2 NUMERICAL ISSUES IN SIMULATING CONSTRAINED ROBOT DYNAMICS

A common approach to formulating the dynamics of closed-chain mechanis ms requires finding the forces of constraint at the loop closures. How ever, there are indications that this approach leads both to ill condi tioned systems that must be inverted and to numerically unstable diffe rential equations of motion. We derive a sufficient condition for ill conditioning of augmented dynamical systems-that the mechanism's traje ctory passes through, or very near, a kinematic singularity. In singul ar regions the equations of motion are also numerically stiff, and the y frequently require special numerical methods for computer solution. We propose a new method of calculating closed-chain dynamics, based on the systematic elimination of variables that are both redundant and t hat may adversely affect the computations. This approach produces nume rically stable solutions of the differential equations of motion, and the equations are apparently much less stiff than the equations produc ed by the traditional force-closure approach.