Evaluation of Direct Collocation Optimal Control Problem Formulations for Solving the Muscle Redundancy Problem.

Area of Science:

• Biomechanics
• Computational modeling
• Human movement analysis

Background:

• Estimating muscle forces during human motion is an indeterminate problem often solved using optimization.
• Modeling muscle activation and contraction dynamics introduces computational challenges for dynamic optimization.

Purpose of the Study:

• To identify a robust and computationally efficient formulation for solving dynamic optimization problems.
• To investigate direct collocation optimal control methods for muscle force estimation.

Main Methods:

• Compared four problem formulations using direct collocation optimal control for walking.
• Investigated explicit vs. implicit contraction dynamics with muscle length or tendon force as state variables.
• Utilized nonlinear equations of contraction dynamics as algebraic path constraints in implicit formulations.

Main Results:

• Implicit contraction dynamics formulations demonstrated robustness and convergence for all initial guesses.
• Explicit contraction dynamics with muscle length as a state variable frequently failed to converge.
• Implicit formulation with tendon force as a state variable was generally the fastest computationally.

Conclusions:

• Implicit representations of muscle contraction dynamics offer a computationally efficient and robust solution for muscle force estimation.
• This approach overcomes limitations of traditional methods like static optimization and computed muscle control.