Figure1: Standing Planar Model of a Human
This research involves designing controllers and improved simulation/integration schemes for multibody systems. A multibody system consists of linked rigid bodies. A multibody model of a standing biped is shown in Figure 1. (Rendering courtesy of Impulse)
We are investigating the control of multibody systems by designing controllers for human models. We are desigining the controllers to make the human model stand, take steps, walk, run, jump, and perform various behaviors. We are also simulating the effects of external loads, such as backpacks. We have designed a controller to make a planar human model stand (shown in Figure 1). The computer model is rendered and simulated using Impulse. I am performing this research with Professor S. Sastry.
We have simulated the controlled multibody system and produced several movies:
We are also investigating integration schemes for multibody systems which better respect the mechanical structure of multibody systems. We are designing simulation methods which preserve invariants of the multibody system. Examples of invariants are energy, momentum, and the symplectic structure. Standard integrators lead to drift in energy and momentum when the system should preserve these values. Several researchers have created energy-momentum and symplectic-momentum integrators. We are developing a procedure to construct mechanical integrators. Some of this work is documented in the last section in my MA mathematics thesis (Compressed Postscript (557KB) , PDF (1.86MB) ). A procedure to construct mechanical integrators from a discrete variational principle is developed in the following technical report:
I am working on this research with Professor J. Marsden in the Control and Dynamical Systems (CDS) group at Caltech.