# Presentation: 036341

## An Analytical Tool for Robot Mission Reliability Prediction 

**An Analytical Tool for Robot Mission Reliability Prediction **

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

## Overview

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

## 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?

## Approach

- Robots in remote or harsh environments
- Robots considered in terms of subsystems:

- Hardware failures

*R(t) = e **- **λ** t*

## Approach

- Extend MTTF (1/λ) to include operating conditions

- Combine MTTF using standard methods

*Poisson temp. model*

*L**10** bearing load*

*Series modules:  **λ**s*=Σ *λ**i*

*Parallel modules:*
*λ**p*= *λ* / (1 + 1⁄2 + ... + 1/*N*)

## Approach

- Explicit enumeration for a simple mission:

- A slightly more complicated mission:

*** **Combinatorial explosion for missions of any real complexity.*

## Approach

**Approach**

- Stochastic simulation for more complex missions:

## Solar Panel Mission

**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

- Assy. Area

*2. Assemble*

*1. Transit*

*3. Return*

## Solar Panel Mission

- Representative subsystem reliabilities from JPL:

| Subsystem | MTTF (hr) |
| --- | --- |
| Power | 4202 |
| Computation & Sensing | 4769 |
| Mobility | 19724 |
| Communications | 11876 |
| Manipulator | 13793 |

- Subsystem usage by task (in hours):

| Subsystem | Transit | Assemble | Return |
| --- | --- | --- | --- |
| Power | 6 | 8 | 6 |
| Computation & Sensing | 6 | 4 | 6 |
| Mobility | 6 | 8 | 6 |
| Communications | 2 | 4 | 2 |
| Manipulator | 0 | 8 | 0 |

## 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

## 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 < crossover w/ 2-robot (red) line

## Solar Panel Mission - Results

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

-  4-robot team with 40% reliability is equally expensive and more reliable than 2-robot team for missions with fewer than 85 panels

- Cost model (Mettas, 2000)

## Multirobot Task Allocation

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

**Notes:**
Simple multirobot exploration mission with with two robots, two target locations

Time assumed to be proportional to distance traveled

## Naive Solution

| Plan |  | D (R1) | D (R2) | Dmax |
| --- | --- | --- | --- | --- |
| A | R1T1 + R1T2 | 15.9 | 0 | 15.9 |
| B | R1T1 + R2T2 | 11.4 | 11.2 | 11.4 |
| C | R2T1 + R1T2 | 7.6 | 13.2 | 13.2 |
| D | R2T1 + R2T2 | 0 | 17.6 | 17.6 |
| E | R1T2 + R1T1 | 11.5 | 0 | 11.5 |
| F | R2T2 + R2T1 | 0 | 15.7 | 15.7 |

**Notes:**
Naive solution does not consider probabilities of failure

For this simple example - enumerate all possible task allocations and calculate max distance travelled

## When Robots Fail

- Dashed lines represent failures

**Notes:**
Consider what happens when failures occur during the chosen (naively optimal) plan

When R1 fails, R2 is assigned to T1 after completing T2
When R2 fails, R1 is assigned to T2 after completing T1

(ignores possibility of task interruption)

the second figure (R2 fails) shows R1 with a suboptimal plan with regard to its final task allocation after failure

## Consider Robot Failure a Priori

- Denominator normalizes over those cases where the mission succeeds

**Notes:**
Find an expected value for the distances which takes into account the possible alternative allocations resulting after robot failure

## Solution Using Expected Distance

|  | Plan | Dnaive | Dexp |
| --- | --- | --- | --- |
| A | R1T1 + R1T2 | 15.9 | 15.9 |
| B | R1T1 + R2T2 | 11.4 | 12.2 |
| C | R2T1 + R1T2 | 13.2 | 13.4 |
| D | R2T1 + R2T2 | 17.6 | 17.4 |
| E | R1T2 + R1T1 | 11.5 | 11.9 |
| F | R2T2 + R2T1 | 15.7 | 15.2 |

## When Robots Fail (revisited)

**Notes:**
Now the backup plans are optimal wrt distance travelled

## Experiments

- Repeat previous calculations for large number of #Robots=2, #Tasks=2 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

## Results - Minimax

**20 x 20 world**

**Pt = 99%**

**20 x 20 world**

**Pt = 99%**

**Notes:**
These graphs show the percent of the time that the naive planner chooses a suboptimal plan

Even when robots are very reliable and world is small, the naive planner chooses a suboptimal plan ~40% of the time.  

## 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

## Results - Minisum

**20 x 20 world**

**Pt = 99%**

**Notes:**
Naive planner performs better under minisum than under minimax for small worlds and reliable robots, which makes sense since minimizing the total distance travelled minimizes the probability of robot failure.

## 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)

## 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

## References

- A. Mettas, "Reliability allocation and optimization for complex systems," *Proc. IEEE Annual Reliability and Maintainability Symp*., 2000, pp. 216–221.
- S. Stancliff, J. Dolan, and A. Trebi-Ollennu, “Towards a Predictive Model of Mobile Robot Reliability,” CMU tech. report CMU-RI-TR-05-38, August, 2005
- S. Stancliff, J. Dolan, and A. Trebi-Ollennu, “Mission Reliability Estimation for Repairable Robot Teams,” *Int. J. Advanced Robotic Systems*, June, 2006.