Singularity-Free Finite-Time Adaptive Optimal Control for Constrained Coordinated Uncertain Robots

This article investigates the singularity-free finite-time adaptive optimal control problem for coordinated robots, where the position and velocity are constrained within the asymmetric yet time-varying ranges. Different from the existing results concerning constrained control, the imposed feasibility conditions are relaxed by skillfully integrating a nonlinear state-dependent function into the backstepping design procedure. Therein, the typical feature of the designed finite-time controller lies in the application of the modified smooth switching function, rendering the designed controller powerful enough to eliminate singularity problem. Notably, with the aid of the constructed optimal cost function and neural network-based critic architecture, the optimal control law is established under the backstepping design framework. It is theoretically verified that the designed controller is of satisfied optimization and finite-time tracking ability, and desired constrained objective in the meanwhile. The validity of the resulting control algorithm is eventually substantiated via two robotic manipulators.