A Numerically Stable Algorithm for Analytic Inverse Kinematics of 7-Degrees-of-Freedom Spherical-Rotational-Spherical Manipulators With Joint Limit Avoidance

This article presents a numerically stable algorithm for analytic inverse kinematics of 7-DoF S-R-S manipulators with joint limit avoidance. The arm angle is used to represent the self-motion manifold within a global arm configuration. The joint limits are analytically mapped to the arm angle space for joint limit avoidance. To profile the relation between the joint angle and arm angle, it is critical to characterize the singular arm angle for each joint. In the-state-of-the art methods, the existence of the singular arm angle is triggered by comparing a discriminant with zero given a threshold. This leads to numerical issues since the threshold is inconsistent among different target poses, leading to incorrect range of the arm angle. These issues are overcome by associating indeterminate joint angles of tangent joints with angles of 0 or ±π of cosine joints, rather than using an independent threshold for each joint. The closed-form algorithm in c++ code to perform numerically stable inverse kinematics of 7-DoF S-R-S manipulators with global arm configuration control and joint limit avoidance is also given.