The virtual erector set: Dynamic simulation with linear recursive constraint propagation

Abstract

We have implemented an algorithm for rigid body dynamics which unifies the advantages of linear recursive algorithms with the advantages of earlier linear algebra based constraint force approaches. No restriction is placed on the joints between links. The algorithm is numerically robust and can deal with arbitrary trees of bodies, including kinematic loops. Motion as well as force constraints on the dynamic behavior of any member of the linkage can be added easily. Through the use of spatial algebra notation-including our extension to account for spatial position-the mathematical expressions are simplified and more efficient to execute. The algorithm has been implemented on workstation class machines and performs at interactive speeds.