Force optimization in redundantly-actuated closed kinematic chains

The authors establish why redundant actuation situations arise, the relationship of redundant actuation to time-varying topologies, and the desirability of redundant actuation. Various techniques are then outlined for solving the optimal force distribution problem, to obtain force setpoints for the controller in real time. Although direct substitutions is by far the fastest of these, its implementation requires a careful monitoring of numerical degeneracies. Solution of the problem using orthogonal decomposition is recommended as it provides the opportunity to introduce inequality constraints, which are important in many problems. An effective technique is introduced for smoothing the discontinuities in the optimal solution, which result from the discontinuous topology