Distance-based Formation Control Using Angular Information Between Robots

Distance-based formation of groups of mobile robots provides an alternative focus for motion coordination strategies respect to the standard consensus-based formation strategies. However, the setup formulation introduces non rigidity problems, multiple formation patterns that verify the distance constraints or local minima appeared when collision avoidance strategies are added to the control laws. This paper proposes a novel combined distance-based potential functions with attractive-repulsive behavior in order to simplify the navigation problem as well as the use of angular information between robots to reduce the likelihood of unwanted formation patterns. Moreover, this approach eliminates the local minima generated by the control laws to reach the desired formation configuration in the case of three robots. The analysis addresses the case of omnidirectional robots and is extended to the case of unicycle-type robots with numerical simulations and real-time experiments.

[1]  Alberto Ortiz,et al.  Extending the potential fields approach to avoid trapping situations , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[2]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[3]  José Luis Gordillo,et al.  Kinematics and Dynamics of a New 16 DOF Humanoid Biped Robot with Active Toe Joint , 2012 .

[4]  Hyo-Sung Ahn,et al.  Distance-based formation control using euclidean distance dynamics matrix: Three-agent case , 2011, Proceedings of the 2011 American Control Conference.

[5]  Zhong-Ping Jiang,et al.  A nonlinear small-gain approach to distributed formation control of nonholonomic mobile robots , 2013, 2013 American Control Conference.

[6]  Karl Henrik Johansson,et al.  Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control , 2010, Autom..

[7]  Dimos V. Dimarogonas,et al.  Sufficient Conditions for Decentralized Potential Functions Based Controllers Using Canonical Vector Fields , 2012, IEEE Transactions on Automatic Control.

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

[9]  E. G. Hernandez-Martinez,et al.  Non-Collision Conditions in Multi-Agent Virtual Leader-Based Formation Control , 2012 .

[10]  Magnus Egerstedt,et al.  Connectivity graphs as models of local interactions , 2004, CDC.

[11]  S. Glavaski,et al.  Connectivity and convergence of formations , 2005, Proceedings of the 2005, American Control Conference, 2005..

[12]  K.J. Kyriakopoulos,et al.  Formation Control and Collision Avoidance for Multi-Agent Systems and a Connection between Formation Infeasibility and Flocking Behavior , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[13]  Javaid Iqbal,et al.  On the Improvement of Multi-Legged Locomotion over Difficult Terrains Using a Balance Stabilization Method: , 2012 .

[14]  Andrew B. Kahng,et al.  Cooperative Mobile Robotics: Antecedents and Directions , 1997, Auton. Robots.

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

[16]  Mireille E. Broucke,et al.  Stabilization of infinitesimally rigid formations of multi-robot networks , 2008, 2008 47th IEEE Conference on Decision and Control.

[17]  Brian D. O. Anderson,et al.  Combining distance-based formation shape control with formation translation , 2012 .

[18]  Sung-Mo Kang,et al.  Distance-based formation control with a single moving leader , 2014, 2014 American Control Conference.

[19]  Xi Chen,et al.  Global Finite-Time Stabilization for Nonholonomic Mobile Robots Based on Visual Servoing , 2014 .

[20]  Karl Henrik Johansson,et al.  On the stability of distance-based formation control , 2008, 2008 47th IEEE Conference on Decision and Control.

[21]  Baris Fidan,et al.  Single-View Distance-Estimation-Based Formation Control of Robotic Swarms , 2013, IEEE Transactions on Industrial Electronics.

[22]  José Antonio Cruz-Ledesma,et al.  Modelling, Design and Robust Control of a Remotely Operated Underwater Vehicle , 2014 .

[23]  E. Aranda-Bricaire,et al.  Multi-agent formation control with collision avoidance based on discontinuous vector fields , 2009, 2009 35th Annual Conference of IEEE Industrial Electronics.

[24]  Jaydev P. Desai,et al.  A Graph Theoretic Approach for Modeling Mobile Robot Team Formations , 2002, J. Field Robotics.

[25]  Lynne E. Parker,et al.  Guest editorial advances in multirobot systems , 2002, IEEE Trans. Robotics Autom..

[26]  Vijay Kumar,et al.  Formation control with configuration space constraints , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[27]  Eduardo Aranda-Bricaire,et al.  Convergence and Collision Avoidance in Formation Control: A Survey of the Artificial Potential Functions Approach , 2011 .

[28]  Dimos V. Dimarogonas,et al.  Distributed cooperative control and collision avoidance for multiple kinematic agents , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[29]  Hyo-Sung Ahn,et al.  Distance-based formation control using Euclidean distance dynamics matrix: General cases , 2011, Proceedings of the 2011 American Control Conference.

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

[31]  Alex Fukunaga,et al.  Cooperative mobile robotics: antecedents and directions , 1995 .

[32]  Ronald C. Arkin,et al.  An Behavior-based Robotics , 1998 .

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

[34]  Shaoshuai Mou,et al.  Toward robust control of minimally rigid undirected formations , 2014, 53rd IEEE Conference on Decision and Control.

[35]  Oussama Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1986 .

[36]  Mireille E. Broucke,et al.  Local control strategies for groups of mobile autonomous agents , 2004, IEEE Transactions on Automatic Control.

[37]  Hengjun Zhang,et al.  Robust Practical Stabilization of Nonholonomic Mobile Robots Based on Visual Servoing Feedback with Inputs Saturation , 2014 .

[38]  Vijay Kumar,et al.  Leader-to-formation stability , 2004, IEEE Transactions on Robotics and Automation.

[39]  Mireille E. Broucke,et al.  Stabilisation of infinitesimally rigid formations of multi-robot networks , 2009, Int. J. Control.

[40]  Petter Ögren,et al.  Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment , 2004, IEEE Transactions on Automatic Control.

[41]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

[42]  E. G. Hernandez-Martinez,et al.  Decentralized Formation Control of Multi-agent Robot Systems based on Formation Graphs , 2012 .

[43]  Ming Cao,et al.  Controlling Rigid Formations of Mobile Agents Under Inconsistent Measurements , 2015, IEEE Transactions on Robotics.

[44]  Karl H. Johansson,et al.  Further results on the stability of distance-based multi-robot formations , 2009, 2009 American Control Conference.

[45]  Shuzhi Sam Ge,et al.  Queues and artificial potential trenches for multirobot formations , 2005, IEEE Transactions on Robotics.

[46]  Mireille E. Broucke,et al.  Formations of vehicles in cyclic pursuit , 2004, IEEE Transactions on Automatic Control.

[47]  Marcio de Queiroz,et al.  Adaptive rigidity-based formation control of uncertain multi-robotic vehicles , 2014, 2014 American Control Conference.