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Platform Diving


We have developed a simulation of a human diver with 38 controlled degrees of freedom. The human model can perform a number of 10 meter platform dives. The dynamic model of the diver consists of 15 rigid bodies connected by rotary joints. The dynamic properties of the rigid bodies were calculated using densities for each body part measured from cadavers[2], and algorithms for computing moments of inertia from polygonal objects[5]. The equations of motion were generated using a commercially available package, that uses a variant of Kane's method with a symbolic simplification phase[8].

The control system for the diver is hierarchical. The low-level control is provided by proportional- derivative servos that move the joints towards their desired values. Balance on the diving board is provided by a controller at the ankle that computes the angle for the ankle that would place the body's center of mass over the feet. This angle serves as a desired angle for the low-level PD control. High-level control for the dive is provided by a state machine that alters the desired configuration of the diver. Five states are used in the 10m platform dives: Compression, Decompression, Flight-Phase 1, Flight-Phase 2, and Entry. The high-level control alters not only the desired values for the joints but also the gain on the low level PD servos. For example, the gains required for the compression phase of the dive are higher than the gains required for the flight phase. The gains and set points for the controllers were tuned by hand to ensure that the diver performs the dive and enters the water vertically.

Research in three fields is relevant to the problem of simulating human divers: robotics, computer graphics, and biomechanics. The diver in this presentation is based on control algorithms for robot locomotion developed by Raibert and Hodgins[7]. From the biomechanics literature, Frohlich[4] and Yeadon[9] provide detailed analysis of human motion in flight, and Eaves[3] provides insight on the mechanics of diving. In the computer graphics community, Badler[1] has developed a system to model kinematics and dynamics of humans, and Magnenat-Thalmann and Thalmann[6] have explored methods for producing realistic animations and images of humans.

  1. Badler, N., Phillips, C., Webber, B., Simulating Humans, Oxford: Oxford University Press, 1993.

  2. Dempster, W., Gaughran, G., "Properties of Body Segments based on Size and Weight," American Journal of Anatomy, Vol 120, pp. 33-54, 1965.

  3. Eaves, G., The Mechanics of Springboard and Firmboard Techniques, A. S. Barnes & Co., New Jersey, 1969.

  4. Frohlich, C., "Do spring board divers violate angular momentum conservation?" American Journal of Physics, Vol 47, pp. 583-592, 1979.

  5. Lien, S., Kajiya, J., "A Symbolic Method for Calculation the Integral Properties of Arbitrary Non-convex Polyhedra," IEEE Computer Graphics and Applications, Vol 4, No 5, pp. 35- 41, 1984.

  6. Magnenat-Thalmann, N., Thalmann, D., Computer Animation: Theory and Practice, Springer-Verlag, New York, 1990.

  7. Raibert, M., and Hodgins, J., "Animation of Dynamic Legged Locomotion," Proceedings of SIGGRAPH `91, (July-August 1991), pp. 349-358, 1991.

  8. Rosenthal, D., Sherman, M., "High Performance Multibody Simulations Via Symbolic Equation Manipulation and Kane's Method," Journal of Astronautical Sciences, Vol. 34 No. 3, pp. 223-239, 1986.

  9. Yeadon, M., "The Simulation of Aerial Movement- IV. A Computer Simulation Model," Journal of Biomechanics, Vol. 23 No.1, pp. 85-89, 1990.

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Copyright 1998

Questions or comments? Email jkh+www@cc.gatech.edu.