Sliding Mode Cooperative Control for Multirobot Systems: A Finite-Time Approach

Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finite-time stability to apply it to the problem of coordinated motion in multiagent systems. We consider a group of agents described by Euler-Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. We further extend these results to multiagent systems involving underactuated dynamical agents such as mobile wheeled robots. For this case, we show that while the position variables can be coordinated in finite time, the orientation variables converge to the steady states asymptotically. Finally, we validate our results experimentally using a wheeled mobile robot platform.