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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 Error1.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