Real-time motion planning for Manipulator based on Configuration Space

1. Real-time motion planning for Manipulator based on Configuration Space Chen Keming Cis Peking University

2. Main Contents • Introduction • My current work • Future work and related work • C-Space visualization for Teleoperation

3. Introduction • Manipulator Motion Planning Problems • Statement: • Compute a collision-free path for a manipulator among obstacles • Inputs: • Geometry of manipulator and obstacles • Kinematics of manipulator (degrees of freedom) • Initial and goal manipulator configurations (placements) • Outputs: • Continuous sequence of collision-free manipulator configurations connecting the initial and goal configurations

4. Introduction • Tool: Configuration Space

5. Introduction • Framework Manipulator representation Discretization Graph searching Configuration space formulation Obstacles representation

6. My Current Work • Motivation: Towards real-time Human-Robot Interaction in dynamic environment • Application • (Mobile based) Manipulator interacts with human without collision • Dual-arm robot (Chen Fen,Ding Fu-qiangand Zhao Xi-fang “Collision-free Path Planning of dual-arm Robot.”ROBOT,vol.24,Mar.2002)

7. My Current Work • Assumption • The input data are readily available at any time • Manipulator representation • Cylinders • Reduction to 3 joints • Obstacles representation • Cylinders • Combination of main body and arms

8. My Current Work • C-Space formulation • Reduction to determine whether 2 cylinders collide in 3D W-Space Case 1: Case 2:

9. My Current Work • Schematic

10. My Current Work • Goal configurations formulation using inverse kinematics • Discretization • Joint 1: 161, Joint 2: 71, Joint 3: 121

11. My Current Work • Lazy C-Space computation due to • Large numbers of points in C-Space(total 1,383,151 points) • Real-time process requirement • Graph searching (A*) • Why use A* • Optimal and complete • Objective values (expanding nodes, time)

12. My Current Work • Speed up A* • OPEN is implemented as • hash table • priority list(implemented as Binary Heap) • CLOSED is implemented as hash table An example (collision checking points: more than 30000) List implementation Hash table and Binary Heap implementation

13. My Current Work • Result:

14. My Current Work • Dealing with dynamic environment • A* Replanner: Plan by A* using all the available information at the start. • Start tracing the optimal path • If there is a discrepancy between the initial map and the actual environment, update the new cost values for the corresponding arcs, run A* again for planning between the current position and the goal.

15. My Current Work • A* Replanner: shortcoming • If the goal configuration is far away, little changes may force the planner to use A* over the whole C-Space, although the changes in the optimal path may be small • Hence, A* replanner can be grossly inefficient computationally for real-time process

16. My Current Work • Optimization --- Dynamic A*(D*) [Stentz, 1994] • Functionally equivalent to A* replanner • Make “local” changes to the map and the resultant optimal path when a discrepancy between map and the environment is found • Essentially prunes the graph search • So, D* could be a proper choice for optimization. But so far, it has only been used in mobile robotics to move a robot to given goal coordinates in unknown terrain [Koenig, 2002].

17. D* Algorithm c(x1,x2)=1 c(x1,x3)=1.4 c(x1,x8)=10000,if x8 is in obstacle,x1 is a freecell c(x1,x9)=10000.4, if x9 is in obstacle, x1 is a freecell

18. Goal Gate Start

34. Exam 1

35. Exam 2

36. My Current Work • Compared with A* replanner in our problem, D* performance superior over A* replanner Checking points per replanning

37. Future work and related work • Modify program, make it more robust with more experiments, speed up with more modifications. • D* Limitation • D* search from goal configuration, what if there are several goal configurations (it’s common in manipulator motion planning)? • When the goal object is moving • Current on-line planning methods using A* based techniques focus on multi-directional search and parallel planning ([Dominik HENRICH, Christian WURLL and Heinz WÖRN, 1998], etc ) • D* should be adapted for our problems

38. Future work and related work • Consult other D*-like replanning algorithms (e.g D* Lite [Koenig, 2002] ) • Survey other real-time motion planning techniques in high dimensional C-Space • Decomposition-based methods ([Kavraki, 2001], [Mediavilla, 2002], etc) • Probabilistic roadmap based methods(most deal with static environment)

39. Future work and related work • Use a more general 3D model to represent manipulator and obstacles • Hierarchy structure • Tree structure

40. Future work and related work • Taxonomy

41. Future work and related work • Experiment using real robot arm: a challenging work Images from cameras Computer vision techniques Motion planning Model parameters

42. C-Space Visualization for Teleoperation • Applications of C-Space Visualization • Provide important qualitative information for mechanical design (E.Sacks, C.Pisula and L.Joskowicz “Visualizing 3D Configuration Spaces for Mechanical Design.” ). • Evaluation of path planning methods • Teleoperation (I.Ivanisevic and J.Lumelsky “Configuration Space as a Means for Augmenting Human Performance in Teleoperation Tasks.”IEEE Trans.Syst.Man,Cyber.,vol.30,pp.471-484,Jun.2000).

43. C-Space Visualization for Teleoperation • It’s easier for humans to handle motion planning problems in C-Space than in W-Space

44. C-Space Visualization for Teleoperation • Challenges • When the computer which generates C-Space data is not the same as the computer which receives humans input, C-Space data must be transfered through network • C-Space data are too large • 161*71*121 for my current implementation • C-Space data change caused by dynamic environment, etc • Poor network bandwidth

45. C-Space Visualization for Teleoperation • So, C-Space data compression is necessary • Additional work Framework： C-Space Data 3D Models Data 3D Model Data Compression C-Space for a Cylinder Object