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Ananya Kumar, Sunny Nahar – Advisor: Red Whi8aker Coopera<ve Localiza<on with Symbio<c Planetary Rovers
The Moon and Mars are rife with uncharted features of immense scien<fic value:
• Caves are prime prospects for water and life. • Pits are a safe haven from radia<on, meteorites,
and temperature varia<ons.
These features are too risky for the primary rover to explore.
Past research on coopera2ve localiza2on: • Some rovers are sta<onary (e.g. Leapfrogging). • Rovers move in fixed forma<ons. • Landmarks are used to localize. • Rovers are iden<cally modeled.
Current approach: • Mo<on is not constrained. • Sensor models are based on planetary analogs. • Parent – child rover model is used. • One rover’s star<ng loca<on might not be known.
The Extended Kalman and Grid filter were tested using simula<ons (300 simula<ons/scenario):
• Rovers take a pseudo-‐random path. • Algorithms observe sensor readings with noise. • Algorithm posi<on es<mates are compared with ground truth. Scenarios: • Twin rovers: Both have moderately accurate sensors. • Parent-‐child rovers: Parent has accurate sensors; child is less accurate. • Camera: One rover can also get the direc<on to other rover. • Sensor error model: Gaussian or Uniform. • Biased sensors: Sensors have biases. • Standard start: Both rovers start at the origin. • Lost child problem: Initialize with child rover position unknown and parent known.
Results
A symbio2c mul2-‐rover system is a possible solu<on, with a primary parent rover and mul<ple child rovers.
• Smaller, inexpensive, and expendable child rovers.
• Child rovers explore surrounding areas and come back to parent.
Mee<ng of the Minds 2015
Introduc2on
A symbio2c mul2-‐rover system is a possible solu<on, with a primary parent rover and mul<ple child rovers.
• Smaller, inexpensive, and expendable child rovers.
• Child rovers explore surrounding areas and come back to parent.
A symbio2c mul2-‐rover system is a possible solu<on, with a primary parent rover and mul<ple child rovers.
• Smaller, inexpensive, and expendable child rovers.
• Child rovers explore surrounding areas and come back to parent.
A symbio2c mul2-‐rover system is a possible solu<on: • Large sophis<cated parent rover. • Smaller, inexpensive, and expendable child rovers.
Issue of Localiza2on for child rovers: • Lack hardware to localize well. • Need to accurately navigate and explore. • Need to return to the parent to recharge baGery.
This research uses coopera2ve localiza2on to improve posi<on es<mates.
Research Ques2on
Grid Filter
Step 3: Rovers correct pose es<mate.
Step 1: Rovers move, incorrectly es<mate pose.
Step 2: Rovers measure distance to each other.
Extended Kalman Filter
Past Research and Current Approach
Step 2: Distance measurement updates grid.
Step 3: Filter improves pose es<mate for both rovers.
• Each rover stores a moving grid of possible loca<ons of its posi<on. • For each grid cell, the rover stores the probability that it is in the grid cell. • The grid is updated when rovers move and take distance measurements. • The maximum likelihood es<mate is used for corrected posi<on.
Rover 2 Position
Rover 1 Position
Rover 1 Estimated Position
Rover 2 Estimated Position
Distance Measurement
By incorpora<ng pairwise distance between rovers, our algorithms significantly improved localiza2on accuracy rela<ve to dead reckoning by the same rovers if ac<ng alone:
• Parent – child: Kalman did 2.3 <mes be8er. • Twin rovers: Grid based method did 1.3 <mes be8er. • Camera: Grid based method did 4.3 <mes be8er. • Sensor bias: Kalman did 1.17 <mes be8er. • Random reboot: Kalman had 95% accuracy.
This research shows coopera2ve localiza2on for planetary explora<on is feasible: • Algorithms work well in a variety of situa<ons and realis<c scenarios. • Algorithms establish a lower bound for what is possible. • Large scope for poten<al research.
Future Work: • Implemen<ng our methodologies on real rovers. • Experiment with other algorithms (unscented Kalman filter, par<cle filter).
Results Parent-‐child, 500m trek
3.29
5.20
1.01
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
Final Error (%)
Odom Grid Kalman
561.7
439.7
241.2
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
Cumula2ve error
Odom Grid Kalman
Kalman had 2.3 2mes lower error, and did be8er than dead reckoning in 294/300 runs.
Twin rovers, 500m trek
Odom Grid Kalman
Grid had 1.25 2mes lower error, and did be8er than dead reckoning in 291/300 runs.
1.34
1.05 1.07
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Final Error (%)
249.7
199.0 198.9
0.0
50.0
100.0
150.0
200.0
250.0
300.0
Cumula2ve Error
Odom Grid Kalman
Parent-‐child, 100m trek with camera
4.70
1.03
1.89
0.00
1.00
2.00
3.00
4.00
5.00
6.00
Final Error (%)
Odom Grid Kalman
Grid had 4.3 2mes lower error, and did be8er than dead reckoning in 299/300 runs.
148.4
34.1
76.3
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
Cumula2ve Error
Odom Grid Kalman
We would like to thank Prof. William Red Whi8aker and Cur<s Boirum for their help and advice on the project, and SURG, CMU, and Boeing for enabling this research.
State es<mator combining predic<on and measurement data: • Learns a con<nuous space Hidden Markov Model. • Extended Kalman is non-‐linear version of Kalman filter. • Op<mal for Gaussian error.
Model: • xk = Rover (x, y) state • Pk = Rover (x, y) covariance • uk-‐1 = Rover (distance,
heading) • zk = Rover (pairwise distance) • wk, vk = Process / Measurement noise • F = State transi<on • H = Observa<on transi<on
Rover 1 Estimated Position
Rover 2 Estimated Position
Method
Rover 1 Corrected Position
Rover 2 Corrected Position
Estimated: Ground truth: Corrected:
Step 1: Both rovers have incorrect pose es<mates.
Test Scenarios
Acknowledgements
Conclusion, Impact, and Future Work
12.83 12.78
10.79
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
Final Error (%)
Parent-‐child, 100m trek with bias
Odom Grid Kalman
Kalman had 1.17 2mes lower error, and did be8er than dead reckoning in 237/300 runs.
312.4 285.4
264.4
0.0
50.0
100.0
150.0
200.0
250.0
300.0
350.0
400.0
Sum Error
Odom Grid Kalman
Method Error (%) 2 × Standard Error
Odom (both rover posi<ons known)
2.70 0.15
Kalman (child lost) 4.10 0.56
Twin rovers, lost twin, 100m trek Parent-‐child, lost child, 100m trek
Kalman got only 4.10% error although loca<on of child rover was ini<ally unknown.
Method Error (%) 2 × Standard Error
Odom (both rover posi<ons known)
0.69 0.04
Kalman (child lost) 5.31 0.69
Kalman got only 5.31% error although loca<on of child rover was ini<ally unknown.
Distance Measurement
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