-- MattSpenko? - 21 Oct 2005
I created this stabilty margin because I wasn't convinced that the center of mass of a climbing robot needed to stay inside the convex hull of the robot's contact points. That is only necessarily true if you do not consider the effects of adhesion. This stability margin does consider adhesion. Most of the math that I did to evaluate this is based on the Papadopoulos and Rey 2000 stability margin, but the concept is simpler. Basically I create the convex hull on contact points and then find the moment from all the forces (including adhesion) to determine if the robot is going to tip over any of the edges of the convex hull.

This stability margin should help us evaluate the following:

1) Leg morphology. By changing the foot contact points we can examine how different leg morphologies can lead to more (or less) stable robots.

2) Required foot adhesion forces. We can use the stability margin tool to evaluate the requied adhesion forces for a foot.

3) Gait. By using a tool like this online we could measure the foot adhesion forces and then determine which foot is acceptable to detach from the wall.

You can run the attached Matlab script. I don't make any assurances that it is completely free of bugs at this point. The script will output a figure that shows the center of mass, the convex hull, and the values of the stabilty margin for each edge of the convex hull.

You will have to go in and change some of the values for adhesion, contact point location, and other parameters by hand. The file is commented enough to do this.

A positive value means that the robot will not tipover that edge. A negative value means that the robot is tipping over that edge. A zero value means that it is about to tipover that edge. A NaN means that it is physically impossible to tipover that edge (the edge is parallel to the force vector acting on the center of mass.