Safe and complete trajectory generation for robot teams with higher-order dynamics

In this work, we consider the labeled multi-robot planning problem. In this paradigm, a team of robots at fixed start positions must navigate to pre-specified and noninterchangable goal positions. While many algorithms have been proposed for finding optimal solutions to this problem, most methods assume that the robots are kinematic agents, whereas in reality, robots often have high-order dynamics that must be respected by their trajectories. Here, we propose a centralized method for generating trajectories for teams of robots with general nth-order dynamics navigating to labeled goals. Our algorithm is safe and complete and additionally allows for decoupled optimization of each robot's trajectory as a Quadratic Program with linear constraints. We present simulation results for teams of up to 20 robots.

[1]  Daniela Rus,et al.  An Effective Algorithmic Framework for Near Optimal Multi-robot Path Planning , 2015, ISRR.

[2]  Antonio Bicchi,et al.  Conflict resolution problems for air traffic management systems solved with mixed integer programming , 2002, IEEE Trans. Intell. Transp. Syst..

[3]  Steven M. LaValle,et al.  Structure and Intractability of Optimal Multi-Robot Path Planning on Graphs , 2013, AAAI.

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

[5]  Vijay Kumar,et al.  Capt: Concurrent assignment and planning of trajectories for multiple robots , 2014, Int. J. Robotics Res..

[6]  John Enright,et al.  Optimization and Coordinated Autonomy in Mobile Fulfillment Systems , 2011, Automated Action Planning for Autonomous Mobile Robots.

[7]  Kostas E. Bekris,et al.  Push and Swap: Fast Cooperative Path-Finding with Completeness Guarantees , 2011, IJCAI.

[8]  Nathan R. Sturtevant,et al.  Enhanced Partial Expansion A , 2014, J. Artif. Intell. Res..

[9]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[10]  Antonio Bicchi,et al.  Decentralized Cooperative Policy for Conflict Resolution in Multivehicle Systems , 2007, IEEE Transactions on Robotics.

[11]  Dinesh Manocha,et al.  Reciprocal Velocity Obstacles for real-time multi-agent navigation , 2008, 2008 IEEE International Conference on Robotics and Automation.

[12]  Steven M. LaValle,et al.  Planning optimal paths for multiple robots on graphs , 2012, 2013 IEEE International Conference on Robotics and Automation.

[13]  Vijay Kumar,et al.  A Complete Algorithm for Generating Safe Trajectories for Multi-robot Teams , 2015, ISRR.

[14]  N. Roy,et al.  Polynomial Trajectory Planning for Quadrotor Flight , 2012 .

[15]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[16]  M. E. Flores.  Real-Time Trajectory Generation for Constrained Nonlinear Dynamical Systems Using Non-Uniform Rational B-Spline Basis Functions , 2008 .

[17]  Dinesh Manocha,et al.  Centralized path planning for multiple robots: Optimal decoupling into sequential plans , 2009, Robotics: Science and Systems.

[18]  Jingjin Yu,et al.  Intractability of Optimal Multirobot Path Planning on Planar Graphs , 2015, IEEE Robotics and Automation Letters.

[19]  Vijay Kumar,et al.  Mixed-integer quadratic program trajectory generation for heterogeneous quadrotor teams , 2012, 2012 IEEE International Conference on Robotics and Automation.