An Analytical Tool for Robot Mission Reliability Prediction

1
An Analytical Tool for Robot Mission Reliability
Prediction

• AISR PI Workshop
• NNX07AV71G-R
• May 7, 2008
• John M. Dolan (jmd_at_cs.cmu.edu)
• Steve Stancliff (CMU)
• Ashitey Trebi-Ollennu (JPL)
• www.cs.cmu.edu/reliability

2
Overview

• Motivation
• Approach
• Two sample missions
• Solar panel assembly (few high-reliability vs.
  more low-reliability robots)
• Task allocation in exploration
• Conclusions

3
Motivation

• Statements about superior robustness of a greater
  number of robots are qualitative
• Minimal prior work Bererton02 on reliability
  modeling for multirobot missions
• Cost, time, and reliability are interdependent
• Team size increase ? time reduced cost higher
• Time reduced ? reliability requirement lower
• Reliability lower ? cost lower
• Be able to answer questions such as
• How does team size affect mission cost, duration,
  and reliability?
• Is it better to use a larger team of less
  reliable (cheaper), or a smaller team of more
  reliable (costlier) robots?
• How is task allocation affected by considering
  reliability?

4
Approach

• Robots in remote or harsh environments
• Robots considered in terms of subsystems

• Hardware failures

R(t) e - ? t
5
Approach

• Extend MTTF (1/?) to include operating conditions

Poisson temp. model
L10 bearing load

• Combine MTTF using standard methods

Series modules ?sS ?i
Parallel modules ?p ? / (1 ½ ... 1/N)
6
Approach

• Explicit enumeration for a simple mission

• A slightly more complicated mission

? Combinatorial explosion for missions of any
real complexity.
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Approach

• Stochastic simulation for more complex missions

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Solar Panel Mission

• Solar panel array installation
• Three subtasks
• Carry the panel to the assembly area
• Assemble the panel
• Return to the base
• Mission-design variables
• Mission duration (number of panels to install)
• Number of robots
• Component reliabilities

Base
1. Transit
3. Return
2. Assemble
Assy. Area
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Solar Panel Mission

• Representative subsystem reliabilities from JPL

• Subsystem usage by task (in hours)

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Solar Panel Mission - Results

• What is the minimum number of (identical) robots
  needed to provide a given mission reliability?

• e.g., 30 panels w/ 95 PoMC requires 4 robots
• Diminishing reliability return as more robots
  added

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Solar Panel Mission - Results

• With excess robots, how much lower can component
  reliabilities be?

? Lower-reliability 4-robot team has higher PoMC
than 2-robot team for mission duration lt
crossover w/ 2-robot (red) line
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Solar Panel Mission - Results

• On an equal-cost basis, do more robots provide
  greater mission reliability?

Cost model (Mettas, 2000)
? 4-robot team with 40 reliability is equally
expensive and more reliable than 2-robot team for
missions with fewer than 85 panels
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Multirobot Task Allocation

• Goal - visit all target locations in shortest
  total mission time

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Naive Solution
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When Robots Fail
Dashed lines represent failures
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Consider Robot Failure a Priori

• Denominator normalizes over those cases where the
  mission succeeds

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Solution Using Expected Distance
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When Robots Fail (revisited)
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Experiments

• Repeat previous calculations for large number of
  Robots2, Tasks2 worlds
• Include probabilistic location for robot failure
  (hand example assumed failure almost at target
  location)
• Look at both minimax (minimum-duration) and
  minisum (minimum total distance / energy) utility
  functions

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Results - Minimax
Pt 99
20 x 20 world
20 x 20 world
Pt 99
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Results - Minimax

• For a 300 x 300 world with Pt 99, the naive
  planner chooses a suboptimal plan 84 of the
  time, and the optimal plan in those cases is on
  average 41 shorter than the chosen plan

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Results - Minisum
Pt 99
20 x 20 world
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Conclusions

• Analytical method developed for trading off
  reliability, cost, and time in configuring
  multirobot teams
• For a specified mission duration, more robots
  with significantly lower individual reliability
  can be more mission-reliable or cost-effective
  than fewer robots with high reliability
• Ignoring possible robot failure in initial
  multirobot task allocation plan ? suboptimal
  plans with respect to the intended metric (e.g.,
  minimum duration or energy)

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Future Work

• Incorporation of different failure models
  modalities
• Consider model for performance degradation rather
  than binary failure for components and robots
• Generalization over mission categories