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Mechatronics, Robotics and Biomechanics 2005
Třešť, September 26-29, 2005
RAPIDLY EXPLORING RANDOM TREES USED FOR MOBILE
ROBOTS PATH PLANNING
Jiří Krejsa, Stanislav Věchet
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Introduction
Rapidly exploring random trees
RRT for walking robot
RRT for wheeled robot
Conclusions
Laboratory of mechatronics and robotics
Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS
Mechatronics, Robotics and Biomechanics 2005
Třešť, September 26-29, 2005
Introduction
• Path planning – finding obstacle free path from init to goal node
• Probabilistic roadmaps
- building roadmap of obstacle free nodes
- interconnect nodes when possible
- connect init and goal
- when path is found it is obstacle free
- probabilistic version: random configurations, local planner
problem: connection problem
• Randomized potential field
– object represented as a point
- treated as particle under artificial potential field U
- U constructed to reflect locally the structure of free space
problem: choice of heuristic potential function
• Possible solution -> Rapidly Exploring Random Trees - RRT
Laboratory of mechatronics and robotics
Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS
Mechatronics, Robotics and Biomechanics 2005
Třešť, September 26-29, 2005
RRT construction algorithm
RRT.init(xinit)
Repeat
For i=1 to CONNECT_CHECK_INTERVAL
xrand = random state
xclosest = GetClosestNode(xrand)
xnew = GenerateNewNode(xclosest , xrand)
xnew = ApplyRestrictions(xclosest , xnew)
If (xnew is OK)
RRT.AddNewNode(xclosest , xnew)
Else
xinit
xclosest
RRT.Trapped
xnew
End if
End for
RRT.TryConnectToGoal
Until GoalReached
xrandom
Laboratory of mechatronics and robotics
Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS
Mechatronics, Robotics and Biomechanics 2005
Třešť, September 26-29, 2005
Obstacle free expansion – uniform covering, no bias
Nodes = 20
60
Naive
tree
RRT
tree
Laboratory of mechatronics and robotics
Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS
1000
Mechatronics, Robotics and Biomechanics 2005
Třešť, September 26-29, 2005
Step length influence
• Increasing step length speeds up the search up to certain point (Dx=170)
• Too high step breaks up the search (Dx>210)
Laboratory of mechatronics and robotics
Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS
Mechatronics, Robotics and Biomechanics 2005
Dx= 30
Nodes = 3469
Path = 169
Dx = 100
Nodes = 876
Path = 57
Laboratory of mechatronics and robotics
Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS
Třešť, September 26-29, 2005
Dx = 200
Nodes = 3215
Path = 31
Mechatronics, Robotics and Biomechanics 2005
Třešť, September 26-29, 2005
RRT for walking robot
- Limited resolution for translational and rotational movement
- Translation:
Dx corresponds to robot step
- Rotation:
candidate node xnew created in direction closest to xrand
in multiples of rotational steps
- Simple test robot used – 4 legs with 2DOF each, HS322 servodrives
- Further restrictions
right only rotation
right only rotation with no straight movement
Laboratory of mechatronics and robotics
Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS
Mechatronics, Robotics and Biomechanics 2005
ares = 10°
avalid - not restricted
ares = 20°
avalid = (0°,90°)
Laboratory of mechatronics and robotics
Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS
Třešť, September 26-29, 2005
ares = 10°
avalid = (10°, 90°)
Mechatronics, Robotics and Biomechanics 2005
Třešť, September 26-29, 2005
RRT for wheeled robot
• Direct path generation
• Node state extension: position, orientation AND velocity vector
• Free parameters: steering angle, acceleration
• New position/orientation calculated from prior node values
• Special cases: constant velocity – steering angle only free parameter
• Higher number of states – higher computational demands
Laboratory of mechatronics and robotics
Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS
Mechatronics, Robotics and Biomechanics 2005
RRT for wheeled robot – constant velocity case
Laboratory of mechatronics and robotics
Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS
Třešť, September 26-29, 2005
Mechatronics, Robotics and Biomechanics 2005
Třešť, September 26-29, 2005
Conclusions
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RRT – solid, fast reliable technique.
Uniform distribution of nodes over the search space.
Useful for number of constraints.
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Simply modifiable to include further constraints.
Future work
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Two trees approach
Acknowledgement:
This work was supported by Czech Ministry of Education under project MSM 0021630518 "Simulation
modelling of mechatronics systems".
Laboratory of mechatronics and robotics
Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS