Humanoid Robot's Inverse Kinematics Using Algebraic Geometry

The most common approach used in modeling humanoid robots is to restrict the motion in two different planes, namely the frontal and sagittal plane, thereby using trigonometric expressions and Euler-angles for its description. In this paper some problems of trajectory interpolation and singularity of motion representation are discussed and the dual quaternion representation is used as an alternative to avoid these problems and to obtain the models ensuring a general spatial analysis of the motion trajectory. The aim of this work is to present a different method to model kinematics of humanoid robots avoiding the restriction to the frontal and sagittal planes. A spatial trajectory is therefore assumed and the joint angles are calculated to move the robot in human like motion. To achieve the goal an algebraic geometry approach based on dual quaternions is used to obtain the inverse kinematics expressions that are then polynomial functions. Simulations are performed to evaluate the model numerically.