Robust decentralised navigation of multi-agent systems with collision avoidance and connectivity maintenance using model predictive controllers

ABSTRACT This paper addresses the problem of navigation control of a general class of 2nd order uncertain nonlinear multi-agent systems in a bounded workspace, which is a subset of , with static obstacles. In particular, we propose a decentralised control protocol such that each agent reaches a predefined position at the workspace, while using local information based on a limited sensing radius. The proposed scheme guarantees that the initially connected agents remain always connected. In addition, by introducing certain distance constraints, we guarantee inter-agent collision avoidance as well as collision avoidance with the obstacles and the boundary of the workspace. The proposed controllers employ a class of Decentralized Nonlinear Model Predictive Controllers (DNMPC) under the presence of disturbances and uncertainties. Finally, simulation results verify the validity of the proposed framework.

[1]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[2]  J. Hendrickx,et al.  Rigid graph control architectures for autonomous formations , 2008, IEEE Control Systems.

[3]  F. Fontes.  A General Framework to Design Stabilizing Nonlinear Model Predictive Controllers , 2001 .

[4]  William B. Dunbar,et al.  Distributed receding horizon control for multi-vehicle formation stabilization , 2006, Autom..

[5]  P. Olver.  Nonlinear Systems , 2013 .

[6]  John S. Baras,et al.  Decentralized control of autonomous vehicles , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[7]  Dimos V. Dimarogonas,et al.  Decentralized abstractions and timed constrained planning of a general class of coupled multi-agent systems , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[8]  Dimos V. Dimarogonas,et al.  Robust Formation Control in SE(3) for Tree-Graph Structures with Prescribed Transient and Steady State Performance , 2018, Autom..

[9]  Denis Gillet,et al.  A hamilton-jacobi formulation for cooperative control of multi-agent systems , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

[10]  Dimos V. Dimarogonas,et al.  A feedback stabilization and collision avoidance scheme for multiple independent non-point agents, , 2006, Autom..

[11]  D. Limón,et al.  Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[12]  Eduardo Sontag,et al.  On characterizations of the input-to-state stability property , 1995 .

[13]  E. Gilbert,et al.  Theory and computation of disturbance invariant sets for discrete-time linear systems , 1998 .

[14]  S. Shankar Sastry,et al.  Decentralized nonlinear model predictive control of multiple flying robots , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[15]  Frank Allgöwer,et al.  Towards a Sampled-Data Theory for Nonlinear Model Predictive Control , 2003 .

[16]  Brian D. O. Anderson,et al.  Maintaining a directed, triangular formation of mobile autonomous agents , 2011, Commun. Inf. Syst..

[17]  George J. Pappas,et al.  Distributed connectivity control of mobile networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[18]  Frank Allgöwer,et al.  State and Output Feedback Nonlinear Model Predictive Control: An Overview , 2003, Eur. J. Control.

[19]  D. Koditschek,et al.  Robot navigation functions on manifolds with boundary , 1990 .

[20]  Lars Grne,et al.  Nonlinear Model Predictive Control: Theory and Algorithms , 2011 .

[21]  Hyo-Sung Ahn,et al.  A survey of multi-agent formation control , 2015, Autom..

[22]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[23]  Francesco Borrelli,et al.  Decentralized Receding Horizon Control and Coordination of Autonomous Vehicle Formations , 2008, IEEE Transactions on Control Systems Technology.

[24]  Francesco Borrelli,et al.  An auto-generated nonlinear MPC algorithm for real-time obstacle avoidance of ground vehicles , 2013, 2013 European Control Conference (ECC).

[25]  Basil Kouvaritakis,et al.  Nonlinear predictive control : theory and practice , 2001 .

[26]  H. Marquez.  Nonlinear Control Systems: Analysis and Design , 2003, IEEE Transactions on Automatic Control.

[27]  W. J. Thron,et al.  Encyclopedia of Mathematics and its Applications. , 1982 .

[28]  Dimos V. Dimarogonas,et al.  Robust Distance-Based Formation Control of Multiple Rigid Bodies with Orientation Alignment , 2016, ArXiv.

[29]  Dimos V. Dimarogonas,et al.  Decentralized Control of Uncertain Multi-Agent Systems with Connectivity Maintenance and Collision Avoidance , 2017, 2018 European Control Conference (ECC).

[30]  Marios M. Polycarpou,et al.  Cooperative Constrained Control of Distributed Agents With Nonlinear Dynamics and Delayed Information Exchange: A Stabilizing Receding-Horizon Approach , 2008, IEEE Transactions on Automatic Control.

[31]  H. ChenT,et al.  A Quasi-Infinite Horizon Nonlinear Model Predictive Control Scheme with Guaranteed Stability * , 1998 .

[32]  Dimos V. Dimarogonas,et al.  Position and orientation based formation control of multiple rigid bodies with collision avoidance and connectivity maintenance , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[33]  Manfred Morari,et al.  Contractive model predictive control for constrained nonlinear systems , 2000, IEEE Trans. Autom. Control..

[34]  Dimos V. Dimarogonas,et al.  Communication-based Decentralized Cooperative Object Transportation Using Nonlinear Model Predictive Control , 2018, 2018 European Control Conference (ECC).

[35]  D. Mayne,et al.  Robust receding horizon control of constrained nonlinear systems , 1993, IEEE Trans. Autom. Control..

[36]  A. Richards,et al.  A decentralized algorithm for robust constrained model predictive control , 2004, Proceedings of the 2004 American Control Conference.

[37]  A. Richards,et al.  Decentralized model predictive control of cooperating UAVs , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[38]  Dimos V. Dimarogonas,et al.  A Nonlinear Model Predictive Control scheme for cooperative manipulation with singularity and collision avoidance , 2017, 2017 25th Mediterranean Conference on Control and Automation (MED).

[39]  Denis Gillet,et al.  Decentralized Coordination of Autonomous Vehicles at intersections , 2011 .

[40]  George J. Pappas,et al.  Flocking in Fixed and Switching Networks , 2007, IEEE Transactions on Automatic Control.

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

[42]  Dimitra Panagou,et al.  A Distributed Feedback Motion Planning Protocol for Multiple Unicycle Agents of Different Classes , 2017, IEEE Transactions on Automatic Control.

[43]  F. Matsuno,et al.  Distributed Model Predictive Control for Multi-Vehicle Formation with Collision Avoidance Constraints , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[44]  Yasushi Hada,et al.  Constrained Model Predictive Control , 2006 .

[45]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[46]  Magnus Egerstedt,et al.  Distributed Coordination Control of Multiagent Systems While Preserving Connectedness , 2007, IEEE Transactions on Robotics.

[47]  L. Magni,et al.  Sampled-Data Model Predictive Control for Nonlinear Time-Varying Systems: Stability and Robustness , 2007 .

[48]  E. Camacho,et al.  Nonlinear Model Predictive Control: An Introductory Review , 2007 .

[49]  Xiaoming Hu,et al.  Formation constrained multi-agent control , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[50]  Dimos V. Dimarogonas,et al.  Novel event-triggered strategies for Model Predictive Controllers , 2011, IEEE Conference on Decision and Control and European Control Conference.

[51]  Francesco Borrelli,et al.  Decentralized receding horizon control for large scale dynamically decoupled systems , 2009, Autom..

[52]  Savvas G. Loizou,et al.  The Multi-Agent Navigation Transformation: Tuning-Free Multi-Robot Navigation , 2014, Robotics: Science and Systems.

[53]  Alessandro Rucco,et al.  A Model Predictive Control-Based Architecture for Cooperative Path-Following of Multiple Unmanned Aerial Vehicles , 2015 .