Stable and Efficient Differential Inverse Kinematics

Inverse kinematics (IK) is an essential algorithm in the computer animation of articulated figures. We propose a differential IK algorithm combining ideas from the pseudoinverse and Jacobian transpose techniques that achieves the efficiency of the former technique while avoiding its inherent instability. An inverse kinematics problem solves for the parameters q in a skeleton that move particular points on the skeleton toward the position of given targets. In a prototypical example, the animator specifies the position of the end of an arm (3 degrees of freedom) and the system must solve for joint angles that satisfy the desired position. The relevant skeletal chain (or portion thereof) generally has more than three parameters so the problem is underconstrained. Algorithms for IK must address the underconstrained as well as nonlinear nature of the problem. The IK problem will be denoted minq ‖p − f(q) ‖ 2. While it ha