Inverse kinematics positioning using nonlinear programming for highly articulated figures

An articulated figure is often modeled as a set of rigid segments connected with joints. Its configuration can be altered by varying the joint angles. Although it is straight forward to compute figure configurations given joint angles (forward kinematics), it is more difficult to find the joint angles for a desired configuration (inverse kinematics). Since the inverse kinematics problem is of special importance to an animator wishing to set a figure to a posture satisfying a set of positioning constraints, researchers have proposed several different approaches. However, when we try to follow these approaches in an interactive animation system where the object on which to operate is as highly articulated as a realistic human figure, they fail in either generality or performance. So, we approach this problem through nonlinear programming techniques. It has been successfully used since 1988 in the spatial constraint system within Jack, a human figure simulation system developed at the University of Pennsylvania, and proves to be satisfactorily efficient, controllable, and robust. A spatial constraint in our system involves two parts: one constraint on the figure, the end-effector, and one on the spatial environment, the goal. These two parts are dealt with separately, so that we can achieve a neat modular implementation. Constraints can be added one at a time with appropriate weights designating the importance of this constraint relative to the others and are always solved as a group. If physical limits prevent satisfaction of all the constraints, the system stops with the (possibly local) optimal solution for the given weights. Also, the rigidity of each joint angle can be controlled, which is useful for redundant degrees of freedom.