The computer-animation of legged animals: simulation, design and control

The development of systems for the three-dimensional computer animation of legged animals involves issues in simulation, design and control. A prototype system, PODA, is described in which the animator may design legged animal motion within the constraints imposed by the mechanics of the physical world. Empirical evidence suggests that limb motion is optimized in terms of a weighted performance index involving both minimization of jerk about the limb's end-effector and the limb's expenditure of energy. Due to the nonlinearity of limb kinematics and dynamics, and additional constraints which must be imposed on the limb's extent and duration of movement, traditional optimal control procedures fail. A new algorithm is contributed which provides a general solution to the optimal velocity distribution of a limb which is constrained to move along a prespecified splined path. The method uses dynamic programming as a means of finding an optimal distribution of control points along that path. Two models for animating body motion are described which have been implemented in PODA. The first is a locomotion system which builds on robotics research on the kinematics of legged locomotion. A mechanically coherent legged animal motion is synthesized from the animator's design of a sequence of periodic gaits and a path to be followed across flat terrain. The second model provides the animator with a means of designing non-periodic free-form dance motion. In each model new techniques are contributed toward the incorporation of body dynamics by integrating the animator's specification of motion with the physical constraints imposed by the mechanics of articulated body movement. It is argued that modeling coordinated body movement which is precisely simulated must be restricted to specialized "expert" movements which are either preconceived or inferred from task-level strategies.