A simple and quick control strategy for a class of first-order nonholonomic manipulator

Abstract

This paper presents a simple and quick control strategy for a class of first-order nonholonomic manipulator: planar n-link manipulator with a passive first joint (no gravity). The control target is driving its endpoint from any initial position to any target position. First, we reduce the planar n-link manipulator to a planar three-link one by maintaining the states (angles and angular velocities) of n-3 active links in the initial value all the time. That is, we only adjust the states of the remaining two active links in the whole control process, and these two adjusted active links are chosen to guarantee that the target position is in the reachable region of the planar n-link manipulator by using the enumeration method. Then, we divide the whole control process into two stages for the reduced planar three-link manipulator. In each stage, the manipulator becomes a planar two-link one by maintaining the states of one adjusted active link to be the constant value. The state constraint existing between the passive first link and the adjusted active link is obtained by using the integral characteristics of a planar two-link manipulator. Meantime, the geometric constraint between the position of the endpoint and angles of all joints is obtained based on the homogeneous coordinate transformation method. According to the above two kinds of constraint, the target angles of the two adjusted active links are calculated by employing the particle swarm optimization algorithm. When the two adjusted active links are controlled to their target angles in turn, the control target of the planar n-link manipulator is completed. Finally, simulation results demonstrate that the proposed control strategy is valid and rapid.