Real-time impulse-based simulation of rigid body systems for haptic display

Haptic displays are devices that let humans touch, feel and manipulate virtual environments. One important class of virtual environments is rigid body systems; i.e., those comprising a collection of rigid bodies interacting via unilateral and bilateral constraints. This thesis addresses the simulation of these rigid body systems given certain constraints imposed by haptic interaction. One constraint is that the simulation must occur in “hard” real-time, meaning that the simulation must keep up with actual time at each and every step (not just on average). A second constraint is that relatively high update rates—500 Hz to 1000 Hz—are required to ensure a realistic feel. A third “constraint” is that fixed time steps are strongly preferred.; In this thesis we analyze various approaches to rigid body simulation in light of these constraints. For instance, we consider the “impulse-based simulation” technique developed by Mirtich and Canny, which has been used successfully for real-time (but not hard real-time) simulations and appears promising for use with haptics. In addition, we consider the problem of contact state determination that arises when two rigid bodies collide. The real time nature of haptics does not allow us to find an exact contact state, so it is necessary to make good approximations. Poor approximations may result in inappropriate energy growth or in non-physical behavior such as “getting stuck.”; In this thesis we also introduce a novel hybrid simulation method, which combines the impulse-based method mentioned above with constraint force methods and so-called “penalty methods.” By integrating the three methods, the hybrid technique effectively deals with the constraints imposed by haptics. Experimental and simulation results demonstrate the efficacy of the new method.