Contents I. Introduction
The movement of kinematic chains is of interest in many areas of science and engineering, including robotics [3], [5], [12], [14] and protein structure prediction [2], [4]. A valuable tool should have the ability to generate (i.e., sample) configurations that satisfies certain hard feasibility constraints, such as kinematic loop closure and collision avoidance, and soft preference constraints, such as low energy and high likelihood. This is computationally challenging: the volume of feasible and favorable configurations is a minuscule subset of the configuration space, whose volume typically shrinks exponentially as dimensionality increases. Moreover, closed-chain constraints, which occur in parallel robots, robot manipulation, legged locomotion, and protein fragments, restrict the feasible set to a lower-dimensional manifold with zero volume.
