Simulation and Control of Articulated Rigid Bodies 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

This dissertation presents algorithms for the simulation and control of articulated rigid bodies and related applications. The first algorithm is 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., maximal rather than generalized coordinates are used with an impulse based approach that allows articulation, contact and collision to be treated in a unified manner. The pre-stabilization method presented differs from post-stabilization in that allowable trajectories are computed 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, thus eliminating drift that can be seen in many traditional methods. This approach works with any black box method for specifying valid joint constraints, and no special considerations are required for arbitrary closed loops or branching. The implementation presented is effectively 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. Articulated characters can then be controlled using a second method described in this work which exploits the fact that proportional derivative (PD) control 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. The time integration used in this method includes an inverse dynamics formulation that automatically incorporates global feedback so that the per-joint predictions are achieved.