1 Synthesizing Parameterized Motions Michiel van de Panne Ryan Kim* Eugene Fiume Dept. of Computer Science *Dept. of Electrical and Computer Engineering University of Toronto Toronto, Canada, M5S 1A4 {van | rkim | elf}@dgp.utoronto.ca Abstract In striving to construct higher level control representations for simulated characters or creatures, one must seek flexible control representations to build upon. We present a method for the synthesis of parameterized, physics-based motions. The method can be applied to both periodic and aperiodic motions. The basis of the method is a low-level control representation in which linear combinations of con- trollers generally produce predictable in-between motions. 1.0 Introduction Many of the most interesting objects to animate, such as humans, animals, and robots, are capable of controlling their own motion using muscles or actuators. While realistic motion can be obtained for these active systems[15] by applying the Newtonian laws of physics, this also requires solving an associated control problem. Informally stated control problems for animation such as “jump from A to B, then walk to the left” can be posed in a variety of ways. In this paper we examine how to produce control solutions that are reusable and can be parameterized. Producing control solutions to a class of motions as opposed to a specific motion eliminates the need to resolve the control problem each time a new variation of a motion is required. Since the first use of physics-based animation for articulated figures by Wilhelms[23] and Arm- strong and Green[1], a variety of control techniques have been proposed. Some of these draw upon control theory or biological motor control, while others focus directly on creating a usable tool for animation. The approaches taken by this latter group can be broadly divided into two classes. The first poses the problem in terms of a trajectory through state-space and time which is subject to the constraints of physics and the constraints of the desired motion. The second approach involves creating a controller which produces motion by directly supplying actuating forces and torques to a mechanical simulation. The first approach has closer ties to keyframing, while the second better reflects the way movement is generated in real humans, animals, and robots. The trajectory-based approach iteratively modifies an initial trajectory towards satisfying the laws of physics and user-imposed constraints while optimizing a user-defined objective function. This method was originally proposed by Witkin and Kass[24] and subsequently extended by Cohen[4]. A problem (or feature) of this method is that the laws of physics are treated as a soft constraint, thus the resulting motion is not guaranteed to be physically plausible. [ to be presented at the Fifth Eurographics Workshop on Animation and Simulation, Sept. 17-18, 1994 ]