Design of Adaptive LQR Control Based on Improved Grey Wolf Optimization for Prosthetic Hand

Assistive technologies, particularly multi-fingered robotic hands (MFRHs), are critical for enhancing the quality of life for individuals with upper-limb disabilities. However, achieving precise and stable control of such systems remains a significant challenge. This study proposes an Improved Grey Wolf Optimization (IGWO)-tuned Linear Quadratic Regulator (LQR) to enhance the control performance of an MFRH. The MFRH was modeled using Denavit-Hartenberg kinematics and Euler-Lagrange dynamics, with micro-DC motors selected based on computed torque requirements. The LQR controller, optimized via IGWO to systematically determine weighting matrices, was benchmarked against PID and PID-PSO controllers under diverse input scenarios. For step input, the IGWO-LQR achieved a settling time of 0.018 s with zero overshoot for Joint 1, outperforming PID (settling time: 0.0721 s; overshoot: 6.58%) and PID-PSO (settling time: 0.042 s; overshoot: 2.1%). Similar improvements were observed across all joints, with Joint 3 recording an IAE of 0.001334 for IGWO-LQR versus 0.004695 for PID. Evaluations under square-wave, sine, and sigmoid inputs further validated the controller's robustness, with IGWO-LQR consistently delivering minimal tracking errors and rapid stabilization. These results demonstrate that the IGWO-LQR framework significantly enhances precision and dynamic response.