Input-constrained formation control of differential-drive mobile robots: geometric analysis and optimisation

This study considers the formation control of differential-drive mobile robots subject to diamond-shaped input constraints. A basic controller form in terms of two feedback functions is proposed in a leader-follower setup. The existence of suitable feedback functions, guaranteeing the achievement of desired formation and the satisfaction of input constraints, is confirmed by a sufficient condition derived from geometric analysis. The geometric analysis also helps selections of feedback functions. Optimal feedback functions are designed to fully exploit the maneuverability of mobile robots. In addition, the performance assignment, which confines the velocities of the follower robot in a specified subset of diamond-shaped input domain to avoid slippage and reduce mechanical wear, is discussed. Simulation results are included to verify the effectiveness of the proposed controllers.

[1]  Dusan M. Stipanovic,et al.  Formation Control and Collision Avoidance for Multi-agent Non-holonomic Systems: Theory and Experiments , 2008, Int. J. Robotics Res..

[2]  Domenico Prattichizzo,et al.  Stabilization of a Hierarchical Formation of Unicycle Robots with Velocity and Curvature Constraints , 2009, IEEE Transactions on Robotics.

[3]  Ji-Sang Sun,et al.  Nonlinear tracking control for nonholonomic mobile robots with input constraints: an experimental study , 2005, Proceedings of the 2005, American Control Conference, 2005..

[4]  Igor Skrjanc,et al.  A Case Study of the Collision-Avoidance Problem Based on Bernstein–Bézier Path Tracking for Multiple Robots with Known Constraints , 2010, J. Intell. Robotic Syst..

[5]  Kostas J. Kyriakopoulos,et al.  Navigation of Multiple Kinematically Constrained Robots , 2008, IEEE Transactions on Robotics.

[6]  Junping Du,et al.  Formation control of mobile robots with input constraints: An elliptic approximation approach , 2011, 2011 11th International Conference on Control, Automation and Systems.

[7]  Ching-Hung Lee,et al.  Tracking control of unicycle-modeled mobile robots using a saturation feedback controller , 2001, IEEE Trans. Control. Syst. Technol..

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

[9]  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..

[10]  Bo Gao,et al.  Pareto-optimal coordination of multiple robots with safety guarantees , 2011, Autonomous Robots.

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

[12]  Domenico Prattichizzo,et al.  Discussion of paper by , 2003 .

[13]  Randal W. Beard,et al.  Trajectory tracking for unmanned air vehicles with velocity and heading rate constraints , 2004, IEEE Transactions on Control Systems Technology.

[14]  Junping Du,et al.  Column formation control of multi-robot systems with input constraints , 2011, IEEE Conference on Decision and Control and European Control Conference.

[15]  Jin Bae Park,et al.  Adaptive Formation Control of Electrically Driven Nonholonomic Mobile Robots With Limited Information , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[16]  Zhong-Ping Jiang,et al.  Saturated stabilization and tracking of a nonholonomic mobile robot , 2001 .

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

[18]  H. Jin Kim,et al.  Nonlinear Model Predictive Formation Flight , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

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

[21]  Yoo Sang Choo,et al.  Leader-follower formation control of underactuated autonomous underwater vehicles , 2010 .

[22]  Guangming Xie,et al.  Leader-following formation control of multiple mobile vehicles , 2007 .

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

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

[25]  Nathan van de Wouw,et al.  Saturated control of time-varying formations and trajectory tracking for unicycle multi-agent systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[26]  Loulin Huang.  Control approach for tracking a moving target by a wheeled mobile robot with limited velocities , 2009 .