A Formal Model of Computation for Sensory-Based Robotics

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A Formal Model of Computation for Sensory-Based
Robotics

• Damian M. Lyons
• Michael A. Arbib
• Presented By Steven Arnold

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Introduction

• Common Approaches to Robot Programming
• General purpose programming languages
• Well understood
• Large amount of control and data structures
• Portable
• Look at what is unique about robots and develop a
  model of computation based upon these
  characteristics
• This paper takes the latter approach and attempts
  to develop a formal model of computation for
  robots that will allow others to later develop a
  control language

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Introduction (cont.)

• Contents of paper
• Key computational characteristics of robots
• Model construction from characteristics
• Formal definition of the model
• Paper introduces the model and does a lot of
  description about specific ways of describing
  schema instances (SIs)

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Characteristics of the Robot Domain

• Robot programs interact with the world
• Sensory input is linked with knowledge to produce
  action
• Known throughout the paper as Sensorimotor
  Computation
• Robots exhibit a flexible, hierarchical
  sensorimotor structure
• Flexible meaning that sensors and effectors can
  be dynamically reconfigured
• Hierarchical meaning that data flows from sensors
  to control to actuators

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Characteristics of the Robot Domain (cont.)

• Robot programs are defined recursively using a
  schema or class structure
• Explained later in examples
• Robot programs are inherently distributed
• Because hardware is distributed the software also
  should be

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The RS (Robot Schema) Model

• Distributed computation based upon nested
  networks and schemas
• To use the sensorimotor structure SIs
  communicate through ports with each other set up
  at instantiation using synchronous message
  passing
• Each schema has a behavior description that
  defines how the SI will act in response to
  communication

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The RS (Robot Schema) Model

• Example Position Control Network
• JPos reads joint position
• JSet takes new position, passes on to motor
  control
• JMot motor controller, takes input value to
  move arm

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The RS (Robot Schema) Model

• Working with primitive schema only can make
  programs extremely complex
• Solution Assemblage Mechanism
• A group of SIs that look and act (from the
  outside) like a single SI
• Jmove()(x) Jpos()(x), Jset(x)(u), Jmot(u)()

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The RS (Robot Schema) Model

• Task Plans
• Task plans is a set of instructions necessary to
  achieve a goal
• Jmove is a task plan, bolt is not
• Sequential Actions
• When one action needs to instantiate after one
  de-instantiates a semicolon is used T1T2

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The RS (Robot Schema) Model

• World Preconditions
• Allows for temporal ordering
• Ex Box building
• Base Side1, Side2, Side3, Side4 Top

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The Formal Definition of RS (cont.)

• Definition 1
• The definition of a basic schema
• Name identifies the schema
• Input Port List ltPortname, Porttypegt pairs for
  input ports
• Output Port List ltPortname, Porttypegt pairs for
  output ports
• Variable List - ltVarName, VarTypegt pairs for all
  internal variables
• Behavior program that loops continuously,
  reading, writing to ports, instantiate other SIs

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The Formal Definition of RS (cont.)

• Definition 2
• Port Automaton (non instantiated schema)

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The Formal Definition of RS (cont.)

• Definition 3
• There are 3 types of SI transitions
• Read-only SI reads from its input port
• Write-only SI writes to its output port
• Internal SI doesnt read to or write from a
  port (state change is caused through
  communication

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The Formal Definition of RS (cont.)

• Definition 4
• A behavior of the PA is any sequence of reads and
  writes to a sequence of states
• Definition 5
• Semantic mapping from schema components to PA
• Port Connection Automaton (PCA) - two PAs
  connected together
• Definition 6
• Network Connection Automaton Multiple Automaton
  connected together

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The Formal Definition of RS (cont.)

• Definition 7
• Assemblage Schema computing agent whose
  behavior is defined as the interaction of a
  number of communicating SIs
• Definition 8
• ???
• Definition 9
• Forall given a specific schema, will loop
  through all instances of the schema

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The Formal Definition of RS (cont.)

• Definition 10
• Split Connector Port automaton with a set of
  output ports and one input port
• (AND) input is valid, all outputs equal input
• (OR) input is valid, one output equal to input,
  all others invalid

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The Formal Definition of RS (cont.)

• Definition 11
• Join Connector Port automaton with a set of
  input ports and one output port
• (AND) all inputs valid, output is one of the
  inputs
• (OR) one input is valid, output is set to valid
  input
• Observation 12
• A connection can be constructed between and input
  port on one SI and output port on another SI such
  that a read to the input port will always
  terminate, even if the output port is never
  written to.

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The Formal Definition of RS (cont.)

• Observation 13
• Using the synchronous communication operations
  and the instantiation operation, it is possible
  to duplicate asynchronous operations

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Example Task Unit Definition Example

• Looks at centered grasp problem
• Center a gripper over an object based on contact
  feedback from the fingers
• Problem when fingers need to be moved together in
  opposing pairs
• Problem is split into two activities
• Moving fingers to contact
• Moving wrist to eliminate conact

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Example Task Unit Definition Example

• Grip FTact()(I,r), tGrip(l,r)(fs),
  FClose(s)()
• FTact reports contact on a specific finger pair
• FClose controls the seperation between fingers
• tGrip schema characterized by