  We propose a novel unifying scheme for parallel implementation of articulated
robot dynamics algorithms. It is based on a unified Lie group notation for
deriving the equations of motion of articulated robots, where various
well-known forward algorithms differ only by their joint inertia matrix
inversion strategies. This new scheme leads to a unified abstraction of
state-of-the-art forward dynamics algorithms into combinations of block
bi-diagonal and/or block tri-diagonal systems, which may be efficiently solved
by parallel all-prefix-sum operations (scan) and parallel odd-even elimination
(OEE) respectively. We implement the proposed scheme on a Nvidia CUDA GPU
platform for the comparative study of three algorithms, namely the hybrid
articulated-body inertia algorithm (ABIA), the parallel joint space inertia
inversion algorithm (JSIIA) and the constrained force algorithm (CFA), and the
performances are analyzed.
