A Synchronization Approach to Trajectory Tracking of Multiple Mobile Robots While Maintaining Time-Varying Formations

In this paper, we present a synchronization approach to trajectory tracking of multiple mobile robots while maintaining time-varying formations. The main idea is to control each robot to track its desired trajectory while synchronizing its motion with those of other robots to keep relative kinematics relationships, as required by the formation. First, we pose the formation-control problem as a synchronization control problem and identify the synchronization control goal according to the formation requirement. The formation error is measured by the position synchronization error, which is defined based on the established robot network. Second, we develop a synchronous controller for each robot's translation to guarantee that both position and synchronization errors approach zero asymptotically. The rotary controller is also designed to ensure that the robot is always oriented toward its desired position. Both translational and rotary controls are supported by a centralized high-level planer for task monitoring and robot global localization. Finally, we perform simulations and experiments to demonstrate the effectiveness of the proposed synchronization control approach in the formation control tasks.

[1]  M. Ani Hsieh,et al.  Pattern generation with multiple robots , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[2]  Lynne E. Parker,et al.  ALLIANCE: an architecture for fault tolerant multirobot cooperation , 1998, IEEE Trans. Robotics Autom..

[3]  Randal W. Beard,et al.  A coordination architecture for spacecraft formation control , 2001, IEEE Trans. Control. Syst. Technol..

[4]  Randal W. Beard,et al.  A decentralized approach to formation maneuvers , 2003, IEEE Trans. Robotics Autom..

[5]  Soon-Jo Chung,et al.  Application of Synchronization to Formation Flying Spacecraft: Lagrangian Approach , 2008, 0803.0170.

[6]  C. McInnes.  Autonomous ring formation for a planar constellation of satellites , 1995 .

[7]  Mu-Tian Yan,et al.  Theory and application of a combined self-tuning adaptive control and cross-coupling control in a retrofit milling machine , 2005 .

[8]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[9]  S. Goddard,et al.  Localization and follow-the-leader control of a heterogeneous group of mobile robots , 2006, IEEE/ASME Transactions on Mechatronics.

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

[11]  Naomi Ehrich Leonard,et al.  Stabilization of symmetric formations to motion around convex loops , 2008, Syst. Control. Lett..

[12]  S. H. Huang,et al.  A Linear Cross-Coupled Control System for High-Speed Machining , 2002 .

[13]  Dong Sun.  Position synchronization of multiple motion axes with adaptive coupling control , 2003, Autom..

[14]  Naomi Ehrich Leonard,et al.  Stabilization of Planar Collective Motion: All-to-All Communication , 2007, IEEE Transactions on Automatic Control.

[15]  Lu Ren,et al.  Integration of saturated PI synchronous control and PD feedback for control of parallel manipulators , 2006, IEEE Transactions on Robotics.

[16]  Wolfram Burgard,et al.  A Probabilistic Approach to Collaborative Multi-Robot Localization , 2000, Auton. Robots.

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

[18]  Masayoshi Tomizuka,et al.  Synchronization of Two Motion Control Axes Under Adaptive Feedforward Control , 1990 .

[19]  Gerard S. Schkolnik,et al.  Autonomous Formation Flight , 2004 .

[20]  Camillo J. Taylor,et al.  A vision-based formation control framework , 2002, IEEE Trans. Robotics Autom..

[21]  Can Wang,et al.  Controlling Swarms of Mobile Robots for Switching between Formations Using Synchronization Concept , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

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

[23]  Gang Feng,et al.  A Model-Free Cross-Coupled Control for Position Synchronization of Multi-Axis Motions: Theory and Experiments , 2007, IEEE Transactions on Control Systems Technology.

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

[25]  Lu Ren,et al.  Synchronous Tracking Control of Parallel Manipulators Using Cross-coupling Approach , 2006, Int. J. Robotics Res..

[26]  Jie Yang,et al.  Global localization of multirobot formations using ceiling vision SLAM strategy , 2007, 2007 14th International Conference on Mechatronics and Machine Vision in Practice.

[27]  Vijay R. Kumar,et al.  Optimal Motion Generation for Groups of Robots: A Geometric Approach , 2004 .

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

[29]  Yael Edan,et al.  Navigation of decentralized autonomous automatic guided vehicles in material handling , 2003, IEEE Trans. Robotics Autom..

[30]  Daniel J. Stilwell,et al.  Platoons of underwater vehicles , 2000 .

[31]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[32]  Kouhei Ohnishi,et al.  Autonomous decentralized control for formation of multiple mobile robots considering ability of robot , 2004, IEEE Transactions on Industrial Electronics.

[33]  Wei Kang,et al.  Formation control of autonomous agents in 3D workspace , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[34]  Mehran Mesbahi,et al.  Formation flying control of multiple spacecraft via graphs , 2001 .

[35]  Robin R. Murphy,et al.  Application of the Distributed Field Robot Architecture to a Simulated Demining Task , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[36]  J. Borenstein,et al.  Cross-coupling motion controller for mobile robots , 1993, IEEE Control Systems.

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

[38]  Pau-Lo Hsu,et al.  Estimation of the contouring error vector for the cross-coupled control design , 2002 .

[39]  Kostas J. Kyriakopoulos,et al.  Nonholonomic navigation and control of cooperating mobile manipulators , 2003, IEEE Trans. Robotics Autom..

[40]  Jian Chen,et al.  Leader-Follower Formation Control of Multiple Non-holonomic Mobile Robots Incorporating a Receding-horizon Scheme , 2010, Int. J. Robotics Res..

[41]  Yoram Koren,et al.  Cross-Coupled Biaxial Computer Control for Manufacturing Systems , 1980 .

[42]  Masayoshi Tomizuka,et al.  Contouring control of machine tool feed drive systems: a task coordinate frame approach , 2001, IEEE Trans. Control. Syst. Technol..

[43]  Kar-Han Tan,et al.  High Precision Formation Control of Mobile Robots Using Virtual Structures , 1997, Auton. Robots.

[44]  Soon-Jo Chung,et al.  Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems , 2007, IEEE Transactions on Robotics.

[45]  Dong Sun,et al.  Adaptive synchronized control for coordination of multirobot assembly tasks , 2002, IEEE Trans. Robotics Autom..

[46]  Henk Nijmeijer,et al.  Mutual synchronization of robots via estimated state feedback: a cooperative approach , 2004, IEEE Transactions on Control Systems Technology.

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

[48]  Syh-Shiuh Yeh,et al.  Analysis and design of integrated control for multi-axis motion systems , 2003, IEEE Trans. Control. Syst. Technol..

[49]  D. Sun,et al.  A Synchronization Approach for the Minimization of Contouring Errors of CNC Machine Tools , 2009, IEEE Transactions on Automation Science and Engineering.

[50]  Richard M. Murray,et al.  Information flow and cooperative control of vehicle formations , 2004, IEEE Transactions on Automatic Control.

[51]  Yoram Koren,et al.  Variable-Gain Cross-Coupling Controller for Contouring , 1991 .

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

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