MODELING AND OPTIMAL CONTROL OF AN UPPER-LIMB BIONIC PROSTHESIS IN THE SAGITTAL PLANE
DOI:
https://doi.org/10.32782/pet-2025-2-5Keywords:
bionic prosthesis, dynamic modeling, sagittal plane, linear -quadratic regulator, OpenSim, MATLABAbstract
The study investigates the modelling and optimal control of a bionic upper-limb prosthesis in the sagittal plane. The aim is to develop a mathematical model of the bionic upper limb, simulate its motion in the sagittal plane, and design a robust linear–quadratic regulator (LQR) to ensure a physiologically natural response of the elbow joint, taking into account angular position, velocity, and acceleration. To describe upper-limb motions, the Lagrangian formalism is employed, enabling derivation of the equations of motion for a two-link arm model. The system of equations is linearized in the vicinity of operating points. Methods of optimal control theory, in particular the synthesis of an LQR controller, are applied to obtain the optimal control law. Computations and simulations are carried out in MATLAB using the open biomechanical arm model from OpenSim. The work combines nonlinear dynamic modelling with a state-space approximation to develop a robust controller. The proposed approach demonstrates the feasibility of effectively reproducing physiological upper-limb movements using an LQR regulator. The obtained results show the system’s ability to maintain stability and motion accuracy even under disturbances and measurement errors, bringing it closer to biological control principles. The designed LQR controller provides stable, accurate, and energy-efficient control of the bionic upper-limb prosthesis in the sagittal plane. The proposed model can serve as a basis for prototyping high-technology bionic devices and for further studies aimed at extending the model to three-dimensional space and integrating neural or EMG signals for more natural control.
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