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. (1995), calculates the forward dynamics of a system comprising N rigid bodies connected 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 limitation in the original, and sheds new light on the relationship between this algorithm and other dynamics algorithms. The new version is applicable to systems with any type of joint, floating bases, and short branches off the main chain. It is obtained using a new technique for analysing constrained rigid-body systems by means of a change of basis in a dual system of vector spaces. This new technique is also described.