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

TL;DR

This study compares direct multiple shooting and direct collocation methods in biomechanical predictive simulations, finding similar performance overall but with some advantages for DC with inverse dynamics constraints.

Contribution

It provides a systematic comparison of DMS and DC methods in biomechanics, highlighting the benefits of DC with inverse dynamics for better solutions and efficiency.

Findings

All methods converged to similar solutions in most cases.

DC with inverse dynamics constraints was faster and more consistent.

No single method was systematically superior across all examples.

Abstract

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.