A technique for analyzing constrained rigid-body systems, and its application to the constraint force algorithm

The constraint force algorithm, as originally described by Fijany et al., c alculates the forward dynamics of a system comprising N rigid bodies connec ted together in an unbranched chain with joints from a restricted class of joint types. It was designed for parallel calculation of the dynamics, and achieves O(log N) time complexity on O(N) processors. This paper presents a new formulation of the Constraint Force Algorithm that corrects a major li mitation in the original, and sheds new light on the relationship between i t and other dynamics algorithms. The new version is applicable to systems w ith any type of joint, floating bases, and short branches off the main chai n. It is obtained using a new technique for analysing constrained rigid-bod y systems by means: of a change of basis in a dual system of vector spaces. This new technique is also described.