Optimal Control Method for a Lower Limb Exoskeleton with Elastic Elements

Introduction. Modern development of exoskeletons opens new horizons for rehabilitation and improving the quality of life of people with limited mobility. The relevance of the study on methods of optimal control of exoskeletons is due to the growing demand in medicine and industry. However, there are numerous challenges related to the efficient control of exoskeletons, especially in the context of the integration of elastic elements. Topics related to optimal control and tuning of system parameters to reach maximum efficiency and user comfort remain insufficiently studied. The objective of this study is to develop a method of optimal control of a lower limb exoskeleton (LLE) with elastic elements while optimizing energy costs and accounting for external disturbances. Materials and Methods. The LLE is represented by a simplified model of an inverted pendulum with elastic elements in the feet. The dynamic model of the LLE was developed using Lagrange equations. The optimal control method was based on the synthesis of a linear quadratic regulator designed to minimize energy costs. To account for the influence of external disturbances, a Kalman filter was integrated into the control loop. The parameters of the mathematical model of the LLE were obtained from published data. System simulation was performed in the Wolfram Mathematica environment. Results. A method of optimal control of the LLE with elastic elements has been developed. This method optimizes energy costs while maintaining vertical equilibrium. The system was modeled using optimal terminal control, followed by optimal feedback control. During feedback control, key parameters affecting system stability were identified: spring stiffness and damping coefficients. Integration of the Kalman filter enabled compensation for external disturbances. Discussion. The use of terminal control within the developed method reduced energy costs by 98% within a specified stabilization timeframe. Optimal values of spring stiffness and damping coefficients for obtaining the best system response were identified. The use of the optimal control method of the LLE in combination with the Kalman filter confirmed the effective compensation of external disturbances and noise, which provided the convergence of transient processes with minimal energy consumption. Conclusion. The proposed method for achieving optimal control while minimizing energy costs is a promising solution in the field of control signal calculation required to ensure stability and determine the optimal energy cost function. This is especially true for medical rehabilitation tasks. These results may be useful for further research and development in the field of robotics and wearable devices.