Determination of minimum-effort motions for general open chains

In this paper we compute approximate minimum effort motions for open chains by solving a finite dimensional minimization problem using B-splines for the path representation. We begin by deriving the gradient of the recursive Newton-Euler dynamics formulation with respect to the parameters of a curve defining the motion, where the kinematics are expressed via the product of matrix exponentials. We then use this gradient to solve joint torque minimization problems for spatial open chains. The advantage of our approach is that the gradients are computed for each local frame recursively, therefore sharing the same efficiency advantages as the original recursive algorithm, and also can be computed for any spatial open chain. The optimization approach is applied to several open chains where minimum effort paths are found