Affine Formation Control for End-Effectors of Networked Manipulators With Maneuvering Leaders and Unknown System Parameters

This article studies the distributed control problem of collectively achieving and maneuvering the formation shape for the end-effectors of networked multiple Euler-Lagrange manipulators. In the formation process, precious few manipulators, called leaders, determine their motions autonomously, whereas a bulk of followers steer themselves to form the target geometric pattern and achieve desired affine transformation. For both undirected and directed graphs, distributed control protocols are proposed to achieve formation in the task space, but through the control inputs injected at joints' level, without using the absolute positions of the end-effectors. Meanwhile, distributed observers and adaptive laws are designed for each follower to estimate its desired behavior and both dynamic and kinematic unknown parameters. Moreover, a new kinematic adaptive law is proposed for undirected graph without using absolute velocity information. The asymptotic convergence of the closed-loop systems is proven, and the effectiveness of the proposed approach is validated by exemplary simulation examples of networked two-link manipulators.