A Method for the Real Time Solution of the Forward Dynamics Problem for Robots Incorporating Friction

A modular and computationally efficient method for solving the forward dynamics problem of robot mechanisms incorporating Coulomb friction is developed. This hybrid approach incorporates both analog and digital components that facilitate real time solutions. Coulomb friction effects associated with both transmissions and bearings are considered. Moreover, the methods accounts for joint flexibility as well as actuator gyroscopic effects. In our approach, the inverse dynamics formulation is used for solving the forward dynamics problem. The positive definiteness property of the inertia matrix of the dynamic equations of motion is exploited by intentionally introducing algebraic loops so that simultaneous algebraic equations are solved without iterations. By resolving these algebraic loops using linear electronics, one avoids the computational burden and time delays associated with purely digital solutions, thus facilitating real time operation. A proof of stability is also presented. The formulation developed here is useful in cases requiring either or both the inverse and forward dynamics solutions typically associated with design and control.