A new ZMP constraint equation with application to motion planning of humanoid using kinematic redundancy

The human body exploits "redundant degree of freedom" to execute various motions in a suitable fashion. This work deals with development of effective redundancy resolution algorithms for the motion control of humanoid. Differently from the typical kinematically redundant robots that are attached to the fixed ground, the ZMP condition should be taken into account in the human body motion in order to guarantee the system stability. For this, a geometric constraint equation is derived by reshaping 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 feedforward fashion. This constraint equation and the kinematic equation of the humanoid model are solved together. A sequential redundancy resolution algorithm exploiting the remaining kinematic redundancy is also proposed to optimize several secondary criteria such as joint limit index and manipulability. The feasibility of the proposed algorithms is verified by simulating a stable standing up motion and a planar walking motion though planar 5 DOF and 6 DOF humanoid models.