Multirobot System Formation Control With Multiple Performance and Feasibility Constraints

Abstract

In this work, we propose a novel framework to address the formation control problem for a class of multirobot systems with two types of constraints, namely the performance constraints and the feasibility constraints. For the performance constraints, we consider the constraint requirements on the distance tracking errors between the real and the desired trajectories for each robot, so that to ensure <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">precise</i> tracking of the robot without deviating too much from its desired trajectory, as well as the constraints on the interrobot distance, so that to ensure the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">safe</i> operation of the team. For the feasibility constraints, we consider the constraints on the heading angle, so that the controllers designed in the brief are feasible. Universal barrier functions are adopted in the controller design and analysis, which is a generic framework that can address systems with different types of constraints in a unified controller architecture. Through rigorous analysis, exponential convergence rate can be guaranteed on the distance tracking errors, while all constraints are satisfied during the operation. A simulation example and an experiment using three AmigoBot mobile robots further demonstrate the efficacy of the proposed control framework.