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Trajectory_Planning.md

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Trajectory Planning

polyhedron-1

  • Path planning algorithms (Dijkstra, Astar, Jump point search)
  • Generating Convex Polytopes(Safe Flight Corridors)
  • Trajectory planning(Ax = b, QP)
  • Trajectory following control(PD controller)

Required

MATLAB(R2019b is tested)

Pic

1. Path Planning

dijkstra Astar Jump Point Search
dijkstra Astar JPS
1.642271 seconds 0.755504 seconds 0.451664 seconds

2. Generating Convex Polytopes

Safe Flight Corridors

  • find_ellipsoid

    polyhedron-1polyhedron-2

  • find_polyhedron

polyhedron-1polyhedron-2

3. Trajectory planning

Compare different Trajectory planning：

  • Trajectory 1: use Ax = b get Trajectory.

closeFormcloseFormcloseForm

The Trajectory pass every Path point.

  • Trajectory 2: use 'Quadratic Programming' get Trajectory. use corridor constraints make Ax< b. x y z separately find minimum-snap.

corridorConstraintscorridorConstraintscorridorConstraints

The Trajectory don't need to pass every Path point.

minSnapValue(X + Y + Z) is : 9376.0901

  • Trajectory 3: use 'Quadratic Programming' get Trajectory. use SFC make Ax < b.

SFCSFCSFC

The Trajectory don't need to pass every Path point.

minSnapValue(X + Y + Z) is : 2958.5877

4. Trajectory following control

Trajectory following by use PD Controller, you can learn by coursera.

Reference

Paper:

[1] D. Harabor and A. Grastien. 2011. "Online Graph Pruning for Pathfinding on Grid Maps". In Proceedings of the 25th National Conference on Artificial Intelligence (AAAI), San Francisco, USA.

[2] S. Liu, M. Watterson, K. Mohta, K. Sun, S. Bhattacharya, C.J. Taylor, et al., "Planning dynamically feasible trajectories for quadrotors using safe flight corridors in 3-d complex environments", IEEE Robotics and Automation Let- ters, vol. 2, no. 3, pp. 1688-1695, July 2017.

[3] D.W.Mellinger,"Trajectory generation and control for quadrotors"Ph.D. dissertation, Univ. Pennsylvania, Philadelphia, PA, 2012.

[4] D. Mellinger and V. Kumar, "Minimum snap trajectory generation and control for quadrotors", inProc. 2011 IEEE Int. Conf. Robot.Autom.,2011

[5] T. Lee, M. Leoky, and N. H. McClamroch, "Geometric tracking control of a quadrotor UAV on SE (3)" in Proc. 49th IEEE Conf. Decis. Control. IEEE, 2010, pp. 5420–5425.

Code:

safe flight corridors: C++ version