Motion Planning and Control Using RRTs Selected SlidesMovies

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Motion Planning and Control Using RRTs Selected SlidesMovies

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Electrical Engineering & Computer Science. Case Western Reserve University. May 2002 ... A pendulum of mass m and length l. Motor at joint can apply discrete torques ... – PowerPoint PPT presentation

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Title: Motion Planning and Control Using RRTs Selected SlidesMovies

1
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

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
q0 (down), qdot0
Goal configuration
qp (up), qdot0

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 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)
14
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?
15
Stair-Climber Example

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