Multi-robot navigation in formation via sequential convex programming

This paper presents a method for navigating a team of robots in formation in 2D and 3D environments with static and dynamic obstacles. The method is local and computes the optimal parameters for the formation within a neighborhood of the robots, allowing for reconfigurations, when required, by considering a set of target formations. The method consists of first computing the largest collision-free convex polytope in a neighborhood of the robots, followed by a constrained optimization via sequential convex programming where the optimal parameters for the formation are obtained. The robots navigate towards the target collision-free formation with individual local planners that account for their dynamics. The approach is efficient and scalable with the number of robots and performed well in simulations with a large team of quadrators and in experiments with two mobile manipulators carrying a rigid object.

[1]  YangQuan Chen,et al.  Formation control: a review and a new consideration , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[2]  Wei Ren,et al.  Distributed coordination architecture for multi-robot formation control , 2008, Robotics Auton. Syst..

[3]  Harold W. Kuhn,et al.  The Hungarian method for the assignment problem , 1955, 50 Years of Integer Programming.

[4]  Paul A. Beardsley,et al.  Object and animation display with multiple aerial vehicles , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[5]  Vijay Kumar,et al.  Towards a swarm of agile micro quadrotors , 2012, Autonomous Robots.

[6]  Steven M. LaValle,et al.  Fast, Near-Optimal Computation for Multi-Robot Path Planning on Graphs , 2013, AAAI.

[7]  Tucker R. Balch,et al.  Behavior-based formation control for multirobot teams , 1998, IEEE Trans. Robotics Autom..

[8]  Robin Deits,et al.  Computing Large Convex Regions of Obstacle-Free Space Through Semidefinite Programming , 2014, WAFR.

[9]  Paul A. Beardsley,et al.  Image and animation display with multiple mobile robots , 2012, Int. J. Robotics Res..

[10]  Angela P. Schoellig,et al.  Generation of collision-free trajectories for a quadrocopter fleet: A sequential convex programming approach , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[11]  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..

[12]  Tucker R. Balch,et al.  Social potentials for scalable multi-robot formations , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[13]  Paul A. Beardsley,et al.  Collision avoidance for aerial vehicles in multi-agent scenarios , 2015, Auton. Robots.

[14]  Vijay Kumar,et al.  Distributed multi-robot task assignment and formation control , 2008, 2008 IEEE International Conference on Robotics and Automation.

[15]  Petter Ögren,et al.  A control Lyapunov function approach to multi-agent coordination , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[16]  Vijay Kumar,et al.  Modeling and control of formations of nonholonomic mobile robots , 2001, IEEE Trans. Robotics Autom..

[17]  John R. Spletzer,et al.  Convex Optimization Strategies for Coordinating Large-Scale Robot Formations , 2007, IEEE Transactions on Robotics.

[18]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[19]  Ross A. Knepper,et al.  Local motion planning for collaborative multi-robot manipulation of deformable objects , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[20]  Vijay Kumar,et al.  Automated composition of motion primitives for multi-robot systems from safe LTL specifications , 2014, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[21]  Vijay Kumar,et al.  A semidefinite programming framework for controlling multi-robot systems in dynamic environments , 2010, 49th IEEE Conference on Decision and Control (CDC).

[22]  D. Bertsekas.  The auction algorithm: A distributed relaxation method for the assignment problem , 1988 .