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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

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CS 415 – A.I.

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  1. CS 415 – A.I. Slide Set 3

  2. 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

  3. 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

  4. 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

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

  6. 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

  7. Mapping • How do we abstract a map? • Efficiency vs Expressiveness • What are the tradeoffs • Dealing with Errors • Examples: • Synchro Drive • Differential Drive

  8. Accurate Relative Localization Using Odometry • Drawing Maps • Depends on relative localization • Can't escape the use of odometry • Have error built in • Overcoming Error • Odometry error modeling • Error Parameters estimation • Covariance matrix estimation • 1 and 2 – systematic errors • 3 – non-systematic errors

  9. 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

  10. 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

  11. 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

  12. 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

  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

  14. 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)‏

  15. Using Predicate Calculus • Predicates can also be more advanced hassize(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

  16. 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

  17. 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

  18. 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?

  19. 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

  20. 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

  21. 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

  22. Deliberative-planning based architecture • 3 Steps (done in order)‏ • Sensing • Planning • Acting (executing the plan)‏ • SPA Architectures

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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)‏

  31. 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

  32. 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)‏

  33. 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

  34. 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

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