Robust control for master–slave manipulator system avoiding obstacle collision under restricted working space

The aim of this work is to design a robust output-based controller for a robotic manipulator (RM) with a master–slave configuration (MSC). The trajectories of the slave robot manipulator (SRM) must fulfil two types of constraints. The first corresponds to the boundaries of the obstacles placed in the given workspace. The second is related to the boundaries of the workspace. The controller must ensure the collision avoidance of the obstacles and the end-effector of the SRM should remain inside of the workspace. The proposed controller satisfies a state feedback structure with time-varying gains. The time-variable gains include an integral compensation that guarantees the collision avoidance with the obstacle satisfying the boundary of the workspace, which is the main contribution of this study. The solution of a matrix inequality characterises the zone of convergence and the suboptimal control gains. A set of numerical simulations using a MSC based on a couple of two-link RMs illustrates the advantages obtained with the proposed method. Also, a set of experimental results demonstrate the effectiveness of the proposed controller.