Derivations of the Balafoutis & Patel Recursive Dynamics Formulation

In the Siggraph 1996 paper, Efficient Generation of Motion Transitions Using Spacetime Constraints [3], we used the Balafoutis and Patel dynamics formulation [1] together with the spacetime optimization animation technique [4] to create high-quality transitions for a full-body human-figure model. Balafoutis and Patel created the most efficient linear-recursive inverse dynamics method currently known. In order to perform gradient-based optimization, such as with BFGS [2], we derived the partials of their equations with respect to joint angle position, velocity, and acceleration. This technical report details the complete dynamics formulation used in [3], including all the partial equations which could not appear in Siggraph due to space limitations. This tech-report is intended as a companion to that paper.