I am working on NXTway_GS LEgo mindstorm robot whose model equations are attached. The Nonlinear state equations are given in terms of theta=Average angle of wheels, psi=Body Pitch Angle and phi=body yaw angle. I want to see the linear position and linear velocity. What could be the simple transformation from angular position to linear position. Please help me.
if the problem is to know the new linear position after rotating a given linear position along a given set of three angles.... then as a starting point, considering center of wheel as origin, you can create a 3D rotation matrix (using yaw, pitch and roll).... The columns of this matrix will represent the three directional axis along which the wheel moves... afterwards you can multiply this 3X3 matrix with appropriate scalers e.g. L along theta, W along phi in order to know the new position....
http://planning.cs.uiuc.edu/node102.html
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