Global reorientation of a free-fall multibody system using periodical joint motions – theory and motion planning

The global reorientation (attitude change in an inertial frame) of a multibody system in 3D space without any external torque under zero angular momentum is a widely observed and interested phenomenon in both science and engineering domains. One notable method to achieve such a reorientation is to move some individual bodies through periodical joint movements along loop paths (looped trajectories), a strategy observed in many animals. Through these periodical movements, the multibody system can reorient its global orientation without changing its final joint configuration (i.e., in the end all the moving joints will return to their initial positions). In this way, animals can gain better mobility and agility during various activities. Investigating the relationship between these periodical joint movements and the system’s global reorientation not only deepens our understanding of animal dynamics but also offers insights for designing and controlling bioinspired robots. In this paper, we unveil the general relationship between such periodical joint movements along looped paths and the 3D global rotation of a general multibody system or one specific body of the system. Based on this general relationship, we found the conditions and limitations for achieving a global reorientation of the system or one of its bodies. From these findings, we further developed novel algorithms of joint path planning for desired global reorientation and demonstrated the algorithms using simulation examples.