Direct multiple shooting and direct collocation perform similarly in biomechanical predictive simulations

Abstract

Direct multiple shooting (DMS) and direct collocation (DC) are two standard transcription methods for solving optimal control problems (OCP) in biomechanics and robotics. They have yet to be 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 no single method outperformed the others systematically. All methods converged to almost the same solution (cost, states, and controls) in all but one OCP, with several local minima found in the latter. Nevertheless, DC based on fourth-order Legendre polynomials provided overall better results, especially regarding dynamics integration accuracy 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 dynamic constraints based on inverse dynamics converged to better and less variable solutions. We recommend starting with this transcription to solve OCPs but keep testing other methods.