Multibody Control and Simulation

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:

• 3D human model balancing (Experiment 1 in Chapter 4 of Ph.D. dissertation) (MPEG 854KB) (Compressed SGI movie 617KB) (Compressed QuickTime 527KB)
• 3D human model hit by a 1.8Kg (4 lb) projectile thrown at 4.5 m/s (10 mph) (Experiment 2 in Chapter 4 of Ph.D. dissertation) (MPEG 833KB) (Compressed SGI movie 643KB) (Compressed QuickTime 512KB)
• Standing Planar Model of a Human (MPEG 1.0MB) , (Compressed SGI movie 670KB) , (Compressed QuickTime 667KB)
• Stumbling Planar Model of a Human (MPEG 972KB) , (Compressed SGI movie 493KB) , (Compressed QuickTime 1.1MB)
• Rising then Crouching Planar Model of a Human (MPEG 725KB) , (Compressed SGI movie 452KB) , (Compressed QuickTime 523KB)

• J. Wendlandt, "Control and Simulation of Multibody Systems". Ph.D. thesis in Mechanical Engineering. University of California at Berkeley. Fall 1997. UCB/ERL Technical Memo M97/48. Compressed Postscript (542KB) , PDF file (2.16MB)
• J. Wendlandt, "A Recursive Workspace Balancing Controller for a 3D Multibody Model of a Biped", 36th IEEE Conference on Decision and Control, San Diego, December 10-12, 1997. Compressed Postscript (90KB) , PDF file (400KB)
• J. Wendlandt and S. Sastry, "Recursive Workspace Control of Multibody Systems: A Planar Biped Example", 35th IEEE Conference on Decision and Control, Kobe, Japan, December 11-13, 1996. Compressed Postscript (92KB) , PDF file (372KB)

• Multibody Control and Simulation. Jeff Wendlandt and Shankar Sastry. March 22, 1996. Natick, MA. Army Research Lab. Compressed Postscript (120KB)

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:

• Jeff M. Wendlandt and Jerrold E. Marsden, "Mechanical Integrators Derived from a Discrete Variational Principle", Caltech CDS Technical Report 96-013. Compressed Postscript (140KB) , PDF (569KB).

I am working on this research with Professor J. Marsden in the Control and Dynamical Systems (CDS) group at Caltech.