3D Bipedal Model With Holonomic Constraints for the Decoupled Optimal Controller Design of the Biomechanical Sit-to-Stand Maneuver

Human voluntary movements are complex physical phenomena due to the complex control mechanism for coordination of limbs in the presence of physiological constraints. In this study, we propose a nonlinear human bipedal model with thirteen generalized coordinates to model sit-to-stand (STS) transfer. The model has three position based holonomic constraints and at the first stage, we decouple the translational variables (constrained system) from rotational variables (unconstrained systems). The unconstrained rotational degrees consist of seven sagittal and three frontal plane angles, which are controlled through their respective joint torques. We further decouple these angles in sagittal and frontal plane systems for a better control strategy. In this scheme, there are three decoupled controllers working together to stabilize the nonlinear model for a STS maneuver while satisfying the holonomic constraints. We adopt $H∞$ and $H2$ controller designs for feedback torques in sagittal and frontal planes, respectively, and provide simulation results to show the improvement in the angular profiles. We further adopt this modeling strategy to study and analyze the neuromuscular disorders by decoupling healthy and neurodeficient extremities. Our study indicates that the decoupling of the bipedal model improves the controllability of the system and produces better angular profiles for a bipedal STS maneuver. This modeling scheme is useful for analysis of neuromuscular disorders and other relevant physiological motor control models.