1. 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.Introduction 2.Rapidly exploring random trees 3.RRT for walking robot 4.RRT for wheeled robot 5.Conclusions

2. 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

3. 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.init(x init ) Repeat For i=1 to CONNECT_CHECK_INTERVAL x rand = random state x closest = GetClosestNode(x rand ) x new = GenerateNewNode(x closest, x rand ) x new = ApplyRestrictions(x closest, x new ) If (x new is OK) RRT.AddNewNode(x closest, x new ) Else RRT.Trapped End if End for RRT.TryConnectToGoal Until GoalReached RRT construction algorithm x init x closest x random x new

4. 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 Naive tree RRT tree Nodes = 20601000 Obstacle free expansion – uniform covering, no bias

5. 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 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)

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

7. 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 for walking robot - Limited resolution for translational and rotational movement - Translation:  x corresponds to robot step - Rotation: candidate node x new created in direction closest to x rand in multiples of rotational steps - Simple test robot used – 4 legs with 2DOF each, HS322 servodrives - Further restrictionsright only rotation right only rotation with no straight movement

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

9. 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 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

10. 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 for wheeled robot – constant velocity case

11. 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 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