Mixed-integer quadratic program trajectory generation for heterogeneous quadrotor teams

We present an algorithm for the generation of optimal trajectories for teams of heterogeneous quadrotors in three-dimensional environments with obstacles. We formulate the problem using mixed-integer quadratic programs (MIQPs) where the integer constraints are used to enforce collision avoidance. The method allows for different sizes, capabilities, and varying dynamic effects between different quadrotors. Experimental results illustrate the method applied to teams of up to four quadrotors ranging from 65 to 962 grams and 21 to 67 cm in width following trajectories in three-dimensional environments with obstacles with accelerations approaching 1g.

[1]  Raffaello D'Andrea,et al.  A simple learning strategy for high-speed quadrocopter multi-flips , 2010, 2010 IEEE International Conference on Robotics and Automation.

[2]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[3]  Gerd Hirzinger,et al.  Energy-efficient Autonomous Four-rotor Flying Robot Controlled at 1 kHz , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[4]  Russ Tedrake,et al.  LQR-trees: Feedback motion planning on sparse randomized trees , 2009, Robotics: Science and Systems.

[5]  B. Moor,et al.  Mixed integer programming for multi-vehicle path planning , 2001, 2001 European Control Conference (ECC).

[6]  J. How,et al.  Multi-vehicle path planning for non-line of sight communication , 2006, 2006 American Control Conference.

[7]  Sebastian Thrun,et al.  ARA*: Anytime A* with Provable Bounds on Sub-Optimality , 2003, NIPS.

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

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

[10]  Alborz Geramifard,et al.  On the Design and Use of a Micro Air Vehicle to Track and Avoid Adversaries , 2010, Int. J. Robotics Res..

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

[12]  Claire J. Tomlin,et al.  Design of guaranteed safe maneuvers using reachable sets: Autonomous quadrotor aerobatics in theory and practice , 2010, 2010 IEEE International Conference on Robotics and Automation.

[13]  Jonathan P. How,et al.  Plume Avoidance Maneuver Planning Using Mixed Integer Linear Programming , 2001 .

[14]  Vijay Kumar,et al.  Trajectory Generation and Control for Precise Aggressive Maneuvers with Quadrotors , 2010, ISER.

[15]  J. How,et al.  Receding horizon path planning with implicit safety guarantees , 2004, Proceedings of the 2004 American Control Conference.