Theory of Computation

Finite State Machines in

Mobile Robots: Sensors & Actuators, Schemas & Behaviors, Reactive

Paradigm, Subsumption

Vladimir Kulyukin

www.vkedco.blogspot.com

Outline

Sensors & Actuators Schemas & Behaviors Reactive Paradigm Subsumption

Sensors & Actuators

Sensor vs. Transducer

● Sensor – a device that measures or detects a real world condition

● Transducer – a device that converts one form of energy to another

● Sensors may employ transducers to measure quantities like mass, pressure, etc.

Active vs. Passive Sensor

● Passive sensors rely on the environment to provide the medium for observation (e.g., a camera that takes snapshots in the ambient light to produce a picture)● Active sensors put out energy in the environment to change it or enhance it (e.g., a camera with a flash is an active sensor

Attributes of a Sensor

• Field of view & range

• Accuracy repeatability & resolution

• Responsiveness in the target domain

• Power consumption

• Hardware reliability

• Size

• Computational complexity

• Interpretation reliability

Field of View and Range

Field of view is the angular extent of the observable world that is seen at any given moment

The horizontal FOV may be different than the vertical FOV Range D

φ

θ

Field of View and Range

Range is the distance at which a sensor can make reliable measurements

Range D

φ

θ

Accuracy

● Accuracy refers to how correct the reading from the sensor is● Error is defined as the difference between the output value of the sensor and the true value● A sensor having high accuracy has very low error

Repeatability

● Repeatability is the variation in measurements taken by a single person or instrument on the same item and under the same conditions.

● Repeatability can be expressed in terms of standard deviation

Resolution

● Resolution refers to the smallest unit that can be measured by the given sensor● What is the resolution of an analog wall clock?● Resolution can also be expressed in terms of number of bits i.e. For a fixed range, a sensor having more number of bits will have a greater resolution

Responsiveness in the Target Domain

Is the particular sensor suited to its target environment?

Example: a laser range finder is not useful in environments that have lots of glass

Power Consumption

● Power consumption is a concern for mobile robots that operate on batteries● Voltage requirement – voltage needed for proper operation and maximum voltage that can be tolerated● In general, active sensors consume more power than passive sensors● Example: if a sensor operates on 1.5V DC and consumes 20mA of current, then its power requirement is:

1.5 V x 20 mA = 30 mW

Hardware Reliability

● Hardware reliability can be affected by:● Power● Operating conditions: temperature, humidity, etc.● Shock

● A sensor having high hardware reliability is preferred over a sensor with low hardware reliability

Size

● The size and the weight of the sensors can affect the overall size of the robot

● Generally, a smaller and lighter sensor is preferred over a bulky or heavy sensor

Computational Complexity

● In a mobile robot, a sensor having high computational complexity can result in less computational power for other activities like planning

● Computational complexity can be expressed in terms of the “Big Oh” notation

Interpretation Reliability

● Interpretation reliability is different from hardware reliability● Interpretation reliability deals with the ability of the robot to determine if the sensor is providing incorrect output● Example: IR Range Sensor

Sensor Interfaces

How is the sensor connected with the (electronics of the) robot?

–Analog

–Digital

–I2C

–RS – 232

–USB

Sensors for Mobile Robotics

● Range Sensors – Provide distance to objects in the environment● Proximity Sensors / Tactile Sensors – Determine if any object in the environment is touching the robot● Location Sensors – Provide information about the location of the robot in the world● Propioceptive Sensors● Vision Sensors – Provide visual representation of the environment● Other Sensors – Thermal, Magnetic, RFID, etc.

Range Sensors

SONAR

Laser Range Finder

IR based range sensors

Proximity Sensors

–IR based proximity sensor

–Tactile sensor

Location Sensors

–GPS

–Beacons

Propioceptive Sensors

–Accelerometer

–Gyroscope

–Encoders

Vision Sensors

–Camera

–Line Detector

Other Sensors

–RFID

–Thermal Sensors

–Compass

Actuators

An actuator is a mechanical device for moving or controlling a mechanism or system

Commonly Used Robotic Actuators

● Motors● Servos● Linear Actuators● Pnuematic Actuators

Motors

–Motors are used to convert electrical energy to mechanical (rotational) energy

–Most motors used for robotics are geared motors

–A reduction gear increases torque at the cost of reducing speed

Source

Servos

–A servo is a special type of motor, where the output shaft can be positioned to a specific angle by sending a PWM signal

–A PWM (pulse width modulated) signal modulates the ON time of the signal

Source

Source

Linear Actuators

A Linear actuator converts electrical energy to linear motion

Source

Pneumatic Actuators

●A pneumatic actuator typically employs energy stored in the form of compressed air to mechanical energy

●Pneumatic actuators are usually used for high power applications

Drives

•Differential drive

•Tricycle drive

•Ackerman steering

•Synchro drive

•Omnidirectional drive

•Tracked Vehicles

Differential Drives

•Inexpensive

•Simple – 2 motors and 2 wheels

•Can perform variety of motions

motors

wheels

Image obtained from http://hackedgadgets.com

Snake Robot

Schemas & Behaviors

Gibson’s Ecology

• “The world is its own best representation.”

• It makes little sense to discuss an agent’s perception independent of the agent’s environment

• Gibson proved the Existence of Affordances

• Affordance is a perceivable potentiality of the environment for an Action

Affordance & Perception

•Affordances are perceivable potentialities of the environment for an action

•Perception serves two functions:

• To release a behavior• To perceive information needed to

accomplish the behavior

Schema Theory: History

• Schemas were conceived by psychologists around 1900

• Schemas represent a basic unit of activity

• Michael Arbib was a computer scientist who first brought schemas into AI Robotics

Arbib’s Application Of Schemas

• A Behavior is a schema composed of a perceptual schema & motor schema

• Perceptual schema embodies sensing

• Motor schema embodies physical activity

Definition Of Schema

A Schema is a basic unit of behavior from which complex actions can be constructed; it consists of the knowledge of how to act or perceive as well as the computational process by which it is enacted. (Ron Arkin)

Schema Theory

• A schema can be used to express the basic unit of activity

• A schema consists of:

• Knowledge on how to act and/or perceive and

• The computational process by which it uses to accomplish that activity

Schema:

Data

Methods

Behaviors as Perceptual & Motor Schemas

Pattern of Motor ActionsBEHAVIORSensory Input

Releaser

Perceptual Schema Motor Schema

Behaviors as Perceptual & Motor Schemas

• Motor schema represents the template for physical activity

• Perceptual schema represents the template for sensing

• The motor schema and the perceptual schema are derived from the schema class

Schema Theory Example: Frog’s Behavior

motor schemasnap

perceptual schemalocate_fly

fly 1activation condition

motor SIsnap(fly1)

perceptual SIlocate_fly(fly1)

behavior

percept, gain

Snap at (x, y, z)

(x, y, z)

Reactive Paradigm

Reactive Robots

• Robots are situated agents operating in an ecological niche

• Behaviors serve as the basic building blocks for robotic actions, and the overall behavior of the robot is emergent

• Only local behavior-specific sensing is permitted

• These systems inherently follow good software design principles

• Animal models of behavior are often cited as a basis for these systems or a particular behavior

Three Levels of Reactive Paradigm

• Level 1: Existence proof of what can/should be done

• Level 2: Decomposition of existence proof into inputs, outputs, & transforms

• Level 3: Implementation

Level 1: Existence Proof

• Sample Task: To seek out humans trapped in a building after an earthquake

• Existence proof: A mosquito can seek out people and so it provides an existence proof that it is possible for a computationally simple agent to find a human being

• At Level 1, agents (mosquitoes & robots, in this case) share a commonality of purpose or functionality

Level 2: Behavior Decomposition into Inputs, Outputs & Transformations

• Creating a flowchart of black-boxes

• Each black-box transforms input to output

• For mosquito, input = thermal image, output = steering command

• At Level 2, agents can exhibit common processes

Level 3: How to implement the process

• This level focuses on how each transformation or black-box is implemented

• At Level 3, agents may have little or no commonality in their implementation: the actual thermal signature of a robot seeking humans in a building destroyed by an earthquake may have little in common with how the actual mosquitoes work

Reactive Paradigm

SENSE ACTSENSE ACTSENSE ACTSENSE ACT

Reactive Paradigm is organized into multiple, concurrent behaviors

Hierarchical Paradigm vs. Reactive Paradigm

SENSE PLAN ACT

SENSE ACT

Hierarchical Paradigm

Reactive Paradigm

Action-Perception Cycle in Hierarchical Paradigm

World

Perception ofEnvironment

CognitiveActivity

Agent acts and modifies world

Decides what to look for

Agent samples and finds potential actions

Subsumption

Subsumption Architecture

• Rodney Brooks invented this architecture at MIT

• Behaviors are released in a stimulus – response way

• No external program coordinates and controls them

Subsumption Layers of Competence

• Modules are grouped into layers of competence

• They reflect a hierarchy of intelligence or competence

• Lower levels encapsulate basic survival functions

• Higher levels create more goal-directed actions as mapping

Example: Level 0: Move

SONAR

COLLIDE

FEELFORCE

RUN AWAY TURN

FORWARD

polar plot

force heading

halt

heading encoders

Example: Level 1: Wander

SONAR

COLLIDE

FEELFORCE

RUN AWAY

TURN

FORWARD

polar plot

force heading

halt

heading encoders

AVOIDWANDERheading

S

modified heading

References

• Murphy, R. Introduction to AI Robotics, MIT Press, 2000.

• Arkin, R. Behavior-Based Robotics, MIT Press, 1999.