Collision avoidance for multiple Lagrangian dynamical systems with gyroscopic forces

This article introduces a novel methodology for dealing with collision avoidance for groups of mobile robots. In particular, full dynamics are considered, since each robot is modeled as a Lagrangian dynamical system moving in a three-dimensional environment. Gyroscopic forces are utilized for defining the collision avoidance control strategy: This kind of forces leads to avoiding collisions, without interfering with the convergence properties of the multi-robot system’s desired control law. Collision avoidance introduces, in fact, a perturbation on the nominal behavior of the system: We define a method for choosing the direction of the gyroscopic force in an optimal manner, in such a way that perturbation is minimized. Collision avoidance and convergence properties are analytically demonstrated, and simulation results are provided for validation purpose.

[1]  Nicholas R. Gans,et al.  Decentralized cooperative mean approach to collision avoidance for nonholonomic mobile robots , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[2]  Giuseppe Oriolo,et al.  Robot Obstacle Avoidance Using Vortex Fields , 1991 .

[3]  R. Ortega Passivity-based control of Euler-Lagrange systems : mechanical, electrical and electromechanical applications , 1998 .

[4]  Yang Yang,et al.  Restoring Connectivity of Mobile Robotic Sensor Networks While Avoiding Obstacles , 2015, IEEE Sensors Journal.

[5]  Lorenzo Sabattini,et al.  Decentralized Connectivity Maintenance For Networked Lagrangian Dynamical Systems With Collision Avoidance , 2015 .

[6]  Lorenzo Sabattini,et al.  Decentralized global connectivity maintenance for interconnected Lagrangian systems in the presence of data corruption , 2013, Eur. J. Control.

[7]  R. Kristiansen,et al.  Formation Modelling and 6DOF Spacecraft Coordination Control , 2007, 2007 American Control Conference.

[8]  O. Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[9]  Dusan M. Stipanovic,et al.  Coordination and collision avoidance for Lagrangian systems with disturbances , 2010, Appl. Math. Comput..

[10]  Jerrold E. Marsden,et al.  Gyroscopic Forces and Collision Avoidance with Convex Obstacles , 2003 .

[11]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[12]  Dusan M. Stipanovic,et al.  Bilateral Teleoperation of Multiple Mobile Agents: Coordinated Motion and Collision Avoidance , 2010, IEEE Transactions on Control Systems Technology.

[13]  Lorenzo Sabattini,et al.  Arbitrarily shaped formations of mobile robots: artificial potential fields and coordinate transformation , 2011, Auton. Robots.

[14]  G. Arfken Mathematical Methods for Physicists , 1967 .

[15]  K. Valavanis,et al.  Unmanned ground vehicle swarm formation control using potential fields , 2007, 2007 Mediterranean Conference on Control & Automation.

[16]  Giuseppe Oriolo,et al.  Local incremental planning for nonholonomic mobile robots , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[17]  Gianluca Antonelli,et al.  Flocking for multi-robot systems via the Null-Space-based Behavioral control , 2008, IROS.

[18]  Daniel E. Koditschek,et al.  Exact robot navigation using artificial potential functions , 1992, IEEE Trans. Robotics Autom..

[19]  Zhenqiang Mi,et al.  Obstacle-avoidance Connectivity Restoration for mobile sensor systems with local information , 2015, 2015 IEEE International Conference on Communications (ICC).

[20]  Lorenzo Sabattini,et al.  Collision avoidance using gyroscopic forces for cooperative Lagrangian dynamical systems , 2013, 2013 IEEE International Conference on Robotics and Automation.

[21]  R. Olfati-Saber,et al.  Collision avoidance for multiple agent systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[22]  Lorenzo Sabattini,et al.  Decentralized connectivity maintenance for cooperative control of mobile robotic systems , 2013, Int. J. Robotics Res..

[23]  Gianluca Antonelli,et al.  The null-space-based behavioral control for autonomous robotic systems , 2008, Intell. Serv. Robotics.

[24]  Andrea Gasparri,et al.  Distributed Control of Multirobot Systems With Global Connectivity Maintenance , 2013, IEEE Trans. Robotics.

[25]  Lorenzo Sabattini,et al.  On decentralized connectivity maintenance for mobile robotic systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[26]  Romeo Ortega,et al.  Passivity-based Control of Euler-Lagrange Systems , 1998 .

[27]  Thomas Stastny,et al.  Collision and Obstacle Avoidance in Unmanned Aerial Systems Using Morphing Potential Field Navigation and Nonlinear Model Predictive Control , 2015 .

[28]  Eric W. Justh,et al.  Boundary following using gyroscopic control , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[29]  Naomi Ehrich Leonard,et al.  Virtual leaders, artificial potentials and coordinated control of groups , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[30]  George J. Pappas,et al.  Stable flocking of mobile agents, part I: fixed topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[31]  Petter Ögren,et al.  Flocking with Obstacle Avoidance: A New Distributed Coordination Algorithm Based on Voronoi Partitions , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[32]  Giuseppe Oriolo,et al.  Local incremental planning for a car-like robot navigating among obstacles , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[33]  Guanrong Chen,et al.  A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements , 2009, Int. J. Control.

[34]  Hassen Salhi,et al.  Provably safe navigation for mobile robots with limited field-of-views in dynamic environments , 2012, Auton. Robots.

[35]  Lorenzo Sabattini,et al.  Decentralized Connectivity Maintenance For Networked Lagrangian Dynamical Systems With Collision Avoidance , 2015 .