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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

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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

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Motivation Introduce a method for coordinating the

trajectories of two robot manipulators so as to avoid collisions between them.

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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.

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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

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The key problems To avoid

1. Collisions between the two robots.

2. Deadlock

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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.

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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.

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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.

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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

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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.

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Task-Completion Diagram

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A Schedule for the task

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Simple scheduling algorithm

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A partial schedule that leads to a deadlock

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How to solve this problem?

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Compute the SW-closure of the collision regions

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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.

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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.

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How to find an optimal / best schedules ?

Answer:

To increase the parallelism of the schedule and change our

selection of path.

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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.

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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.

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Further discussion Changing the Task Testing for Collisions

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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

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Thank you