Approximate Motion Synthesis of Robotic Systems via a Polar Decomposition Based Displacement Metric

This paper presents a novel methodology for approximate motion synthesis using a PD based distance metric. Finite planar locations are represented using homogenous transformations, which can then be approximated by rotations using the polar decomposition based distance metric. A bi-invariant metric calculates the distance between two locations of a rigid body. A multidimensional nested optimization procedure is then used to determine the optimum design parameters of a planar dyad to minimize the distances from the moving dyad to a finite number of desired locations. The result is an implementation of the methodology for approximate motion synthesis.