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

Main Contents  Introduction  My current work  Future work and related work  C-Space visualization for Teleoperation

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

Introduction  Tool: Configuration Space

Introduction  Framework Manipulator representation Obstacles representation Configuration space formulation Discretization Graph searching

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-qiang and Zhao Xi-fang “ Collision-free Path Planning of dual-arm Robot. ” ROBOT,vol.24,Mar.2002)

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

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

My Current Work – Schematic

My Current Work – Goal configurations formulation using inverse kinematics  Discretization – Joint 1: 161, Joint 2: 71, Joint 3: 121

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)

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

My Current Work  Result:

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.

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

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].

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)= , if x9 is in obstacle, x1 is a freecell x9x2x3 x8x1x5 x7x6x7

6 h=6 k=6 b= h=5 k=5 b= h=4 k=4 b= h=3 k=3 b= h=2 k=2 b= h=1 k=1 b= h=0 k=0 b= 5 h=6.4 k=6.4 b= h=5.4 k=5.4 b= h=4.4 k=4.4 b= h=3.4 k=3.4 b= h=2.4 k=2.4 b= h=1.4 k=1.4 b= h=1 k=1 b= 4 h=6.8 k=6.8 b= h=5.8 k=5.8 b= h=4.8 k=4.8 b= h=3.8 k=3.8 b= h=2.8 k=2.8 b= h=2.4 k=2.4 b= h=2 k=2 b= 3 h=7.2 k=7.2 b= h=6.2 k=6.2 b= h=5.2 k=5.2 b= h=4.2 k=4.2 b= h=3.8 k=3.8 b= h=3.4 k=3.4 b= h=3 k=3 b= 2 h=7.6 k=7.6 b= h=6.6 k=6.6 b= h=5.6 k=5.6 b= h=5.2 k=5.2 b= h=4.8 k=4.8 b= h=4.4 k=4.4 b= h=4 k=4 b= 1 h=8.0 k=8.0 b= h=7.0 k=7.0 b= h=6.6 k=6.6 b= h=6.2 k=6.2 b= h=5.8 k=5.8 b= h=5.4 k=5.4 b= h=5 k=5 B= r/c Goal Start Gate

6 h=6 k=6 b= h=5 k=5 b= h=4 k=4 b= h=3 k=3 b= h=2 k=2 b= h=1 k=1 b= h=0 k=0 b= 5 h=6.4 k=6.4 b= h=5.4 k=5.4 b= h=4.4 k=4.4 b= h=3.4 k=3.4 b= h=2.4 k=2.4 b= h=1.4 k=1.4 b= h=1 k=1 b= 4 h=6.8 k=6.8 b= h=5.8 k=5.8 b= h=4.8 k=4.8 b= h=3.8 k=3.8 b= h=2.8 k=2.8 b= h=2.4 k=2.4 b= h=2 k=2 b= 3 h=7.2 k=7.2 b= h=6.2 k=6.2 b= h=5.2 k=5.2 b= h=4.2 k=4.2 b= h=3.8 k=3.8 b= h=3.4 k=3.4 b= h=3 k=3 b= 2 h=7.6 k=7.6 b= h=6.6 k=6.6 b= h=5.6 k=5.6 b= h=5.2 k=5.2 b= h=4.8 k=4.8 b= h=4.4 k=4.4 b= h=4 k=4 b= 1 h=8.0 k=8.0 b= h=7.0 k=7.0 b= h=6.6 k=6.6 b= h=6.2 k=6.2 b= h=5.8 k=5.8 b= h=5.4 k=5.4 b= h=5 k=5 b= r/c (7,6)0 Statek

6 h=6 k=6 b= h=5 k=5 b= h=4 k=4 b= h=3 k=3 b= h=2 k=2 b= h=1 k=1 b=(7,6) h=0 k=0 b= 5 h=6.4 k=6.4 b= h=5.4 k=5.4 b= h=4.4 k=4.4 b= h=3.4 k=3.4 b= h=2.4 k=2.4 b= h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h=6.8 k=6.8 b= h=5.8 k=5.8 b= h=4.8 k=4.8 b= h=3.8 k=3.8 b= h=2.8 k=2.8 b= h=2.4 k=2.4 b= h=2 k=2 b= 3 h=7.2 k=7.2 b= h=6.2 k=6.2 b= h=5.2 k=5.2 b= h=4.2 k=4.2 b= h=3.8 k=3.8 b= h=3.4 k=3.4 b= h=3 k=3 b= 2 h=7.6 k=7.6 b= h=6.6 k=6.6 b= h=5.6 k=5.6 b= h=5.2 k=5.2 b= h=4.8 k=4.8 b= h=4.4 k=4.4 b= h=4 k=4 b= 1 h=8.0 k=8.0 b= h=7.0 k=7.0 b= h=6.6 k=6.6 b= h=6.2 k=6.2 b= h=5.8 k=5.8 b= h=5.4 k=5.4 b= h=5 k=5 b= r/c (6,6)1 (7,5)1 (6,5)1.4 Statek

6 h=6 k=6 b= h=5 k=5 b= h=4 k=4 b= h=3 k=3 b= h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h=6.4 k=6.4 b= h=5.4 k=5.4 b= h=4.4 k=4.4 b= h=3.4 k=3.4 b= h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h=6.8 k=6.8 b= h=5.8 k=5.8 b= h=4.8 k=4.8 b= h=3.8 k=3.8 b= h=2.8 k=2.8 b= h=2.4 k=2.4 b= h=2 k=2 b= 3 h=7.2 k=7.2 b= h=6.2 k=6.2 b= h=5.2 k=5.2 b= h=4.2 k=4.2 b= h=3.8 k=3.8 b= h=3.4 k=3.4 b= h=3 k=3 b= 2 h=7.6 k=7.6 b= h=6.6 k=6.6 b= h=5.6 k=5.6 b= h=5.2 k=5.3 b= h=4.8 k=4.8 b= h=4.4 k=4.4 b= h=4 k=4 b= 1 h=8.0 k=8.0 b= h=7.0 k=7.0 b= h=6.6 k=6.6 b= h=6.2 k=6.2 b= h=5.8 k=5.8 b= h=5.4 k=5.4 b= h=5 k=5 b= r/c (7,5)1 (6,5)1.4 (5,6)2 (5,5)2.4 Statek

6 h=6 k=6 b(1,6)= h=5 k=5 b= h=4 k=4 b= h=3 k=3 b= h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h=6.4 k=6.4 b(1,5)= h=5.4 k=5.4 b= h=4.4 k=4.4 b= h=3.4 k=3.4 b= h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h=6.8 k=6.8 b(1,4)= h=5.8 k=5.8 b= h=4.8 k=4.8 b= h=3.8 k=3.8 b= h=2.8 k=2.8 b= h=2.4 k=2.4 b=(7,5) h=2 k=2 b=(7,5) 3 h=7.2 k=7.2 b(1,3)= h=6.2 k=6.2 b= h=5.2 k=5.2 b= h=4.2 k=4.2 b= h=3.8 k=3.8 b= h=3.4 k=3.4 b= h=3 k=3 b= 2 h=7.6 k=7.6 b(1,2)= h=6.6 k=6.6 b= h=5.6 k=5.6 b= h=5.2 k= b= h=4.8 k=4.8 b= h=4.4 k=4.4 b= h=4 k=4 b= 1 h=8.0 k=8.0 b(1,1)= h=7.0 k=7.0 b= h=6.6 k=6.6 b= h=6.2 k=6.2 b= h=5.8 k=5.8 b= h=5.4 k=5.4 b= h=5 k=5 b= r/c (6,5)1.4 (5,6)2 (7,4)2 (6,4)2.4 (5,5)2.4 Statek

6 h=6 k=6 b(1,6)= h=5 k= b= h=10003 k=4 b=(4,6) h=3 k=3 b=(5,6) h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h=6.4 k=6.4 b(1,5)= h=5.4 k= b= h= k=4.4 b=(4,6) h=3.4 k=3.4 b=(5,6) h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h=6.8 k=6.8 b(1,4)= h=5.8 k= b= h=4.8 k= b= h=3.8 k=3.8 b=(5,5) h=2.8 k=2.8 b=(6,5) h=2.4 k=2.4 b=(7,5) h=2 k=2 b=(7,5) 3 h=7.2 k=7.2 b(1,3)= h=6.2 k= b= h=5.2 k= b= h=4.2 k=4.2 b=(5,4) h=3.8 k=3.8 b=(6,4) h=3.4 k=3.4 b=(7,4) h=3 k=3 b=(7,4) 2 h=7.6 k=7.6 b(1,2)= h=6.6 k=6.6 b= h=5.6 k=5.6 b= h=5.2 k=5.2 b= h=4.8 k=4.8 b= h=4.4 k=4.4 b= h=4 k=4 b= 1 h=8.0 k=8.0 b(1,1)= h=7.0 k=7.0 b= h=6.6 k=6.6 b= h=6.2 k=6.2 b= h=5.8 k=5.8 b= h=5.4 k=5.4 b= h=5 k=5 b= r/c (7,3)3 (6,3)3.4 (4,5)3.4 (5,3)3.8 (4,4)3.8 (3,6)4 (4,3)4.2 (3,5)4.4 Statek

6 h=20004 k=6 b=(2,6) h=10004 k=5 b=(3,6) h=10003 k=4 b=(4,6) h=3 k=3 b=(5,6) h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h= k=6.4 b=(2,6) h= k=5.4 b=(3,6) h= k=4.4 b=(4,6) h=3.4 k=3.4 b=(5,6) h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h= k=6.8 b=(2,5) h= k=5.8 b=(3,5) h= k= b=(4,5) h=3.8 k=3.8 b=(5,5) h=2.8 k=2.8 b=(6,5) h=2.4 k=2.4 b=(7,5) h=2 k=2 b=(7,5) 3 h=8.0 k=8.0 b=(2,2) h= k=6.2 b=(3,4) h= k=5.2 b=(4,4) h=4.2 k=4.2 b=(5,4) h=3.8 k=3.8 b=(6,4) h=3.4 k=3.4 b=(7,4) h=3 k=3 b=(7,4) 2 h=7.6 k=7.6 b=(2,2) h=6.6 k=6.6 b=(3,2) h=5.6 k=5.6 b=(4.3) h= k=5.2 b=(5,3) h=4.8 k=4.8 b=(6,3) h=4.4 k=4.4 b=(7,3) h=4 k=4 b=(7,3) 1 h=8.0 k=8.0 b=(2,2) h=7.0 k=7.0 b=(3,2) h=6.6 k=6.6 b=(3,2) h=6.2 k=6.2 b=(5,2) h=5.8 k=5.8 b=(6,2) h=5.4 k=5.4 b=(7,2) h=5 k=5 b=(7,2) r/c (1,6)6 (1,5)6.4 (1,4)6.8 (1,2)7.6 (1,3)8.0 (1,1)8.0 Statek

6 h=20004 k=6 b=(2,6) h=10004 k=5 b=(3,6) h=10003 k=4 b=(4,6) h=3 k=3 b=(5,6) h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h= k=6.4 b=(2,6) h= k=5.4 b=(3,6) h= k=4.4 b=(4,6) h=3.4 k=3.4 b=(5,6) h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h= k=6.8 b=(2,5) h= k=5.8 b=(3,5) h= k=4.8 b=(4,5) h=3.8 k=3.8 b=(5,5) h=2.8 k=2.8 b=(6,5) h=2.4 k=2.4 b=(7,5) h=2 k=2 b=(7,5) 3 h=8.0 k=8.0 b=(2,2) h= k=6.2 b=(3,4) h= k=5.2 b=(4,4) h=4.2 k=4.2 b=(5,4) h=3.8 k=3.8 b=(6,4) h=3.4 k=3.4 b=(7,4) h=3 k=3 b=(7,4) 2 h=7.6 k=7.6 b=(2,2) h=6.6 k=6.6 b=(3,2) h=5.6 k=5.6 b=(4.3) h= k=5.2 b h=4.8 k=4.8 b=(6,3) h=4.4 k=4.4 b=(7,3) h=4 k=4 b=(7,3) 1 h=8.0 k=8.0 b=(2,2) h=7.0 k=7.0 b=(3,2) h=6.6 k=6.6 b=(3,2) h=6.2 k=6.2 b=(5,2) h=5.8 k=5.8 b=(6,2) h=5.4 k=5.4 b=(7,2) h=5 k=5 b=(7,2) r/c (1,6)6 (1,5)6.4 (1,4)6.8 (1,2)7.6 (1,3)8.0 (1,1)8.0 Statek

6 h=20004 k=6 b=(2,6) h=10004 k=5 b=(3,6) h=10003 k=4 b=(4,6) h=3 k=3 b=(5,6) h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h= k=6.4 b=(2,6) h= k=5.4 b=(3,6) h= k=4.4 b=(4,6) h=3.4 k=3.4 b=(5,6) h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h= k=6.8 b=(2,5) h= k=5.8 b=(3,5) h= k=4.8 b=(4,5) h=3.8 k=3.8 b=(5,5) h=2.8 k=2.8 b=(6,5) h=2.4 k=2.4 b=(7,5) h=2 k=2 b=(7,5) 3 h=8.0 k=8.0 b=(2,2) h= k=6.2 b=(3,4) h= k=5.2 b=(4,4) h=4.2 k=4.2 b=(5,4) h=3.8 k=3.8 b=(6,4) h=3.4 k=3.4 b=(7,4) h=3 k=3 b 2 h=7.6 k=7.6 b=(2,2) h=6.6 k=6.6 b=(3,2) h=5.6 k=5.6 b=(4.3) h= k=5.2 b=(5,3) h=4.8 k=4.8 b=(6,3) h=4.4 k=4.4 b=(7,3) h=4 k=4 b=(7,3) 1 h=8.0 k=8.0 b=(2,2) h=7.0 k=7.0 b=(3,2) h=6.6 k=6.6 b=(3,2) h=6.2 k=6.2 b=(5,2) h=5.8 k=5.8 b=(6,2) h=5.4 k=5.4 b=(7,2) h=5 k=5 b=(7,2) r/c (1,6)6 (1,5)6.4 (1,4)6.8 (1,2)7.6 (1,3)8.0 (1,1)8.0 Statek

(4,3)4.2 (1,6)6 (1,5)6.4 (1,4)6.8 (1,2)7.6 (1,3)8.0 (1,1)8.0 Statek 6 h=20004 k=6 b=(2,6) h=10004 k=5 b=(3,6) h=10003 k=4 b=(4,6) h=3 k=3 b=(5,6) h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h= k=6.4 b=(2,6) h= k=5.4 b=(3,6) h= k=4.4 b=(4,6) h=3.4 k=3.4 b=(5,6) h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h= k=6.8 b=(2,5) h= k=5.8 b=(3,5) h= k=4.8 b=(4,5) h=3.8 k=3.8 b=(5,5) h=2.8 k=2.8 b=(6,5) h=2.4 k=2.4 b=(7,5) h=2 k=2 b=(7,5) 3 h=8.0 k=8.0 b=(2,2) h= k=6.2 b h= k=5.2 b=(4,4) h=4.2 k=4.2 b=(5,4) h=3.8 k=3.8 b=(6,4) h=3.4 k=3.4 b=(7,4) h=3 k=3 b=(7,4) 2 h=7.6 k=7.6 b=(2,2) h=6.6 k=6.6 b=(3,2) h=5.6 k=5.6 b=(4.3) h= k=5.2 b=(5,3) h=4.8 k=4.8 b=(6,3) h=4.4 k=4.4 b=(7,3) h=4 k=4 b=(7,3) 1 h=8.0 k=8.0 b=(2,2) h=7.0 k=7.0 b=(3,2) h=6.6 k=6.6 b=(3,2) h=6.2 k=6.2 b=(5,2) h=5.8 k=5.8 b=(6,2) h=5.4 k=5.4 b=(7,2) h=5 k=5 b=(7,2) r/c

6 h=20004 k=6 b=(2,6) h=10004 k=5 b h=10003 k=4 b h=3 k=3 b=(5,6) h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h= k=6.4 b=(2,6) h= k=5.4 b=(3,6) h= k=4.4 b=(4,6) h=3.4 k=3.4 b=(5,6) h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h= k=6.8 b=(2,5) h= k=5.8 b=(3,5) h= k=4.8 b=(4,5) h=3.8 k=3.8 b=(5,5) h=2.8 k=2.8 b=(6,5) h=2.4 k=2.4 b=(7,5) h=2 k=2 b=(7,5) 3 h=8.0 k=8.0 b=(2,2) h= k=6.2 b=(3,4) h= k=5.2 b=(4,4) h=4.2 k=4.2 b=(5,4) h=3.8 k=3.8 b=(6,4) h=3.4 k=3.4 b=(7,4) h=3 k=3 b=(7,4) 2 h=7.6 k=7.6 b=(2,2) h=6.6 k=6.6 b=(3,2) h= k=5.6 b=(4.3) h= k=5.2 b=(5,3) h=4.8 k=4.8 b=(6,3) h=4.4 k=4.4 b=(7,3) h=4 k=4 b=(7,3) 1 h=8.0 k=8.0 b=(2,2) h=7.0 k=7.0 b=(3,2) h=6.6 k=6.6 b=(3,2) h=6.2 k=6.2 b=(5,2) h=5.8 k=5.8 b=(6,2) h=5.4 k=5.4 b=(7,2) h=5 k=5 b=(7,2) r/c (3,2)5.6 (1,6)6 (1,5)6.4 (1,4)6.8 (1,2)7.6 (1,3)8.0 (1,1)8.0 Statek

6 h=20004 k=6 b=(2,6) h=10004 k=5 b h=10003 k=4 b=(4,6) h=3 k=3 b=(5,6) h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h= k=6.4 b=(2,6) h= k=5.4 b=(3,6) h= k=4.4 b=(4,6) h=3.4 k=3.4 b=(5,6) h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h= k=6.8 b=(2,5) h= k=5.8 b=(3,5) h= k=4.8 b=(4,5) h=3.8 k=3.8 b=(5,5) h=2.8 k=2.8 b=(6,5) h=2.4 k=2.4 b=(7,5) h=2 k=2 b=(7,5) 3 h=8.0 k=8.0 b=(2,2) h= k=6.2 b=(3,4) h= k=5.2 b=(4,4) h=4.2 k=4.2 b=(5,4) h=3.8 k=3.8 b=(6,4) h=3.4 k=3.4 b=(7,4) h=3 k=3 b=(7,4) 2 h=7.6 k=7.6 b=(2,2) h= k=6.6 b=(3,2) h= k=5.6 b=(4.3) h= k=5.2 b=(5,3) h=4.8 k=4.8 b=(6,3) h=4.4 k=4.4 b=(7,3) h=4 k=4 b=(7,3) 1 h=8.0 k=8.0 b=(2,2) h= k=7.0 b=(3,2) h= k=6.6 b=(3,2) h=6.2 k=6.2 b=(5,2) h=5.8 k=5.8 b=(6,2) h=5.4 k=5.4 b=(7,2) h=5 k=5 b=(7,2) r/c (1,6)6 (4,1)6.2 (1,5)6.4 (3,1)6.6 (2,2)6.6 (1,4)6.8 (2,1)7.0 (1,2)7.6 (1,3)8.0 (1,1)8.0 Statek

6 h=20004 k=6 b=(2,6) h=10004 k=5 b h=10003 k=4 b=(4,6) h=3 k=3 b=(5,6) h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h= k=6.4 b=(2,6) h= k=5.4 b=(3,6) h= k=4.4 b=(4,6) h=3.4 k=3.4 b=(5,6) h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h= k=6.8 b=(2,5) h= k=5.8 b=(3,5) h= k=4.8 b=(4,5) h=3.8 k=3.8 b=(5,5) h=2.8 k=2.8 b=(6,5) h=2.4 k=2.4 b=(7,5) h=2 k=2 b=(7,5) 3 h=8.0 k=8.0 b=(2,2) h= k=6.2 b=(3,4) h= k=5.2 b=(4,4) h=4.2 k=4.2 b=(5,4) h=3.8 k=3.8 b=(6,4) h=3.4 k=3.4 b=(7,4) h=3 k=3 b=(7,4) 2 h=7.6 k=7.6 b=(2,2) h= k=6.6 b=(3,2) h= k=5.6 b=(4.3) h= k=5.2 b=(5,3) h=4.8 k=4.8 b=(6,3) h=4.4 k=4.4 b=(7,3) h=4 k=4 b=(7,3) 1 h=8.0 k=8.0 b=(2,2) h= k=7.0 b=(3,2) h= k=6.6 b=(3,2) h=6.2 k=6.2 b=(5,2) h=5.8 k=5.8 b=(6,2) h=5.4 k=5.4 b=(7,2) h=5 k=5 b=(7,2) r/c (1,6)6 (4,1)6.2 (1,5)6.4 (3,1)6.6 (2,2)6.6 (1,4)6.8 (2,1)7.0 (1,2)7.6 (1,3)8.0 (1,1)8.0 Statek

6 h=20004 k=6 b=(2,6) h=10004 k=5 b=(3,6) h=10003 k=4 b=(4,6) h=3 k=3 b=(5,6) h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h= k=6.4 b=(2,6) h= k=5.4 b=(3,6) h= k=4.4 b=(4,6) h=3.4 k=3.4 b=(5,6) h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h= k=6.8 b=(2,5) h= k=5.8 b)=(3,5) h= k=4.8 b=(4,5) h=3.8 k=3.8 b=(5,5) h=2.8 k=2.8 b=(6,5) h=2.4 k=2.4 b=(7,5) h=2 k=2 b=(7,5) 3 h=8.0 k=8.0 b=(2,2) h= k=6.2 b=(3,4) h= k=5.2 b=(4,4) h=4.2 k=4.2 b=(5,4) h=3.8 k=3.8 b=(6,4) h=3.4 k=3.4 b=(7,4) h=3 k=3 b=(7,4) 2 h=7.6 k=7.6 b=(2,2) h= k=6.6 b=(3,2) h= k=5.6 b=(4.3) h= k=5.2 b=(5,3) h=4.8 k=4.8 b=(6,3) h=4.4 k=4.4 b=(7,3) h=4 k=4 b=(7,3) 1 h=8.0 k=8.0 b=(2,2) h= k=7.0 b=(3,2) h= k=6.6 b=(3,2) h=6.2 k=6.2 b=(5,2) h=5.8 k=5.8 b=(6,2) h=5.4 k=5.4 b=(7,2) h=5 k=5 b=(7,2) r/c (4,1)6.2 (1,5)6.4 (3,1)6.6 (2,2)6.6 (1,4)6.8 (2,1)7.0 (1,2)7.6 (1,3)8.0 (1,1)8.0 Statek

6 h=20004 k=6 b=(2,6) h=10004 k=5 b=(3,6) h=10003 k=4 b=(4,6) h=3 k=3 b=(5,6) h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h= k=6.4 b=(2,6) h= k=5.4 b=(3,6) h= k=4.4 b=(4,6) h=3.4 k=3.4 b=(5,6) h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h= k=6.8 b=(2,5) h= k=5.8 b=(3,5) h= k=4.8 b=(4,5) h=3.8 k=3.8 b=(5,5) h=2.8 k=2.8 b=(6,5) h=2.4 k=2.4 b=(7,5) h=2 k=2 b=(7,5) 3 h=8.0 k=8.0 b=(2,2) h= k=6.2 b=(3,4) h= k=5.2 b=(4,4) h=4.2 k=4.2 b=(5,4) h=3.8 k=3.8 b=(6,4) h=3.4 k=3.4 b=(7,4) h=3 k=3 b=(7,4) 2 h=7.6 k=7.6 b=(2,2) h= k=6.6 b=(3,2) h=7.6 k=7.6 b=(4.1) h= k=5.2 b=(5,3) h=4.8 k=4.8 b=(6,3) h=4.4 k=4.4 b=(7,3) h=4 k=4 b=(7,3) 1 h=8.0 k=8.0 b=(2,2) h= k=7.0 b=(3,2) h=7.2 k=7.2 b=(4,1) h=6.2 k=6.2 b=(5,2) h=5.8 k=5.8 b=(6,2) h=5.4 k=5.4 b=(7,2) h=5 k=5 b=(7,2) r/c (5,2)4.8 (5,1)5.8 (3,2)5.6 (1,5)6.4 (3,1)6.6 (2,2)6.6 (1,4)6.8 (2,1)7.0 (1,2)7.6 (1,3)8.0 (1,1)8.0 Statek

6 h=20004 k=6 b=(2,6) h=10004 k=5 b=(3,6) h=10003 k=4 b=(4,6) h=3 k=3 b=(5,6) h=2 k=2 b=(6,6) h=1 k=1 b=(7,6) h=0 k=0 b= 5 h= k=6.4 b=(2,6) h= k=5.4 b=(3,6) h= k=4.4 b=(4,6) h=3.4 k=3.4 b=(5,6) h=2.4 k=2.4 b=(6,6) h=1.4 k=1.4 b=(7,6) h=1 k=1 b=(7,6) 4 h= k=6.8 b=(2,5) h= k=5.8 b=(3,5) h= k=4.8 b=(4,5) h=3.8 k=3.8 b=(5,5) h=2.8 k=2.8 b=(6,5) h=2.4 k=2.4 b=(7,5) h=2 k=2 b=(7,5) 3 h=8.0 k=8.0 b=(2,2) h= k=6.2 b=(3,4) h= k=5.2 b=(4,4) h=4.2 k=4.2 b=(5,4) h=3.8 k=3.8 b=(6,4) h=3.4 k=3.4 b=(7,4) h=3 k=3 b=(7,4) 2 h=7.6 k=7.6 b=(2,2) h= k=6.6 b=(3,2) h=7.6 k=7.6 b=(4.1) h= k=5.2 b=(5,3) h=4.8 k=4.8 b=(6,3) h=4.4 k=4.4 b=(7,3) h=4 k=4 b=(7,3) 1 h=8.0 k=8.0 b=(2,2) h= k=7.0 b=(3,2) h=7.2 k=7.2 b=(4,1) h=6.2 k=6.2 b=(5,2) h=5.8 k=5.8 b=(6,2) h=5.4 k=5.4 b=(7,2) h=5 k=5 b=(7,2) r/c

Exam 1

Exam 2

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

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

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)

Future work and related work  Use a more general 3D model to represent manipulator and obstacles – Hierarchy structure – Tree structure

Future work and related work – Taxonomy

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

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 ,Jun.2000).

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

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

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