Impulse-based Dynamic Simulation of Rigid Body Systems

Impulse based Dynamic Simulation of Rigid Body Systems by Brian Vincent Mirtich Doctor of Philosophy in Computer Science University of California at Berkeley Professor John F Canny Chair Dynamic simulation is a powerful application of today s computers with uses in elds rang ing from engineering to animation to virtual reality This thesis introduces a new paradigm for dynamic simulation called impulse based simulation The paradigm is designed to meet the twin goals of physical accuracy and computational e ciency Obtaining physically ac curate results is often the whole reason for performing a simulation however in many applications computational e ciency is equally important Impulse based simulation is designed to simulate moderately complex systems at interactive speeds To achieve this performance certain restrictions are made on the systems to be simulated The strongest restriction is that they comprise only rigid bodies The hardest part of rigid body simulation is modeling the interactions that occur between bodies in contact The most commonly used approaches are penalty methods followed by analytic methods Both of these approaches are constraint based meaning that constraint forces at the contact points are continually computed and applied to deter mine the accelerations of the bodies Impulse based simulation is a departure from these approaches in that there are no explicit constraints to be maintained at contact points Rather all contact interactions between bodies are a ected through collisions rolling slid ing resting and colliding contact are all modeled in this way The approach has several advantages including simplicity robustness parallelizability and an ability to e ciently simulate classes of systems that are di cult to simulate using constraint based methods The accuracy of impulse based simulation has been experimentally tested and is su cient for many applications The processing of collisions is a critical aspect of the impulse based approach E cient algorithms are needed for detecting the large number of collisions that occur without missing any Furthermore the physical accuracy of the simulator rests upon the accuracy of the collision response algorithms This thesis describes these essential algorithms and their underlying theory It describes how the algorithms for simple rigid body simulation may be extended to systems of articulated rigid bodies To prove the method is truly practical the algorithms have been implemented in the prototype simulator Impulse Many experiments performed with Impulse are described Professor John F Canny Dissertation Committee Chair