Hierarchical Model Predictive Control for Multi-Robot Navigation

Ensuring the stability is the most important requirement for the navigation control of multi-robot systems with no reference trajectory. The popular heuristic-search methods cannot provide theoretical guarantees on stability. In this paper, we propose a Hierarchical Model Predictive Control scheme that employs reachable sets to decouple the navigation problem of linear dynamical multirobot systems. The proposed control scheme guarantees the stability and feasibility, and is more efficient and viable than other Model Predictive Control schemes, as evidenced by our simulation results.

[1]  Mario Sznaier,et al.  Suboptimal control of linear systems with state and control inequality constraints , 1987, 26th IEEE Conference on Decision and Control.

[2]  Maria L. Gini,et al.  Adaptive Learning for Multi-Agent Navigation , 2015, AAMAS.

[3]  Pavel Janovsky,et al.  Finding coordinated paths for multiple holonomic agents in 2-d polygonal environment , 2014, AAMAS.

[4]  F. Borrelli,et al.  A study on decentralized receding horizon control for decoupled systems , 2004, Proceedings of the 2004 American Control Conference.

[5]  Stephen J. Roberts,et al.  Conservative collision prediction and avoidance for stochastic trajectories in continuous time and space , 2014, AAMAS.

[6]  Jun-ichi Imura,et al.  Controlled invariant feasibility - A general approach to enforcing strong feasibility in MPC applied to move-blocking , 2009, Autom..

[7]  Gianluca Antonelli,et al.  Decentralized centroid and formation control for multi-robot systems , 2013, 2013 IEEE International Conference on Robotics and Automation.

[8]  J. Rawlings,et al.  The stability of constrained receding horizon control , 1993, IEEE Trans. Autom. Control..

[9]  Jonathan P. How,et al.  Cooperative Distributed Robust Trajectory Optimization Using Receding Horizon MILP , 2011, IEEE Transactions on Control Systems Technology.

[10]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[11]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.

[12]  William B. Dunbar,et al.  Model predictive control of coordinated multi-vehicle formations , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[13]  Francis J. Doyle,et al.  Distributed model predictive control of an experimental four-tank system , 2007 .

[14]  Jonathan Rossiter,et al.  Proceedings of 2013 IEEE International Conference on Robotics and Automation ICRA2013 , 2013 .

[15]  T. Keviczky,et al.  Hierarchical design of decentralized receding horizon controllers for decoupled systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[16]  Romain Bourdais,et al.  Distributed MPC Under Coupled Constraints Based on Dantzig-Wolfe Decomposition , 2014 .

[17]  Peter Gritzmann,et al.  Minkowski Addition of Polytopes: Computational Complexity and Applications to Gröbner Basis , 1993, SIAM J. Discret. Math..

[18]  Manfred Morari,et al.  Multi-Parametric Toolbox 3.0 , 2013, 2013 European Control Conference (ECC).

[19]  Andrés Rosales,et al.  Formation control and trajectory tracking of mobile robotic systems – a Linear Algebra approach , 2010, Robotica.

[20]  Yu Tian,et al.  Formation control of mobile robots subject to wheel slip , 2012, 2012 IEEE International Conference on Robotics and Automation.

[21]  William B. Dunbar,et al.  Cooperative control of multi-vehicle systems using cost graphs and optimization , 2003, Proceedings of the 2003 American Control Conference, 2003..