  Direct multiple shooting (DMS) and direct collocation (DC) are two common
transcription methods for solving optimal control problems (OCP) in
biomechanics and robotics. They have rarely been compared in terms of solution
and speed. Through five examples of predictive simulations solved using five
transcription methods and 100 initial guesses in the Bioptim software, we
showed that not a single method outperformed systematically better. All methods
converged to almost the same solution (cost, states, and controls) in all but
one OCP, with several local minima being found in the latter. Nevertheless, DC
based on fourth-order Legendre polynomials provided overall better results,
especially in terms of dynamic consistency compared to DMS based on a
fourth-order Runge-Kutta method. Furthermore, expressing the rigid-body
constraints using inverse dynamics was usually faster than forward dynamics. DC
with dynamics constraints based on inverse dynamics converged to better and
less variable solutions. Consequently, we recommend starting with this
transcription to solve OCPs but keep testing other methods.
