theory of computation (fall 2013): finite state machines in mobile robots: sensors &...
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Theory of Computation
Finite State Machines in
Mobile Robots: Sensors & Actuators, Schemas & Behaviors, Reactive
Paradigm, Subsumption
Vladimir Kulyukin
www.vkedco.blogspot.com
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Outline
Sensors & Actuators Schemas & Behaviors Reactive Paradigm Subsumption
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Sensors & Actuators
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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.
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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
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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
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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
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Field of View and Range
Range is the distance at which a sensor can make reliable measurements
Range D
φ
θ
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Sensor Interfaces
How is the sensor connected with the (electronics of the) robot?
–Analog
–Digital
–I2C
–RS – 232
–USB
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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.
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Range Sensors
SONAR
Laser Range Finder
IR based range sensors
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Proximity Sensors
–IR based proximity sensor
–Tactile sensor
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Location Sensors
–GPS
–Beacons
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Propioceptive Sensors
–Accelerometer
–Gyroscope
–Encoders
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Vision Sensors
–Camera
–Line Detector
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Other Sensors
–RFID
–Thermal Sensors
–Compass
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Actuators
An actuator is a mechanical device for moving or controlling a mechanism or system
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Commonly Used Robotic Actuators
● Motors● Servos● Linear Actuators● Pnuematic Actuators
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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
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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
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Linear Actuators
A Linear actuator converts electrical energy to linear motion
Source
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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
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Drives
•Differential drive
•Tricycle drive
•Ackerman steering
•Synchro drive
•Omnidirectional drive
•Tracked Vehicles
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Differential Drives
•Inexpensive
•Simple – 2 motors and 2 wheels
•Can perform variety of motions
motors
wheels
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Image obtained from http://hackedgadgets.com
Snake Robot
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Schemas & Behaviors
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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
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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
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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
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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
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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)
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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
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Behaviors as Perceptual & Motor Schemas
Pattern of Motor ActionsBEHAVIORSensory Input
Releaser
Perceptual Schema Motor Schema
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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
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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)
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Reactive Paradigm
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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
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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
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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
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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
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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
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Reactive Paradigm
SENSE ACTSENSE ACTSENSE ACTSENSE ACT
Reactive Paradigm is organized into multiple, concurrent behaviors
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Hierarchical Paradigm vs. Reactive Paradigm
SENSE PLAN ACT
SENSE ACT
Hierarchical Paradigm
Reactive Paradigm
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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
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Subsumption
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Subsumption Architecture
• Rodney Brooks invented this architecture at MIT
• Behaviors are released in a stimulus – response way
• No external program coordinates and controls them
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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
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Example: Level 0: Move
SONAR
COLLIDE
FEELFORCE
RUN AWAY TURN
FORWARD
polar plot
force heading
halt
heading encoders
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Example: Level 1: Wander
SONAR
COLLIDE
FEELFORCE
RUN AWAY
TURN
FORWARD
polar plot
force heading
halt
heading encoders
AVOIDWANDERheading
S
modified heading
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References
• Murphy, R. Introduction to AI Robotics, MIT Press, 2000.
• Arkin, R. Behavior-Based Robotics, MIT Press, 1999.