Inverse Kinematics of the RTX Robot; Geometric Approach and the Solution of Non-Uniqueness

One of the major concepts in an advanced robotic manipulator control system is the ability of transforming the world Cartesian coordinates of the end-effector into joint coordinates, on which the control actions are developed. This transform is non-unique, while the analytic algebraic approach and the numerical iterative approach only give one solution. This paper applies a geometric approach to a translation-roll-roll type RTX robot with a roll-pitch-yaw wrist. The geometric approach is a straightforward method and especially effective for six-degree-of-freedom non-redundant robots with three wrist joint axes intersecting at one point. Through introducing configuration parameters the non-uniqueness of the inverse transform equation has been solved. The optimal configuration for each moving step can be calculated based on a suitable performance criterion.