Decentralized formation control with variable shapes for aerial robots

We address formation control for a team of quadrotors in which the robots follow a specified group trajectory while safely changing the shape of the formation according to specifications. The formation is prescribed by shape vectors which dictate the relative separations and bearings between the robots, while the group trajectory is specified as the desired trajectory of a leader or a virtual robot in the group. Each robot plans its trajectory independently based on its local information of neighboring robots which includes both the neighbor's planned trajectory and an estimate of its state. We show that the decentralized trajectory planners (a) result in consensus on the planned trajectory for predefined shapes and (b) achieve safe reconfiguration when changing shapes.

[1]  Vijay Kumar,et al.  Minimum snap trajectory generation and control for quadrotors , 2011, 2011 IEEE International Conference on Robotics and Automation.

[2]  George J. Pappas,et al.  Input-to-state stability on formation graphs , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[3]  Petter Ögren,et al.  Formations with a Mission: Stable Coordination of Vehicle Group Maneuvers , 2002 .

[4]  Vijay Kumar,et al.  Trajectory generation and control for precise aggressive maneuvers with quadrotors , 2012, Int. J. Robotics Res..

[5]  Richard M. Murray,et al.  Real Time Trajectory Generation for Differentially Flat Systems , 1996 .

[6]  Tom Burr,et al.  Introduction to Matrix Analytic Methods in Stochastic Modeling , 2001, Technometrics.

[7]  Marcello R. Napolitano,et al.  Design and Flight Testing Evaluation of Formation Control Laws , 2006, IEEE Transactions on Control Systems Technology.

[8]  Karl Henrik Johansson,et al.  A Study On Distributed Model Predictive Consensus , 2008, ArXiv.

[9]  Taeyoung Lee,et al.  Geometric tracking control of a quadrotor UAV on SE(3) , 2010, 49th IEEE Conference on Decision and Control (CDC).

[10]  Antonio Franchi,et al.  A passivity-based decentralized approach for the bilateral teleoperation of a group of UAVs with switching topology , 2011, 2011 IEEE International Conference on Robotics and Automation.

[11]  John R. Hauser,et al.  Unconstrained receding horizon control of nonlinear systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[12]  Richard M. Murray,et al.  DISTRIBUTED COOPERATIVE CONTROL OF MULTIPLE VEHICLE FORMATIONS USING STRUCTURAL POTENTIAL FUNCTIONS , 2002 .

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

[14]  V. Ramaswami,et al.  4. Birth-and-Death Processes , 1999 .

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

[16]  Jie Yu,et al.  Unconstrained receding-horizon control of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[17]  Thomas Kämpke,et al.  Distance Patterns in Structural Similarity , 2006, J. Mach. Learn. Res..

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

[19]  Mehran Mesbahi,et al.  On state-dependent dynamic graphs and their controllability properties , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[20]  Vijay Kumar,et al.  The GRASP Multiple Micro-UAV Testbed , 2010, IEEE Robotics & Automation Magazine.

[21]  Taeyoung Lee,et al.  Geometric tracking control of the attitude dynamics of a rigid body on SO(3) , 2010, Proceedings of the 2011 American Control Conference.

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

[23]  Vijay Kumar,et al.  Trajectory design and control for aggressive formation flight with quadrotors , 2012, Auton. Robots.

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

[25]  S. Shankar Sastry,et al.  Decentralized nonlinear model predictive control of multiple flying robots , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[26]  George J. Pappas,et al.  Feasible formations of multi-agent systems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).