7.4.2 Active-Passive Link Decompositions

An alternative sampling-based approach is to perform an active-passive decomposition, which is used to generate samples in ${{\cal C}_{clo}}$ by directly sampling active variables, and computing the closure values for passive variables using inverse kinematics methods. This method was introduced in [432] and subsequently improved through the development of the random loop generator in [244,246]. The method serves as a general framework that can adapt virtually any of the methods of Chapter 5 to handle closed kinematic chains, and experimental evidence suggests that the performance is better than the method of Section 7.4.1. One drawback is that the method requires some careful analysis of the linkage to determine the best decomposition and also bounds on its mobility. Such analysis exists for very general classes of linkages [244].