Decentralized Prescribed-Time Control of Robotic Arm-Finger Systems for Grasping and Moving Tasks

The control of a humanoid robot equipped with one arm and multiple fingers, designed primarily for grasping and manipulating various objects, is investigated. Synchronizing the movements of the fingers is a challenging task, as each joint must reach the desired angle simultaneously to ensure a firm grasp. The success of this task hinges on the synchronization of convergence times for each finger joint; otherwise, the object may slip or escape. This challenge is further intensified by uncertainties in the dynamics of the hand or the object. We present decentralized prescribed-time tracking control strategies for the dynamical system comprising the arm-finger combination. In this system, the fingers are primarily used for grasping the object while the arm is responsible for moving, tilting, or flipping it. To streamline the controller structure and simplify the stability analysis, we design a linear controller based on the maximum eigenvalue of a parameter matrix and establish a new technical lemma, which paves the way for the stability analysis of the prescribed-time tracking and the reduction of the input efforts of the actuator. We develop robust and decentralized adaptive control schemes separately for the arm and fingers, achieving better transient performance with less prior knowledge and lower computation costs. Finally, we validate the proposed controller's performance through kinematic simulations of grasping and moving tasks in 3-D, alongside numerical simulations that demonstrate the tracking performance of our algorithm in the joint space.