Encoding Robotic Sensor States
for Q-Learning using the
Self-Organizing Map
Gabriel J. Ferrer
Department of Computer Science
Hendrix College
Outline

Statement of Problem

Q-Learning

Self-Organizing Maps

Experiments

Discussion
Statement of Problem



Goal

Make robots do what we want

Minimize/eliminate programming
Proposed Solution: Reinforcement Learning

Specify desired behavior using rewards

Express rewards in terms of sensor states

Use machine learning to induce desired actions
Target Platform

Lego Mindstorms NXT
Robotic Platform
Experimental Task

Drive forward

Avoid hitting things
Q-Learning

Table of expected rewards (“Q-values”)



Indexed by state and action
Algorithm steps

Calculate state index from sensor values

Calculate the reward

Update previous Q-value

Select and perform an action
Q(s,a) = (1 - α) Q(s,a) + α (r + γ max(Q(s',a)))
Q-Learning and Robots



Certain sensors provide continuous values

Sonar

Motor encoders
Q-Learning requires discrete inputs

Group continuous values into discrete “buckets”

[Mahadevan and Connell, 1992]
Q-Learning produces discrete actions

Forward

Back-left/Back-right
Creating Discrete Inputs


Basic approach

Discretize continuous values into sets

Combine each discretized tuple into a single index
Another approach

Self-Organizing Map

Induces a discretization of continuous values

[Touzet 1997] [Smith 2002]
Self-Organizing Map (SOM)


2D Grid of Output Nodes

Each output corresponds to an ideal input value

Inputs can be anything with a distance function
Activating an Output

Present input to the network

Output with the closest ideal input is the “winner”
Applying the SOM


Each input is a vector of sensor values

Sonar

Left/Right Bump Sensors

Left/Right Motor Speeds
Distance function is sum-of-squared-differences
SOM Unsupervised Learning
• Present an input to the network
• Find the winning output node
• Update ideal input for winner and neighbors
– weightij = weightij + (α * (inputij – weightij))
• Neighborhood function
e
d 2
2c 2
Experiments

Implemented in Java (LeJOS 0.85)

Each experiment

240 seconds (800 Q-Learning iterations)

36 States

Three actions

Both motors forward

Left motor backward, right motor stopped

Left motor stopped, right motor backward
Rewards

Either bump sensor pressed: 0.0

Base reward:


1.0 if both motors are going forward

0.5 otherwise
Multiplier:

Sonar value greater than 20 cm: 1

Otherwise, (sonar value) / 20
Parameters

Discount (γ): 0.5

Learning rate (α):


1/(1 + (t/100)), t is the current iteration (time step)

Used for both SOM and Q-Learning [Smith 2002]
Exploration/Exploitation

Epsilon = α/4

Probability of random action

Selected using weighted distribution
Experimental Controls

Q-Learning without SOM

Qa States


Current action (1-3)

Current bumper states

Quantized sonar values (0-19 cm; 20-39; 40+)
Qb States

Current bumper states

Quantized sonar values (9) (0-11 cm…; 84-95; 96+)
SOM Formulations

36 Output Nodes

Category “a”:



Length-5 input vectors

Motor speeds, bumper values, sonar value
Category “b”:

Length-3 input vectors

Bumper values, sonar value
All sensor values normalized to [0-100]
SOM Formulations

QSOM

Based on [Smith 2002]

Gaussian Neighborhood


Neighborhood size is one-half SOM width
QT

Based on [Touzet 1997]

Learning rate is fixed at 0.9

Neighborhood is immediate Manhattan neighbors

Neighbor learning rate is 0.4
Quantitative Results
Qa
Qb
QSOMa
QSOMb
QTa
QTb
Mean
607.97
578.91
468.86
534.49
456.19
545.61
StDv
81.92
76.95
39.39
160.41
85.07
57.98
Median 608.75
667.5
485.11
587.64
442.62
560.77
Min
506.47
528.67
410.2
354.25
378.72
481.55
Max
723
540.55
495
661.59
547.22
594.5
Mean/It 0.76
0.72
0.59
0.67
0.57
0.68
StDv/It
0.1
0.05
0.2
0.11
0.07
0.1
Qualitative Results



QSOMa

Motor speeds ranged from 2% to 50%

Sonar values stuck between 90% and 94%
QSOMb

Sonar values range from 40% to 95%

Best two runs arguably the best of the bunch
Very smooth SOM values in both cases
Qualitative Results



QTa

Sonar values ranged from 10% to 100%

Still a weak performer on average

Best performer similar to QTb
QTb

Developed bump-sensor oriented behavior

Made little use of sonar
Highly uneven SOM values in both cases
Experimental Area
First Movie

QSOMb

Strong performer (Reward: 661.89)

Minimum sonar value: 43.35% (110 cm)
Second Movie

Also QSOMb

Typical bad performer (Reward: 451.6)


Learns to avoid by always driving backwards

Baseline “not-forward” reward: 400.0
Minimum sonar value: 57.51% (146 cm)

Hindered by small filming area
Discussion

Use of SOM on NXT can be effective



More research needed to address shortcomings
Heterogeneity of sensors is a problem

Need to try NXT experiments with multiple sonars

Previous work involved homogeneous sensors
Approachable by undergraduate students

Technique taught in junior/senior AI course