Efficient formulation of the force-distribution equations for simple closed-chain robotic mechanisms

Force distribution is the inverse dynamics problem for multiple-chain systems in which the motion is completely specified and the internal forces/torques to effect this motion are to be determined. A computationally efficient formulation for the force-distribution problem is presented. This formulation is applicable to a number of simple closed-chain robotic mechanisms, including dexterous hands, multiple manipulators, and multilegged vehicles. Modeling of chain contacts is relatively general so that hard point contact, soft finger contact or rigid contact with an irregularly-shaped object or with uneven terrain may be handled. The dynamic effects of the chains and physical limits on their actuators are efficiently included in the formulation through the use of the inverse dynamics and Jacobian relationships for each chain. Based on this efficient formulation, a variety of methods may then be developed to solve the force-distribution problem