R. Featherstone et A. Fijany, A technique for analyzing constrained rigid-body systems, and its application to the constraint force algorithm, IEEE ROBOT, 15(6), 1999, pp. 1140-1144
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.