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This paper focuses on developing a consistent methodology for deriving a closed-form inverse kinematic joint solution of a humanoid robot with decision equations to select a proper solution from multiple solutions. Most researchers resort to iterative methods for inverse kinematics using the Jacobian matrix to avoid the difficulty of finding a closed-form joint solution. Since a closed-form joint solution, if available, has many advantages over iterative methods, we have developed a novel reverse-decoupling method by viewing the kinematic chain of a limb of a humanoid robot in reverse order and then decoupling it into the positioning and orientation mechanisms, and finally utilizing the inverse-transform technique to derive a consistent joint solution for the humanoid robot. The proposed method presents a simple and efficient procedure for finding the joint solution for most of the existing humanoid robots. Extensive computer simulations of the proposed approach on a Hubo KHR-4 humanoid robot show that it can be applied easily to most humanoid robots such as HOAP-2, HRP-2 and ASIMO humanoid robots with slight modifications.

This paper focuses on the development of a model-based feedback controller to realize high versatility of fully actuated planar bipedal robotic walking. To conveniently define both symmetric and asymmetric walking patterns, we propose to use the left and the right legs for gait characterization. In addition to walking pattern tracking error, a biped's position tracking error in Cartesian space is included in the output function in order to enable high-level task planning and control such as multi-agent coordination. A feedback controller based on input–output linearization and proportional–derivative control is then synthesized to realize exponential tracking of the desired walking pattern as well as the desired global position trajectory. Sufficient stability conditions of the hybrid time-varying closed-loop system are developed based on the construction of multiple Lyapunov functions. In motion planning, a new method of walking pattern design is introduced, which decouples the planning of global motion and walking pattern. Finally, simulation results on a fully actuated planar biped show the effectiveness of the proposed walking strategy.