Sources of Error in a Rigid Body Simulation of Rigid parts on a vibrating Rigid plate

Trajectory of circle motion	Experimental videos (can be seen below)

As in many other fields, simulation is becoming an increasingly important tool for supporting research in robotics. Not surprisingly, many of the important problems that could yield to closed-form analysis have been solved and studied thoroughly. Problems characterized by intermittent contact is one particularly important type of robotics problems for which research must rely on simulation techniques. Evidence of this need for simulation is the recent trend of robotics researchers studying grasping, assembly, and dexterous manipulation problems using Open Dynamic Engine (ODE http://www.ode.org ). ODE was developed for computer game applications, which has led its developers to trade physical accuracy for simulation speed and believable results. The fact that researchers are using ODE (hoping that it will work well enough for their particular problem) shows the strong need for a physically accurate simulation tool.

In this paper, we present initial results verifying the accuracy of the Stewart-Trinkle time-stepping method, which lies at the core of the dVC physics engine. This method is derived directly from the instantaneous dynamic model written as dynamic complementarity problem using Euler approximations of derivatives and including constraint stabilization terms. The resulting simulation method requires the solution of one complementarity problem per time step. One of the benefits of our time-stepper is that as the time step goes to zero, the solution trajectories converge to a solution of the original instantaneous-time problem. Additional results are presented showing the effects of various sources of model approximation errors. Most of the problems studied had time-stepping sub-problems formulated as linear complementarity problems (LCPs). These were simulated using dVC. However, custom C-code was written for problem whose sub-problems were formulated as nonlinear complementarity problems (NCPs). All the LCPs and NCPs were solved by the state-of-the-art complementarity solver, PATH ( http://www.cs.wisc.edu/cpnet/cpnetsoftware/ ).

Videos

A video of Tom Vose's vibratory plate system executing circle trajectory can be seen here. The video shows a part moving on a semi-circular path caused by vibratory input designed using dVC. The second half of the video show the part moving with input designed analytically by Vose, Umbanhower, and Lynch. Listen to the audio track and notice that the trajectory designed by dVC takes advantage of larger vibrational amplitudes that cause contact breaking (you can hear the chattering). The second half of the video is quiet, because the analytically-designed vibration required the assumption that the part could never lose contact with the plate.

A related video produced by of our simulation software can be found here.

Publications

S. Berard, B. Nguyen, and J.C. Trinkle. Sources of error in a rigid body simulation of rigid parts on a vibrating rigid plate. ACM Symposium on Applied Computing.

S. Berard, B. Nguyen, K. Anderson, and J.C. Trinkle. Sources of error in a simulation of rigid parts on a vibrating rigid plate. Technical Report 08-10, Department of Computer Science, Rensselaer Polytechnic Institute, 2008.

-- BinhNguyen - 26 Sep 2009 -- Edited by JeffTrinkle - 06 Oct 2009