Deadlock-Free and Collision-Free Coordination of Two Robot Manipulators

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Deadlock-Free and Collision-Free Coordination of
Two Robot Manipulators

• By Patrick A. ODonnell and Tomás Lozano-Pérez
• MIT Artificial Intelligence Laboratory
• 545 Technology Square
• Cambridge, MA., 02139
• Presented 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 robots
  configuration space.
• Trajectory the time history of positions along a
  path, that is, a curve through the robots state
  space.
• Path Vs Trajectory a given path may have
  infinitely many possible trajectories.

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Environment

• Robotss paths are predictable We can predict
  the paths of manipulators off-line to avoid all
  the other static objects in the environments.
• Robotss 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
• robotss 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 Scheduling

• Ai...... lock( Ri,j ) Ai
  unlock( Ri,j ) .........
• Bj...... lock( Ri,j ) Bj
  unlock( Ri,j ) .........
• Each shaded Ri,j becomes a lock .
• When reaching the region of Ri,j
• As controller must grab the locks of the
  shaded
• Ri,j, for all j before executing path
  segment Ai.
• Bs controller must grab the locks of the
  shaded
• Ri,j, for all i before executing path
  segment Bj.

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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 approachScheduling
• 1. Approach statement
• 2. Avoid deadlock problem
• 3. Modification and moving deeper in
  discussion
• Further discussion

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• Thank you