View Full Version : Simulating dynamics with stiff inertia matrix

Mitch Maltenfort
05-21-2004, 02:59 AM
Hello, list.

I'm posting here today because I'm trying to run a simulation of a 7 dof limb -- spherical knee, 2 dof at knee and ankle.

(Disclaimer: after several years studying motoneuronal circuits, I'm trying to branch out into biomechanics. As we all know, nothing is as dangerous as a scientist outside his specialty...)

I set up the equations for an n-link manipulator (Yoshikawa, "Foundations of Robotics," pp. 91 - 95 on Maple, told Maple to generate Matlab code with optimzations. (The optimized code required about 2000 intermediate variables!). The Matlab code was then compiled as a MEX-file for speed.

I've confirmed that when confined to a plane (x and y orientation angles = 0), these matrices (Jacobian, inertia matrix in joint coordinates, centrifugal and Coriolis coefficients)and those from a planar, 3-link model of the limb have the same values in their corresponding elements.

I've been attempting to test the 7 dof model by simulating a simple gravity drop -- have the foot under the hip and release. I set up the ODE on Matlab, so that the angular acceleration was determined from the inertia matrix and the gravitational and joint interaction torques. That's when I ran afoul of a problem normally associated with Jacobians -- the inertia matrix was becoming near-singular, and integration was grinding to a halt.

I've been looking at ways of beating this. After reading Mussa-Ivaldi and Hogan's paper, I'm leery of using the pseudo-inverse for integration. I could change my transformation matrices to put in lateral offsets of joint centers, but that seems ad hoc.

Can anyone advise? Thanks in advance.

On a related note: if anybody's interested in the Maple worksheets I put together, or the generated Matlab code, let me know. You're welcome in advance.

Mitchell Gil Maltenfort
Dept. of Neurobiology and Anatomy
Drexel University College of Medicine
2900 Queen Lane
Phila, PA 19129

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