O SIGGRAPH ' 90 , Dallas , August 6-10 , 1990

Accurate simulation of Newtonian mechanics is essential for simulating realistic motion of jointed figures. Dynamic simulation requires, however, a large amount of computation when compared to kinematic methods, and the control of dynamic figures can be quite complex. We have implemented an efficient forward dynamic simulation algorithm for articulated figures which has a computational complexity linear in the number of joints. In addition, we present a strategy for the coordination of the locomotion of a six-legged figure a simulated insect which has two main components: a gait controller which sequences stepping, and motor programs which control motions of the figure by the application of forces. The simulation is capable of generating gait patterns and walking phenomena observed in nature, and our simulated insect can negotiate planar and uneven terrain in a realistic manner. The motor program techniques should be generally applicable to other control problems. 1. COORDINATING AND CONTROLLING JOINTED FIGURE MOTION Realistic modeling and animation of human and animal figures has long been a goal of researchers in computer graphics. There are two aspects to the synthesis of motor behavior [1]: • The Coordinat ion problem. How do we organize the movements of a complicated figure into coherent, useful motions? In other words, given a jointed figure with many degrees of freedom (DOFs), how do we decide which DOFs are needed to perform a given motion, and how do these movements vary with respect to each other? • The Control problem. Given a set of DOFs, Emd appropriate time-varying parameters for each DOF necessary to effect a given motion. In this paper we will describe approaches to both problems. We use physically-based methods with dynamic motor control This work was" supported in part by National Science Foundation Grant IRI-8712772, and equipment grants from Hewlettopackard Co., Gould Electronics, Inc., and Apple Computer, Inc. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. to generate realistic movements, and we use biologically-based mechanisms to coordinate complex patterns of movement. In particular, we have implemented a dynamics simulation algorithm based on the work of Featherstone [2; 3], which is more efficient than dynamic simulation algorithms previously reported in the computer graphics literature. We use this algorithm to compute the movements of a six-legged virtual insect. Based on results from ethology and physiology, we coordinate its adaptive gait over planar and uneven terrain using coupled-oscillators, reflexes and a set of motor programs which apply controlling forces. In the next section, we discuss related work. In Section 3 we describe the major components of our dynamic locomotion simulator. We conclude with a discussion of results we have obtained so far.