A direct collocation framework for optimal control simulation of pedaling using OpenSim

Abstract

The direct collocation (DC) method has shown low computational costs in solving optimization problems in human movements, but it has rarely been used for solving optimal control pedaling problems. Thus, the aim of this study was to develop a DC framework for optimal control simulation of human pedaling within the OpenSim modeling environment. A planar bicycle-rider model was developed in OpenSim. The DC method was formulated in MATLAB to solve an optimal control pedaling problem using a data tracking approach. Using the developed DC framework, the optimal control pedaling problem was successfully solved in 24 minutes to ten hours with different objective function weightings and number of nodes from two different initial conditions. The optimal solutions for equal objective function weightings were successful in terms of tracking, with the model simulated pedal angles and pedal forces within ±1 standard deviation of the experimental data. With these weightings, muscle tendon unit (MTU) excitation patterns generally matched with burst timings and shapes observed in the experimental EMG data. Tracking quality and MTU excitation patterns were changed little by selection of node density above 31, and the optimal solution quality was not affected by initial guess used. The proposed DC framework could easily be turned into a predictive simulation with other objective functions such as fastest pedaling rate. This flexible and computationally efficient framework should facilitate the use of optimal control methods to study the biomechanics, energetics, and control of human pedaling.