1. A Formal Model of Computation for Sensory-Based Robotics
Damian M. Lyons
Michael A. Arbib
Presented By: Steven Arnold

2. 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

3. 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 (SI’s)

4. 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

5. 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

6. The RS (Robot Schema) Model
Distributed computation based upon nested networks and schemas
To use the sensorimotor structure SI’s 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

7. 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

8. The RS (Robot Schema) Model
Working with primitive schema only can make programs extremely complex
Solution – Assemblage Mechanism
A group of SI’s that look and act (from the outside) like a single SI
Jmove()(x) = [Jpos()(x), Jset(x)(u), Jmot(u)()]

9. 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 T1;T2

10. The RS (Robot Schema) Model
World Preconditions
Allows for temporal ordering
Ex: Box building
Base; [Side1, Side2, Side3, Side4]; Top

11. The Formal Definition of RS (cont.)
The definition of a basic schema
Name – identifies the schema
Input Port List – <Portname, Porttype> pairs for input ports
Output Port List – <Portname, Porttype> pairs for output ports
Variable List - <VarName, VarType> pairs for all internal variables
Behavior – program that loops continuously, reading, writing to ports, instantiate other SI’s

12. The Formal Definition of RS (cont.)
Port Automaton (non instantiated schema)

13. The Formal Definition of RS (cont.)
There are 3 types of SI transitions
Read-only – SI reads from it’s input port
Write-only – SI writes to it’s output port
Internal – SI doesn’t read to or write from a port (state change is caused through communication

14. The Formal Definition of RS (cont.)
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 PA’s connected together
Definition 6
Network Connection Automaton – Multiple Automaton connected together

15. The Formal Definition of RS (cont.)
Assemblage Schema – computing agent whose behavior is defined as the interaction of a number of communicating SI’s
Definition 8
???
Definition 9
Forall – given a specific schema, will loop through all instances of the schema

16. The Formal Definition of RS (cont.)
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

17. The Formal Definition of RS (cont.)
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.

18. The Formal Definition of RS (cont.)
Observation 13
Using the synchronous communication operations and the instantiation operation, it is possible to duplicate asynchronous operations

19. 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

20. 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: