  Benchmarks of state-of-the-art rigid-body dynamics libraries report better
performance solving the inverse dynamics problem than the forward alternative.
Those benchmarks encouraged us to question whether that computational advantage
would translate to direct transcription, where calculating rigid-body dynamics
and their derivatives accounts for a significant share of computation time. In
this work, we implement an optimization framework where both approaches for
enforcing the system dynamics are available. We evaluate the performance of
each approach for systems of varying complexity, for domains with rigid
contacts. Our tests reveal that formulations using inverse dynamics converge
faster, require less iterations, and are more robust to coarse problem
discretization. These results indicate that inverse dynamics should be
preferred to enforce the nonlinear system dynamics in simultaneous methods,
such as direct transcription.
