A Safe, high-precision reinforcement learning-based optimal control of surgical continuum robots: A monotone tube boundary approach with prescribed-time control capability

This paper introduces a novel approach to the prescribed-time control of continuum surgical robots, focusing on four key areas: enhanced system safety, tailored transient tracking, steady-state tracking enhancement, and optimal learned control. The main contribution is the application of system state constraints on tracking error, transforming these constraints into an unconstrained problem using a monotone tube boundary. This method avoids the complexity of Model Predictive Control (MPC) and Control Barrier Functions (CBF) techniques, as well as the conservatism and fixed-boundary issues associated with the Barrier Lyapunov Function (BLF) method. By using a monotone tube boundary, the approach allows for the pre-assignment of transient characteristics for tracking error, avoiding excessive overshoot and lack of adjustability seen with the Prescribed Performance Function (PPF). The prescribed-time control philosophy enables pre-determination of settling time, enhancing precision and convergence rates essential for surgical applications. Additionally, an optimized prescribed-time control strategy using an actor-critic neural network-based Reinforcement Learning (RL) approach ensures controller optimality, reducing control effort, power consumption, and heat generation in the robot's actuators. The method adapts to dynamic environments, ensuring robust performance in various surgical scenarios. Simulation results on a two-segment continuum robot demonstrate the proposed method's advantages over state-of-the-art techniques.