Algorithmic differentiation improves the computational efficiency of OpenSim-based trajectory optimization of human...

Area of Science:

• Biomechanics
• Computational Science
• Human Movement Analysis

Background:

• Finite differences (FD) are commonly used for derivative calculations in trajectory optimization.
• Algorithmic differentiation (AD) offers a more accurate and potentially faster alternative.
• OpenSim is a widely used software for musculoskeletal modeling and biomechanical analysis.

Purpose of the Study:

• To demonstrate the computational advantages of using AD over FD in OpenSim-based human movement trajectory optimization.
• To evaluate the impact of different AD tools, linear solvers, and derivative orders on computational efficiency.
• To facilitate the use of detailed musculoskeletal models in biomechanical applications.

Main Methods:

• Implemented AD in OpenSim using a custom source code transformation tool and the ADOL-C library.
• Developed an interface between OpenSim and CasADi for trajectory optimization.
• Conducted simulations of perturbed balance, 2D walking, and 3D walking using direct collocation and implicit differential equations.

Main Results:

• AD via the custom tool was 1.8–17.8 times faster than FD and 3.6–12.3 times faster than ADOL-C.
• Linear solver efficiency varied by problem; no single solver was consistently superior.
• Second-order derivatives were more efficient for balance but less for walking simulations.
• Simulations produced physiologically realistic walking gaits.

Conclusions:

• AD drastically reduces computational time for trajectory optimization problems compared to FD.
• Combining AD with direct collocation and implicit differential equations lessens the computational burden for human movement analysis.
• This approach will enable wider application of detailed musculoskeletal models in biomechanics.