Hierarchical Decentralized LQR Control for Formation-Keeping of Cooperative Mobile Robots in Material Transport Tasks

Abstract

This study provides a formation-keeping method based on consensus for mobile robots used in cooperative transport applications that prevents accidental damage to the objects being carried. The algorithm can be used to move both rigid and elastic materials, where the desired formation geometry is predefined. The cooperative mobile robots must maintain formation even when encountering unknown obstacles, which are detected using each robot's on-board sensors. Local actions would then be taken by the robot to avoid collision. However, the obstacles may not be detected by other robots in the formation due to line-of-sight or range limitations. Without sufficient communication or coordination between robots, local collision avoidance protocols may lead to the loss of formation geometry. This problem is most notable when the object being transported is deformable, which reduces the physical force interaction between robots when compared to rigid materials. Thus, a decentralized, hierarchical LQR control scheme is proposed that guarantees formation-keeping despite local collision avoidance actions, for both rigid and elastic objects. Representing the cooperative robot formation using multi-agent system framework, graph Laplacian potential and Lyapunov stability analysis are used to guarantee tracking performance and consensus. The effectiveness and scalability of the proposed method are illustrated by computer simulations of line (2 robots) and quadrilateral (4 robots) formations. Different communication topologies are evaluated and provide insights into the minimum bandwidth required to maintain formation consensus.