Shanno Quadratic Algorithms for Effective Force and Position Control in Bilateral Teleoperation

Bilateral teleoperation allows humans to interact with remote environments using robotic systems, but network-induced communication delays frequently degrade stability and tracking performance. Force feedback, which is crucial for accuracy, has issues with chattering and instability. Nonlinear dynamics is a challenge for fuzzy logic and PID controllers, and force sensors and a restricted number of degrees of freedom reduce the robot's adaptability. This study creates a mathematical model for bilateral teleoperation systems that takes network effects and communication delays into consideration to address these problems. The adaptability required in these systems cannot be handled by traditional tuning techniques. The proposed approach uses Nonlinear Model Predictive Control (NMPC) to forecast the behavior of the master-slave system over a limited period. The optimization problem incorporates variables like motion constraints, target tracking, operator input, and environmental interactions. To maximize NMPC performance, a Sequential Shanno Quadratic Optimizer (SSQO) is used. Nonlinear control problems are reduced to quadratic sub-problems by the SQP method, and their curvature is dynamically estimated by the BFGS algorithm, which also directs parameter tuning for faster convergence. The proposed method achieves significant improvements, reducing force (X position) error to 0.01 seconds, stabilizing position tracking within 0.5 seconds, and reaching a desired angle of 2 radians in 5.2 seconds. The overall system performance in bilateral teleoperation is improved by this hybrid control strategy, which also improves stability, safety, and control precision under erratic conditions.