Abstract This work deals with development of effective redundancy resolution algorithms for the motion control of manipulator. Differently from the typical kinematically redundant robots that are attached to the fixed ground, the ZMP condition should be taken into account in the manipulator motion in order to guarantee the system stability. In this paper, a new motion planning algorithm for redundant manipulator not fixed to the ground is introduced. A sequential redundancy resolution algorithm is proposed, which ensures the ZMP (Zero Moment Point) stability, the planned operational motion, and additional sub‐criteria such as joint limit index. A geometric constraint equation derived by reshaping the existing ZMP equation enables one to employ the sequential redundancy algorithm. The feasibility of the proposed algorithm is verified by simulating a redundant manipulator model.