Rachel Weinstein Petterson, Ph.D.

Weinstein, R. Simulation and Control of Articulated Rigid Bodies.. Stanford University, Department of Computer Science

A dissertation submitted to the Department of Computer Science and the Committee on Graduate Studies of Stanford University in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Weinstein, R., Guendelman, E. and Fedkiw, R. Impulse Based Control of Joints and Muscles. IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 1, pp. 37-46, Jan/Feb, 2008. website with videos

We propose a novel approach to proportional derivative (PD) control exploiting the fact that these equations can be solved analytically for a single degree of freedom. The analytic solution indicates what the PD controller would accomplish in isolation without interference from neighboring joints, gravity and external forces, outboard limbs, etc. Our approach to time integration includes an inverse dynamics formulation that automatically incorporates global feedback so that the per joint predictions are achieved. This effectively decouples stiffness from control so that we obtain the desired target regardless of the stiffness of the joint, which merely determines when we get there. We start with simple examples to illustrate our method, and then move to more complex examples including PD control of line segment muscle actuators.

Weinstein, R., Guendelman, E. and Fedkiw, R. Impulse-Based PD Control for Joints and Muscles. Sketches, Proceedings of ACM SIGGRAPH 2006. Video (requires Divx)

Weinstein, R., Teran, J. and Fedkiw, R. Dynamic Simulation of Articulated Rigid Bodies with Contact and Collision. IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 3, pp. 365-374, May/Jun, 2006. website with videos

We propose a novel approach for dynamically simulating articulated rigid bodies undergoing frequent and unpredictable contact and collision. In order to leverage existing algorithms for nonconvex bodies, multiple collisions, large contact groups, stacking, etc., we use maximal rather than generalized coordinates and take an impulse based approach that allows us to treat articulation, contact and collision in a unified manner. Traditional constraint handling methods are subject to drift, and we propose a novel pre-stabilization method that does not require tunable potentially stiff parameters as does Baumgarte stabilization. This differs from post-stabilization in that we compute allowable trajectories before moving the rigid bodies to their new positions, instead of correcting them after the fact when it can be difficult to incorporate the effects of contact and collision. A post-stabilization technique is used for momentum and angular momentum. Our approach works with any black box method for specifying valid joint constraints, and no special considerations are required for arbitrary closed loops or branching. Moreover, our implementation is linear both in the number of bodies and in the number of auxiliary contact and collision constraints, unlike many other methods that are linear in the number of bodies but not in the number of auxiliary constraints.

Weinstein, R., Teran, J. and Fedkiw, R. Pre-stabilization for Rigid Body Articulation with Contact and Collision. Sketches, Proceedings of ACM SIGGRAPH 2005. Video (requires Divx)

Pivkin, I., Hueso, E., Weinstein, R., Laidlaw, D. H., Swartz, S. and Karniadakis, G. Simulation and Visualization of Air Flow Around Bat Wings During Flight. In Proceedings of International Conference on Computational Science, pages 689-694, 2005.