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We propose an inverse kinematic control framework for a position controlled humanoid robot with bounded joint range, velocity, and acceleration limits. The proposed framework comprises two components, an inverse kinematics algorithm and a damping controller. The proposed IKTC (Inverse Kinematics with Task Corrections) algorithm is based on the second order task-priority method in order to ensure the velocity-continuity of the solution. When the minimum norm solution exceeds the joint bounds, the problem is treated as a quadratic optimization problem with box constraints; an optimal task correction that lets the solution satisfy the constraints is found. In order to express the three kinds of joint constraints as a second order box constraint, a novel method is also proposed. The joint stiffness of a position controlled humanoid robot necessitates a damping controller to attenuate jolts caused by repeated contacts. We design a damping controller by using an inverted pendulum model with a compliant joint that takes into account the compliance around the foot. By using ZMP [20] measurement, the proposed damping controller is applicable not only in SSP (Single Support Phase) but also in DSP (Double Support Phase). The validity of the proposed methods is shown by imitating a captured whole-body human motion with a position controlled humanoid robot

Inverse Kinematic Control of Humanoids under Joint Constraints