Motion Planning and Control Using RRTs Selected SlidesMovies

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Motion Planning and ControlUsing RRTsSelected
Slides/Movies

• Michael M. Curtiss (MS Studennt)
• Michael S. Branicky (Advisor)
• Electrical Engineering Computer Science
• Case Western Reserve University
• May 2002

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New Applications of RRTs

• We have applied/extended them to
• Nonlinear planning
• pendulum swing-up, acrobot
• Prioritized multi-agent planning
• air traffic control

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Pendulum Swing-Up

• A pendulum of mass m and length l
• Motor at joint can apply discrete torques
• Initial configuration
• q0 (down), qdot0
• Goal configuration
• qp (up), qdot0

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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
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Pendulum Swing-Up (Cont.)
Torques -4, -2, -1, 0, 1, 2, 4, 4000
iterations
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Acrobot Swing-Up
adapted from Sutton Barto
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Acrobot The Movie
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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

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Multi-Agent Planning The Movie
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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

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Dynamic Safety Envelopes

• Lregion(v2/2)Amax
• Can always stop without hitting other agents

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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)

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Hybrid RRT Algorithm

• BUILD_RRT(sinit)
• 1 T.init(sinit)
• 2 for k1 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)
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Hybrid RRT Changes

• Include discrete state in state space (SX?Q)
• Redefine distance metric
• Non-trivial systems must account for discrete
  state changes in the distance metric
• Stair climbing example, (S-20,202?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?
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Stair-Climber Example