinematic equation of loaded pin-jointed bar mechanisms is hereby established based on FEA, and the driving condition of internal rigid-body (mechanism) displacements is presented for the length actuation of active members. A numerical strategy is proposed to trace the shortest path of pure mechanism displacement from the initial configuration to the given target configuration. With the emphasis on the constraints of structural stability and range of motion, the Rapidly-exploring Random Tree (RRT) method is adopted for the path planning of the loaded pin-jointed bar mechanisms. The RRT method is further modified to be applicable for the path planning when the target configuration is implicitly defined by its distance to be as close as possible to a geometrical boundary, at which the conventional RRT algorithm fails to track multiple feasible paths. An adaptive strategy is also suggested to improve the sampling efficiency of RRT. Considering loose and tight constraints of structural stability respectively, a loaded planar Pantadome is employed as the numerical example to investigate the validity of the path planning method proposed in this paper.