INVERSE KINEMATICS POSITIONING USING NONLINEAR-PROGRAMMING FOR HIGHLYARTICULATED FIGURES

An articulated figure is often modeled as a set of rigid segments conn ected with joints. Its configuration can be altered by varying the joi nt angles. Although it is straightforward to compute figure configurat ions 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 posi tioning constraints, researchers have proposed several different appro aches. However, when we try to follow these approaches in an interacti ve animation system where the object on which to operate is as highly articulated as a realistic human figure, they fail in either generalit y or performance. So, we approach this problem through nonlinear progr amming techniques. It has been successfully used since 1988 in the spa tial constraint system within Jack(R), a human figure simulation syste m developed at the University of Pennsylvania, and proves to be satisf actorily efficient, controllable, and robust. A spatial constraint in our system involves two parts: one constraint on the figure, the end-e ffector, and one on the spatial environment, the goat. These two parts are dealt with separately, so that we can achieve a neat modular impl ementation. Constraints can be added one at a time with appropriate we ights designating the importance of this constraint relative to the ot hers and are always solved as a group. If physical limits prevent sati sfaction of all the constraints, the system stops with the (possibly l ocal) optimal solution for the given weights. Also, the rigidity of ea ch joint angle can be controlled, which is useful for redundant degree s of freedom.