Single-network based adaptive dynamic programming optimal control for robotic manipulator with joint limitation under input saturation

This paper proposes an optimal control method based on adaptive dynamic programming (ADP) for manipulators with joint limitation under input saturation. The asymmetric input saturation problem is solved by introducing a smooth function, by which the saturation and nonsmooth issues of the input caused by the actuators can be handled. Joint limitation of the manipulator is transformed through a transfer function, which is incorporated into the cost function of the whole robotic system, to guarantee the joint limitation will not be violated. Meanwhile, due to the difficulty in solving Hamilton-Jacobi-Bellman (HJB) equation, the critic network is constructed utilising radial basis function neural networks (RBFNNs) to approximate the cost function. This approach effectively overcomes the curse of dimensionality problem associated with dynamic programming. Subsequently, an ADP-based optimal controller is designed for the robotic system. Lyapunov synthesis is used in the stability analysis to prove all the signals are convergent and ultimately uniformly bounded (UUB). Simulations are conducted on a planar 3-DOF manipulator to validate the effectiveness of the proposed method. The results demonstrate the improved performance and feasibility of the developed ADP-based optimal control strategy in handling joint limitations and input saturation challenges in robotic systems.