Robust kinetics estimation from kinematics via direct collocation

Introduction Accurate joint moment analysis is essential in biomechanics, and the integration of direct collocation with markerless motion capture offers a promising approach for its estimation. However, markerless motion capture can introduce varying degrees of error in tracking trajectories. This study aims to evaluate the effectiveness of the direct collocation method in estimating kinetics when joint trajectory data are impacted by noise.Methods We focused on walking and squatting movements as our target activities. To assess the method's robustness, we created five groups with differing noise levels-noise-free, mild noise, noisy group1, noisy group2, and a Gaussian noise group-in the joint center trajectories. Our approach involved combining joint center tracking with biological terms within the direct collocation scheme to address noise-related challenges. We calculated kinematics, joint moments, and ground reaction forces for comparison across the different noise groups.Results For the walking task, the mean absolute errors (MAEs) for the knee flexion moments were 0.103, 0.113, 0.127, 0.129, and 0.116 Nm/kg across the respective noise levels. The corresponding MAEs of the ankle flexion moment were 0.130, 0.133, 0.145, 0.131, and 0.138 Nm/kg. The hip flexion moment had MAEs of 0.182, 0.204, 0.242, 0.246, and 0.249 Nm/kg in the respective groups. In squatting, the MAEs of ankle flexion moments were 0.207, 0.219, 0.217, 0.253, and 0.227 Nm/kg in the noise-free, mild noise, noisy group1, noisy group2, and the Gaussian noise group, respectively. The MAEs of the knee flexion moments were 0.177, 0.196, 0.198, 0.197, and 0.221 Nm/kg, whereas the mean MAEs of the hip flexion moments were 0.125, 0.135, 0.141, 0.161, and 0.178 Nm/kg in the respective groups.Conclusion The results highlight that the direct collocation method incorporating both tracking and biological terms in the cost function could robustly estimate joint moments during walking and squatting across various noise levels. Currently, this method is better suited to reflect general activity dynamics than subject-specific dynamics in clinical practice. Future research should focus on refining cost functions to achieve an optimal balance between robustness and accuracy.