[Show abstract][Hide abstract] ABSTRACT: New gait planning using a nonholonomic model with difference equation constraints is proposed for biped robot walking. A model of a pivoting telescopic segment is used as the kinematic foothold selection model of a bipedal robot. The repetitive and discontinuous constraints of pivoting, expanding, and contracting make up the set of walking trajectory data. The k-step reachable region is defined as the set of the k-th state that the system can reach from the initial state, and the motion planning is solved using the Jacobian matrix of the state with regard to the input series. The difference equation constraints can be discussed as a digital control of continuous-time nonholonomic systems. The gait planning is modified based on the limiting condition for the HRP-2 humanoid robot. Energy consumption is evaluated based on the linear-pendulum model and the gait planning is optimized. The feasibility of the proposed walking planning is demonstrated through a numerical simulation and an experiment involving the HRP-2 humanoid robot.