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The Use of Kane's Dynamical Equations in Robotics

Extensive experience has shown that the use of general- purpose, multibody-dynamics computer programs for the numerical formulation and solution of equations of motion of robotic devices leads to slow evaluation of actuator forces and torques and slow simulation of robot motions. In this paper, it is shown how improvements in computational efficiency can be effected by using Kane's dynamical equations to formulate explicit equations of motion. To these ends, a detailed analysis of the Stanford Arm is presented in such a way that each step in the analysis serves as an illustrative example for a general method of attack on problems of robot dynamics. Simulation results are reported and are used as a basis for discussing questions of computational efficiency.