NUS CS5247 Deadlock-Free and Collision-Free Coordination of Two Robot Manipulators By Patrick A....
-
Upload
hilary-ellis -
Category
Documents
-
view
217 -
download
0
Transcript of NUS CS5247 Deadlock-Free and Collision-Free Coordination of Two Robot Manipulators By Patrick A....
NUS CS5247
Deadlock-Free and Deadlock-Free and Collision-Free Collision-Free
Coordination of Two Coordination of Two Robot ManipulatorsRobot Manipulators
By Patrick A. O’Donnell and Tomás Lozano-PérezBy Patrick A. O’Donnell and Tomás Lozano-PérezMIT Artificial Intelligence Laboratory MIT Artificial Intelligence Laboratory
545 Technology Square545 Technology SquareCambridge, MA., 02139Cambridge, MA., 02139
Presented by Zhang JingboPresented by Zhang Jingbo
NUS CS5247 2
Outline Motivation, Background and Our goal The key problems and Some terminology Environment and Goals for our trajectory
coordinator Related work and Previous approaches Our approach Further discussion Summary
NUS CS5247 3
Motivation Introduce a method for coordinating the
trajectories of two robot manipulators so as to avoid collisions between them.
NUS CS5247 4
Background Whenever multiple robots must operate in close
proximity to each other, the potential for collision must be taken into account in specifying the robot trajectories.
NUS CS5247 5
Our goal To allow the motions of each manipulator to be
planned nearly independently and to allow the execution of the path segments to be asynchronous.
That is,
(1). Coordinating two robot manipulators so as to avoid collisions between them;
(2). Guarantee the trajectories will reach their goals
NUS CS5247 6
The key problems To avoid
1. Collisions between the two robots.
2. Deadlock
NUS CS5247 7
Some terminology Path: the shape of the curve in the robot’s
configuration space. Trajectory: the time history of positions along a
path, that is, a curve through the robot’s state space.
Path Vs Trajectory: a given path may have infinitely many possible trajectories.
NUS CS5247 8
Environment Robots’s paths are predictable: We can predict
the paths of manipulators off-line to avoid all the other static objects in the environments.
Robots’s trajectories are less predictable: Eg, arc welding, sensor-based operation, unavoidable error in the controller.
NUS CS5247 9
Goals for our trajectory coordinator It should be possible to plan the path for each
manipulator essentially independently. The resulting trajectories should guarantee that
the manipulators will reach their goals. It should be possible to execute the trajectories
without precise time coordination between the manipulators.
The safety of the manipulators should not depend on accurate trajectory control of individual manipulators.
NUS CS5247 10
Related work and Previous approaches
Global and local approaches to trajectory coordination of multiple manipulators. Global methods Local methods
Drawbacks for these two methods Global methods: depend on carefully controlled trajectories; the methods are computationally intensive Local methods: based on actual measurements of the robots’s positions; cannot guarantee reaching goals; May reach a deadlock; Not suited when the paths are tightly constrained
NUS CS5247 11
Our approach —— Scheduling Decouple the path specification step from the trajectory
specification step. Avoid all collisions by using time.
Assumption about the path: a. The path planned off-line and composed of a
sequence of path segments. b. The path constrained within the bounding box of the
initial and final joint values of the segment. c. Paths can be produced by typical linear joint
interpolations. d. Executing time for each path segment can be estimate
roughly.
NUS CS5247 12
Task-Completion Diagram
NUS CS5247 13
A Schedule for the task
NUS CS5247 14
Simple scheduling algorithm
NUS CS5247 15
A partial schedule that leads to a deadlock
NUS CS5247 16
How to solve this problem?
NUS CS5247 17
Compute the SW-closure of the collision regions
NUS CS5247 18
Some modifications and moving on
We make the segment length be proportional to estimated time.
The safe areas including the goal and the origin must be connected.
Two methods to construct a schedule.
1. local method:
a. Greedy Schedule with central controller
b. Greedy Schedule with decentralized version.
2. global method: marching down a list that
issuing START/WAIT commands.
NUS CS5247 19
Decentralized Greedy SchedulingAAii :: ...... lock( R...... lock( Ri,j i,j ) A) Aii unlock( R unlock( Ri,ji,j ) ......... ) .........BBjj :: ...... lock( R...... lock( Ri,ji,j ) B ) Bjj unlock( R unlock( Ri,ji,j ) ......... ) .........
Each shaded REach shaded Ri,ji,j becomes a “lock” . becomes a “lock” .When reaching the region of RWhen reaching the region of Ri,j i,j :: — — A’s controller must grab the locks of the A’s controller must grab the locks of the
shadedshaded RRi,ji,j, , for all jfor all j before executing path segment A before executing path segment Ai.i. — — B’s controller must grab the locks of the B’s controller must grab the locks of the
shadedshaded RRi,ji,j, , for all ifor all i before executing path segment B before executing path segment Bj.j.
NUS CS5247 20
How to find an optimal / best schedules ?
Answer:
To increase the parallelism of the schedule and change our
selection of path.
NUS CS5247 21
NUS CS5247 22
Principles about how to increase the potential parallelism
We pick Ri,j or a larger collision region formed from the union of several Ri,j such that:
1. The region is shaded because of a collision and not because of the SW-closure operation.
2. The initial and final positions of the path segments giving rise to the collision region are free of collision.
3. The region is large enough that it causes a significant increase in the total time of the best schedule to go around it.
NUS CS5247 23
The impact of variable segment time Earlier, we indicated that in many applications,
the execution times for path segments cannot be predicted reliably, especially in situations involving sensing or variable-time processes.
May change the choice of the best schedule. Strategy: simply redo the coordination.
NUS CS5247 24
NUS CS5247 25
Further discussion Changing the Task Testing for Collisions
NUS CS5247 26
Summary Background introduction
1. Motivation and Our goal
2. The key problem
3. Relative work and previous approaches Our approach——Scheduling
1. Approach statement
2. Avoid deadlock problem
3. Modification and moving deeper in discussion Further discussion
NUS CS5247 27
Thank you