Laboratory of mechatronics and robotics Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS Mechatronics,

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

RAPIDLY EXPLORING RANDOM TREES USED FOR MOBILE ROBOTS PATH PLANNING

Jiří Krejsa, Stanislav Věchet

1. Introduction2. Rapidly exploring random trees3. RRT for walking robot4. RRT for wheeled robot5. Conclusions



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 plannerproblem: 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 spaceproblem: choice of heuristic potential function

• Possible solution -> Rapidly Exploring Random Trees - RRT



RRT.init(xinit)

RepeatFor 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)

ElseRRT.Trapped

End ifEnd forRRT.TryConnectToGoal

Until GoalReached

RRT construction algorithm

xinit

xclosest

xrandom

xnew



Naivetree

RRTtree

Nodes = 20 60 1000

Obstacle free expansion – uniform covering, no bias



Step length influence

• Increasing step length speeds up the search up to certain point (x=170)• Too high step breaks up the search (x>210)



x= 30 x = 100 x = 200Nodes = 3469 Nodes = 876 Nodes = 3215Path = 169 Path = 57 Path = 31



RRT for walking robot

- Limited resolution for translational and rotational movement

- Translation: x 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



res = 10° res = 20° res = 10°valid - not restricted valid = (0°,90°) valid = (10°, 90°)



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



RRT for wheeled robot – constant velocity case



Conclusions

• RRT – solid, fast reliable technique.• Uniform distribution of nodes over the search space.• Useful for number of constraints.• Simply modifiable to include further constraints.

Acknowledgement:This work was supported by Czech Ministry of Education under project MSM 0021630518 "Simulation modelling of mechatronics systems".

Future work• Two trees approach

Documents

Laboratory of mechatronics and robotics Institute of solid mechanics, mechatronics and biomechanics, BUT & Institute of Thermomechanics, CAS Mechatronics,