1 / 15

Motion Planning and Control Using RRTs [Selected Slides/Movies]

Motion Planning and Control Using RRTs [Selected Slides/Movies]. Michael M. Curtiss (MS Studennt) Michael S. Branicky (Advisor) Electrical Engineering & Computer Science Case Western Reserve University May 2002. New Applications of RRTs. We have applied/extended them to: Nonlinear planning

patch
Télécharger la présentation

Motion Planning and Control Using RRTs [Selected Slides/Movies]

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Motion Planning and ControlUsing RRTs[Selected Slides/Movies] Michael M. Curtiss (MS Studennt) Michael S. Branicky (Advisor) Electrical Engineering & Computer Science Case Western Reserve University May 2002

  2. New Applications of RRTs We have applied/extended them to: • Nonlinear planning • pendulum swing-up, acrobot • Prioritized multi-agent planning • air traffic control

  3. Pendulum Swing-Up • A pendulum of mass m and length l • Motor at joint can apply discrete torques • Initial configuration: q=0 (down), qdot=0 • Goal configuration: q=p (up), qdot=0

  4. Pendulum Swing-Up • A pendulum of mass m and length l • Motor at joint can apply torques {-1,0,1} single tree, 3300 nodes dual tree, 5600 nodes

  5. Pendulum Swing-Up (Cont.) Torques = {-4, -2, -1, 0, 1, 2, 4}, 4000 iterations

  6. Acrobot Swing-Up [adapted from Sutton & Barto]

  7. Acrobot: The Movie

  8. Multi-Agent Planning • Planning for simplified air traffic control • Airplanes take off from one of six airports and fly to a destination airport • Airplanes cannot occupy the same cell at the same time, except adjacent to airports • Airplanes cannot fly directly in front of or behind other airplanes (preventing swapping) • Prioritized Planning • A path is planned for each agent in turn • Paths are treated as obstacles in space-time for all future agents, and are immutable once planned

  9. Multi-Agent Planning: The Movie

  10. Nonholonomic Airplanes • Six airports • W-Space = [-1,1] x [-1,1] • Safety-radius of 0.03 • Rate-constrained turning • Unicycle equations of motion: • Prioritized Planning:

  11. Dynamic Safety Envelopes • Lregion=(v2/2)Amax • Can always stop without hitting other agents

  12. Hybrid Trajectories • Hybrid problems require finding valid trajectories from sinit to sgoal • Trajectory is defined as a sequence of states s, where s=(x,q)

  13. Hybrid RRT Algorithm BUILD_RRT(sinit) 1 T.init(sinit); 2 for k=1 to K do 3 srandRANDOM_STATE(); 4 EXTEND(T, srand); 5 return T EXTEND(T, s) 1 snearNEAREST_METRIC_NEIGHBOR(s, T) 2 if (NEW_STATE(s, snear, snew, unew) then 3 T.add_vertex(snew) 4 T.add_edge(snear, snew, unew)

  14. Hybrid RRT Changes • Include discrete state in state space (S=XQ) • Redefine distance metric • Non-trivial systems must account for discrete state changes in the distance metric • Stair climbing example, (S=[-20,20]2{1,2,3,4}): • Introduce switching as an operator • Unrestricted (switching control) or restricted (stair climber) • Autonomous (pogo stick) or controlled (gear shifting) (c1,c2) = x1-x22 + 20 q1-q2

  15. Stair-Climber Example

More Related