Differential Geometric Approach to Trajectory Planning: Cooperative Transport by a Team of Autonomous Marine Vehicles

In this paper we addressed the cooperative transport problem for a team of autonomous surface vehicles (ASVs) towing a single buoyant load. We consider the dynamics of the constrained system and decompose the cooperative transport problem into a collection of subproblems. Each subproblem consists of an ASV and load pair where each ASV is attached to the load at the same point. Since the system states evolve on a smooth manifold, we use the tools from differential geometry to model the holonomic constraint arising from the cooperative transport problem and the non-holonomic constraints arising from the ASV dynamics. We then synthesize distributed feedback control strategies using the proposed mathematical modeling framework to enable the team transport the load on a desired trajectory. We experimentally validate the proposed strategy using a team of micro ASVs.

[1]  R. Montgomery.  A Tour of Subriemannian Geometries, Their Geodesics and Applications , 2006 .

[2]  Guofan Wu,et al.  Geometric control of multiple quadrotors transporting a rigid-body load , 2014, 53rd IEEE Conference on Decision and Control.

[3]  Calin Belta,et al.  Abstraction and control for Groups of robots , 2004, IEEE Transactions on Robotics.

[4]  L. Colombo.  A variational-geometric approach for the optimal control of nonholonomic systems , 2017, 1701.04766.

[5]  Taeyoung Lee,et al.  Geometric control of multiple quadrotor UAVs transporting a cable-suspended rigid body , 2014, 53rd IEEE Conference on Decision and Control.

[6]  Leonardo Colombo,et al.  A geometric approach to the optimal control of nonholnomic mechanical systems , 2014, 1410.5682.

[7]  Eduardo Martinez.  Lie algebroids in classical mechanics and optimal control. , 2007 .

[8]  Meeko M. K. Oishi,et al.  Lift of a cable-suspended load by a quadrotor: A hybrid system approach , 2015, 2015 American Control Conference (ACC).

[9]  Reza Langari,et al.  A novel approach for tracking control of differential drive robots subject to hard input constraints , 2016, 2016 American Control Conference (ACC).

[10]  Anthony M. Bloch,et al.  Controllability and motion planning of multibody systems with nonholonomic constraints , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[11]  Andrew D. Lewis,et al.  Simple mechanical control systems with constraints , 2000, IEEE Trans. Autom. Control..

[12]  S. Jayasuriya,et al.  Unifying geometric approach to real-time formation control , 2008, 2008 American Control Conference.

[13]  M. Ani Hsieh,et al.  Cooperative transport of a buoyant load: A differential geometric approach , 2017, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[14]  Vijay Kumar,et al.  Cooperative manipulation and transportation with aerial robots , 2009, Auton. Robots.

[15]  M. Ani Hsieh,et al.  Design of the Multi-Robot Coherent Structure Testbed (mCoSTe) for Distributed Tracking of Geophysical Fluid Dynamics , 2014 .

[16]  M. Ani Hsieh,et al.  Dynamic Adaptive Robust Backstepping Control Design for an Uncertain Linear System , 2016 .

[17]  A. D. Lewis,et al.  Geometric control of mechanical systems : modeling, analysis, and design for simple mechanical control systems , 2005 .

[18]  Sonia Martínez,et al.  On nonlinear controllability and series expansions for Lagrangian systems with dissipative forces , 2002, IEEE Trans. Autom. Control..

[19]  P. Krishnaprasad,et al.  Nonholonomic mechanical systems with symmetry , 1996 .