ZMP-based motion planning algorithm for kinematically redundant manipulator standing on the ground

The human body can be modeled as a kinematically redundant manipulator which exploits "redundant degrees of freedom" to execute various motions in a suitable fashion. Differently from the typical kinematically redundant robots that are attached to the fixed ground, the zero moment point (ZMP) condition should be taken into account not to fall down. Thus, this paper investigates a motion planning algorithm for kinematically redundant manipulator standing on the ground. For this, a geometric constraint equation is derived from the existing ZMP equation. This constraint equation is formed like a second-order kinematic equation, which enables one to plan the ZMP trajectory in a feed-forward fashion. This constraint equation and the kinematic equation of the manipulator model are solved together. Then, the solution of this composite equation guarantees both the desired operational motion and the ZMP trajectory. The feasibility of the proposed algorithms is verified by simulating and experimenting several motions though a planar 3-DOF manipulator model.