Control and Simulation of Multibody Systems

Jeffrey M. Wendlandt, Mechanical Engineering, University of California at Berkeley

Creating predictive models for human motion is an important and challenging problem with wide-ranging applications in animation, virtual environments, sports equipment design, and human training. Creating these models requires dynamic simulation as well as sophisticated control algorithms. The fact that the system is in contact with the environment and is governed by complex equations of motion provides additional challenges. One must also develop control algorithms to coordinate the degrees of freedom. In this talk, I describe my thesis work in creating predictive, dynamic models for human motion. A first step in creating models for walking, running, and jumping is developing a balancing controller. A workspace balancing controller is presented that utilizes recursive multibody dynamics algorithms to formulate the model for the controller. Simulation results of the system balancing and moving between set points are shown.

Real-time simulation of multibody systems in contact with the environment, while difficult to achieve, is a desirable property in a control development platform. In pursuit of this goal, numerical integrators for mechanical systems have been created which naturally preserve invariants and structure of the continuous-time system. These mechanical integrators are symplectic-momentum integrators and are based on a discrete variational principle analogous to Hamilton's principle. The discrete variational principle is first described. It is then explained how to use this theory to create a general procedure to construct symplectic-momentum integrators for mechanical systems with constraints. This methodology is combined with a contact model with stiction and sliding friction to produce a simulator for rigid bodies interacting with the environment. The mechanical integrators combined with the contact model is an important component of the multibody simulation platform under development. The simulation platform will enable one to quickly prototype controlled multibody systems and develop predictive models of human motion.