Passive implementation of multibody simulations for haptic display

The development of complex virtual environment simulations is a challenging problem in haptic display. Due to the dynamic interactions between the human operator, mechanism, sensors, actuators and physics-based simulation, provision of stability guarantees is both an interesting theoretical question and an important practical concern. Most existing virtual environments rely on the careful tuning of environment and control parameters to ensure stability. Whenever changes are made to the environment (such as changing the length of an object), these parameters have to be re-tuned. While merely annoying for relatively simple environments, this process becomes impractical for complex ones.; The focus of this work is the development of a software architecture that permits the simulation of complex multibody environments on a haptic display. This architecture separates the haptic display from the simulation, such that stability of the haptic display is not strongly dependent on simulation parameters. These simulations exhibit vastly improved stability properties compared to previous implementations. Since the haptic display and virtual environment are still weakly connected, guidelines for the design of virtual environments are presented.; Specifically, this thesis presents four distinct results associated with the proposed software architecture. The first result is a detailed passivity analysis of a 1 degree of freedom haptic display, generalizing previous analyses and providing design guidelines for the proposed software architecture. This result also substantiates discrete-time passivity as an exemplar for physics-based simulation methods. The second result is the establishment of a connection between the incremental conservation properties of physics-based numerical methods and discrete-time passivity of their numerical operators. This connection has important implications about which numerical methods are appropriate for use with haptic displays. The third result shows that discrete-time passive numerical operators require the solution of implicit equations. For reasons that are discussed, implicit equations are usually not solvable in real-time, making them difficult to use with haptic displays. The final result is an improved tuning procedure that preserves device passivity even with numerical methods that are not discrete-time passive.