Control system modeling for robot manipulators by use of a canonical transformation

A nonlinear transformation for simplifying the robot dynamic formulation and control system modeling is presented. This is a canonical transformation in the Hamiltonian formulation of robot dynamics, and it can be embodied in a special decomposition of the total inertia matrix. In simplification by using this canonical transformation, the dynamic system is not only transformed to a linear model with the Brunovsky canonical form, the input formulation is also reduced to a simple recovery form. By taking advantage of the linearity of the robot dynamic equation with respect to the total inertia matrix, a detailed procedure of the realization is then described. A 3-D robot example illustrates the feasibility and computational efficiency of this procedure. And it also shows that the realization procedure for the canonical transformation can be summed up in two major steps: seek an imaginary robot and solve a reduced equation.