Forward and Inverse Kinematics for a Small-Sized Humanoid Robot

This paper examines the forward and inverse kinematics of a small-sized low-cost commercial humanoid robot providing closed form solutions for both kinematic problems. The analyzed robot has 16 degrees-of-freedom: five for each leg and three for each arm, actuated by sixteen digital servomotors, like those used in aeromodelism. Each leg is a serial kinematic chain that uses three degrees of freedom to control the position of the foot, and two more to orient it,resembling a human ankle. Unfortunately, this ankle has been designed with an offset that prevents a direct decoupling of the position and orientation of the foot, situation that generally leads to the lack of a closed form solution in most cases. The proposed solution deals with this problem; it uses a geometrical approach that effectively solves the inverse kinematic problem by means of an analytical algorithm.