CS 415 – A.I.

CS 415 – A.I.

Slide Set 3

Representation and Search

• Representational System – function is to capture the essential features of a problem domain and make the information accessible– Abstraction – being able to efficiently store the features of

the problem domain• Note: the features will undoubtedly change

– Balance trade-offs between efficiency and expressiveness

Representation in Mobile Robotics

• Kinematics – basic study of how mechanisms move– Basic goal: given all the angles and movement,

what is you point in space at this time– 2 Frames of Reference• Global Frame of Reference

– Robot gets through layers of representations (maps, etc)

• Local Frame of Reference– Don't know what the world looks like– Remember how far I've traveled

• Given global frame of reference– If the robot moves how do we keep up with where

we are in space– Kinematic Equations• A system of equations that determines our x,y position

and our rotation (angle Θ) after k control steps• See second page of ARL paper

– Synchro Drive Robots– Also exist for Differential Drive Robots

• Store as a matrix system– Perform matrix operations to transform and solve

• Regardless, everyone should work in the same frame of reference– Homogenous Transform• Do matrix operations to transform from one frame of

reference to another

How far has the robot moved?

• Apply power, robot moves, right?– Power does not relate well to speed

• So, other options:– Check the particular motor velocity (left/right)– Some visual cue for how fast you're going– Encode inside motor• How many 'ticks' has the motor made as it rotated• Use PID, proportional integral derivative

– Integral and derivative → smooths error/gives result

Mapping

• How do we abstract a map?• Efficiency vs Expressiveness–What are the tradeoffs

• Dealing with Errors– Examples: • Synchro Drive• Differential Drive

Accurate Relative Localization Using Odometry

• Drawing Maps– Depends on relative localization• Can't escape the use of odometry

– Have error built in• Overcoming Error

1.Odometry error modeling2.Error Parameters estimation3.Covariance matrix estimation 1 and 2 – systematic errors 3 – non-systematic errors

Systematic Errors

• Define these for the robot based on the appropriate error model for the drive type– Differential Drive → given in the literature• Borenstein paper

– Synchro Drive → given in this paper• Major source: wheel misalignment

– Major source of distortion for theta (angular velocity): drag AND rotate the robot

– Provable by geometric analysis of kinematic equation

Non-systematic Errors

• PC (POSTECH CMU)-method– 1st get the error model – 2nd use PC-method to generate error parameters

and covariance matrix• Based on sensor-based navigation through the

Generalized Voronoi Graph (GVG)– Voronoi extensively covered in literature– Creates a well-understood path based on obstacles– Robot drives it forward (FOP) and backward (BOP)

• 2 diff odom paths, same real-world path

• Give an initial CFOP and CBOP based on error model and initial error parameters guess

• Then, find the error parameters that minimize error between CFOP and CBOP– Steepest descent method

• Now, build an error covariance matrix based on 3 assumptions and worst-case analysis

A little error, uncorrected, tends to flourish

• See Fig 8– Note: one possible approach, reset the odometry

before the error gets too bad• See Fig 9• See Fig 12• See Fig 13

Representation/Search - Considerations

• Real-time Systems– Is it schedulable

• Has a lot to do with efficiency/expressiveness– How are we storing things (fast to slow)

• I/O• Memory • Registers• Cache

– What Language are we using (fast to slow)• Assembly• C• C++• Java• Python

Other Forms of Representation• Example: A robot might be stacking elements from a

table on top of one another• Might give the following predicates (state facts about

our domain):clear(c)clear(a)ontable(a)ontable(b)on(c,b)cube(b)cube(a)pyramid(c)

• Might also define a set of rules which relate to these predicates For all X if there does not exist any Y where on(Y,X) than this implies clear(X)

Using Predicate Calculus• Predicates can also be more advancedhassize(bluebird,small)hascovering(bird,feathers)hascolor(bluebird,blue)hasproperty(bird,flies)isa(bluebird,bird)isa(bird,vertebrae)• Predicates are not functions in the sense of higher-level

languages, nor should you think of them in terms of programming– There is no set of predicate functions– Any predicate can be defined

• They are strictly useful for representing knowledge in conjunction with rules

Search

• What are the possible moves?– The computer knows because of the knowledge

representation• All moves are either stored or can be inferred from the

stored knowledge and set of rules.

• What is the best move?– This is the domain of search– Example: Tic Tac Toe

Limitations of State-Space Search

• Not sufficient to automate intelligent behavior– How big is the state-space for chess?• 10120 different board configurations

– Larger than # molecules in the universe– Larger than the number of seconds since the “big bang”

– How big is the state-space for human language?• Untold possibilities

• State-Space Representation and Search is an important tool only

Exhaustive Search vs. Heuristic Search

• Exhaustive Search– Brute force attempting all possible combinations

till an optimized solution is found• Heuristic Search– Humans don’t use exhaustive search– Instead, we use rules of thumb based on what

seems most “promising”– Heuristic – a strategy for selectively searching a

state space ---- Examples?

Autonomous Robotics

• Key: operating in an unknown environment– Exploration: the act of moving through an unknown

environment while building a map that can be used for subsequent navigation• The world is not made of right angles

– Kinds of space: Open, Closed, Unknown– Frontiers: regions on the boundary between open

and unknown space

The Many Faces of Control

• Deliberative Control• Reactive Control• Hybrid Control• Behavior-Based Control

Emergent Behavior

Note: some info taken from The Robotics Primer by Maja J. Mataric.

Highly recommend this book

Deliberative Control• Think Hard, Act Later– Throw back to the early days of AI• Example: Chess• Useful When:

– There's time to do it– Without strategy, things go bad

• Planning– i.e. - Programming Assignment 1• But, done automatically

– Search• (DFS, BFS, etc), Goal-Oriented, Forward-Oriented

Deliberative-planning based architecture

• 3 Steps (done in order)– Sensing– Planning– Acting (executing the plan)

• SPA Architectures

• The Good– Can expect to find many (all possible?) paths to the

goal– Can cherry-pick the one that's best• Optimization

• The Bad– All the time it takes isn't always necessary– Assumes you have stored knowledge

• The Ugly– Not possible except in relatively small search spaces• Almost never possible in real-time

Additional Drawbacks

• Sensor data is coming all the time• Planning for all possible actions is memory

intensive– Only need one action really

• World model must always be accurate and updated– The real world is a dynamic place– Can't make it hold still while I act

Reactive Control

• Don't think, react– Tight link between sensors and actuators– Doesn't have a world model– A set of rules is executed based on sensor states

• Mutually-exclusive Conditions– One sensor state, one action– Keeps control system simple• But, how many sensor states are there? Many.• Giant lookup table, slow response

• Rules should be generated at Design-Time– Designer thinks, robot does not– Designer identifies important sensor states /

situations• Actions can get stuck in loop– Use a little randomness– Keep a bit of history

• We want our robot to do multiple things (multi-tasking)– Action Selection• Command Arbitration (choose a command)• Command Fusion (combine the commands)

– Example• Avoid Object• Follow-wall

• Subsumption Architecture– More on this later

Hybrid Control

• Reactive – fast but inflexible• Deliberative – slow but smart• Hybrid – best of both worlds– 3 components• A reactive layer (on bottom)• A planner (on top)• A layer that links the above two together

– (in the middle)

– 3-layer architecture

Middle Layer

• Has to:– Compensate for shortcomings of reactive and

deliberative layers– Reconcile different time-scales– Deal with different representations– Reconcile any contradictory commands

• Gopher bots (hospital deliveries): The What-ifs Problem– Need to get to room fast, but no plan– Taking optimal route, suddenly blocked

• By priority personnel, because of outdated map– Always having to go to same room

• Dealing with changes– This is where the middle layer comes in– No one “correct” answer• Dynamic Replanning• Off-line Planning• On-line Planning• Building in domain knowledge

• The middle-layer is hard– Best solutions are case-specific (so far)

Behavior-based Control

• What we know– Reactive is inflexible, no representation, or learning– Deliberative systems are slow– Hybrid systems are hard and complex– Biology (our model) has evolved from simple and

consistent components• BBC → implemented as collections of behaviors

What are behaviors

• Many answers to this, but some commonalities– Achieve/maintain particular goals– Take time, are not instantaneous• More complex than simple actions

– Take input from sensors and other behaviors– Send output to effectors and other behaviors

• Behaviors can work at multiple levels of abstraction (levels of specificity)

How they are used• Executed in parallel, controller can respond immediately when

needed• Networks of behaviors store state and construct world models• Designed to work on the same time-scale• Internal behavior structure is not necessarily one-to-one with

external behavior– Interesting behavior is the result of complex interaction

between internal behavior structures– Example: Robot flocking– Emergent Behavior

• Key challenge: distributing knowledge over the behavior structure

Example: Mapping

• Build a plant-watering robot, also builds a map of plants as it goes– Distribute map data over behaviors– Link behaviors that are adjacent in the environment

• Examples:– Toto: Behavior-based robot for mapping and

navigation at MIT