Algorithmic differentiation improves the computational efficiency of OpenSim-based optimal control simulations of movement

Algorithmic differentiation (AD) is an alternative to finite differences (FD) for evaluating function derivatives. The primarily aim of this study was to demonstrate the computational benefits of using AD instead of FD in OpenSim-based optimal control simulations. The secondary aim was to evaluate computational choices including different AD tools, different linear solvers, and the use of first- or second-order derivatives. First, we enabled the use of AD in OpenSim through a custom source code transformation tool and through the operator overloading tool ADOL-C. Second, we developed an interface between OpenSim and CasADi to perform optimal control simulations. Third, we evaluated computational choices through simulations of perturbed balance, two-dimensional predictive simulations of walking, and three-dimensional tracking simulations of walking. We performed all simulations using direct collocation and implicit differential equations. Using AD through our custom tool was between 1.8 ± 0.1 and 17.8 ± 4.9 times faster than using FD, and between 3.6 ± 0.3 and 12.3 ± 1.3 times faster than using AD through ADOL-C. The linear solver efficiency was problem-dependent and no solver was consistently more efficient. Using second-order derivatives was more efficient for balance simulations but less efficient for walking simulations. The walking simulations were physiologically realistic. These results highlight how the use of AD drastically decreases computational time of optimal control simulations as compared to more common FD. Overall, combining AD with direct collocation and implicit differential equations decreases the computational burden of optimal control simulations, which will facilitate their use for biomechanical applications.