Intelligent Robotics

1
Intelligent Robotics

• Today Wednesday Localization Navigation

Workers Of The World, Meet Your Robot Replacements
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Where am I?

• Localization
• Given an initial estimate, q, of the robots
  location in configuration space (C-space),
  maintain an ongoing estimate of the robot pose
  with respect to the map, P(q).

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Overview of Location
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Hybrid Robot Architecture

• Deliberative planner provides advice to the
  reactive controller

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If your robot has a map, why is it difficult for
it to know where it is?

• Sensors are the fundamental input for the process
  of perception, therefore the degree sensors can
  discriminate the world state is critical
• Sensor Aliasing
• Many-to-one mapping between environmental states
  to the robots perceptual inputs
• Amount of information is generally insufficient
  to identify the robots position from a single
  sensor reading

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Why is it difficult for a robot to know where it
is?

• Sensor Noise
• Adds a limitation on the consistency of sensor
  readings
• Often the source of noise problems is that some
  environmental features are not captured by the
  robots representation.
• Dynamic Environments
• Obstacle Avoidance

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The Configuration Space (C-space)

• A set of reachable areas constructed from
  knowledge of both the robot and the world
• How to create it
• First abstract the robot as a point object.
  Then, enlarge the obstacles to account for the
  robots footprint and degrees of freedom

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C-Space the robot has...

• A Footprint
• The amount of space a robot occupies
• Degrees of Freedom
• The number of variables necessary to fully
  describe a robots configuration in space
• Six DoF
• Most Use 2 DoF
• Why? When would you need more?

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C-Space Accommodate Robot Size
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The Cartographer Spatial Memory

• Data structures and methods for interpreting and
  storing sensory input with relation to the
  robots world
• Representation of the world
• Sensory input interpretation
• Path planning evaluation
• Collection of information about the current
  environment

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Map Representations

• Quantitative (Metric Representations)
• Topological (Landmarks)
• Important considerations
• Sufficiently represent the environment
• Enough detail to navigate potential problems
• Space and time complexity
• Sufficiently represent the limitations of the
  robot
• Support for map changes and re-planning
• Compatibility with reactive control layer

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Using Dead Reckoning to Estimate Pose x,y,T

• ded reckoning or deduced reckoning
• Reckon to determine by reference to a fixed
  basis
• Keep track off the current position by noting how
  far the robot has traveled on a specific heading
• Used for maritime navigation
• Proprioceptive

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Dead Reckoning with Shaft Encoders

• How far has a wheel traveled?
• distance 2 PI radius revolutions

reflectance sensor
slot sensor
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How far has the robot traveled and how far has
it turned?
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Which way am I going?

• Heading
• Percentage of the circumference of the circle
  with radius d

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How far have I gone?

• Half the distance of the arc at the end of the
  motion
• Distance moved for center of the robot

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Adding it up

• (x,y,T)
• Update the position information at each sensor
  update.
• How large can a single segment be?
• What does this assume?

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Many Types of Mobile Bases

• Differential Drive
• Two independently driven wheels on opposite sides
  of the robot
• 3 DoF pose x,y,T
• Holonomic Assumption robot can be treated as a
  mass-less point that can move in any direction

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Some of the Various Types of Mobile Bases
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Topological Representation

• Use of Landmarks
• Natural or Artificial
• Passive or Active
• Based on a specific sensing modality
• Vision, laser, sonar, IR

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Example (movies)
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Errors

• Systematic Errors vs. Random Errors
• Can they be managed?

(movie)
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What makes a good Landmark

• Perceivable from many different viewpoints
• Persistence
• Distinct features
• Readily recognizable
• Unique features
• Avoid sensor aliasing

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What would make good landmarks in the EB?
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Example of Using Landmarks in Mapp
representation Distinctive Places
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Distinctive Places
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Another Use of LandmarksTriangulation

• A single landmark can be used as a beacon
• Given 2 landmarks the robots pose can be
  constrained on the arc of a circle
• Given 3 landmarks the robots pose can be
  determined to a point

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Metric Representations

• Coordinate system representation
• Path is decomposed into waypoints
• As opposed to landmarks
• Path planning is usually based on some measure of
  optimal or best path
• Graph search or graph coloring methods

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World Representations
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Meadow Map

• Extend boundaries to accommodate size of robot
• Divide free space into convex polygons
• Connecting corners
• Create waypoints by determining the midpoints of
  lines that border two polygons
• Use graph search method for path planning

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Meadow Map

• What problems would the robot encounter using a
  Meadow Map?
• Are there other problems with using a Meadow Map?

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Voronoi Graph

• Decompose the space into regions around each
  point, such that all the points in the region
  around p_i are closer to p_i than any other point
  in S.
• Voronoi edges become equidistant from boundary
  points
• Voronoi vertex is created where Voronoi edges meet

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Voronoi Graph

• Use a graph search method for path planning
• Advantages and Disadvantages?

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Regular Grid

• Subdivide space into same size grid spaces
• Use center of square or vertices as waypoints
• Considered as 4 connected or 8 connected

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Regular Grid

• Advantages Disadvantages?

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Quadtree Representation

• Recursively divides a square into four smaller
  squares until each square is either filled with
  free space or non-free space
• Center of squares are used as waypoints

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Path PlanningWave Front Planners

• Graph coloring algorithm.
• Obstacles nodes and the Goal node are assigned
  their own unique values.
• Typically 1 and 2, respectively.
• From the goal, color each bordering region with
  a value indicating its proximity to the goal.
• Continue until start node is reached.
• Coloring whole grid may yield a more optimal
  solution.
• Follow the gradient from the start node toward
  the goal node.

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Mechanics
Starting Grid
The Goal node is assigned 2, Obstacle nodes
with 1 and all other nodes are set to 0. The
colored 0 at node (7, 0) is the robots start
position.
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Mechanics
Ending Grid (after complete propagation)
Note that this example assumes that the robot can
move diagonally (typically 8 edges per
node). Question How can difficult terrain be
modeled?
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Queue Approach
Gary Mayer, Implementation of a Deliberative
Robot Control Architecture on an Inexpensive
Robot Platform, SIUE MS Thesis, 2004

• An efficient means to propagate the wave (on a
  computer with sufficient memory and processing
  power) is to use a queue.
• Note the robot Start node.
• Assign the values of 1 to all Obstacles nodes and
  2 to the Goal node. Set all others to 0.
• Push the goal node into the queue.
• Pop the first item from the queue and set it as
  the current node.
• Examine all nodes connected to the current node.
  Push those nodes that have values equal to 0 into
  the queue and assign a value to them equal to one
  greater than the current node.
• Repeat steps 4 and 5 until either the Start node
  is reached or all nodes are assigned a value
  greater than 0.

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Loop Approach
Gary Mayer, Implementation of a Deliberative
Robot Control Architecture on an Inexpensive
Robot Platform, SIUE MS Thesis, 2004

• For computers without a lot of memory and
  processing power, a simple loop approach will
  work. Note that this restricts the dimensions of
  the world to a grid.
• Use a column traversal loop embedded in a row
  traversal loop.
• Note the robot Start node.
• Set a Change flag to FALSE.
• Set the Current node to node (0, 0).
• If Current node is not an Obstacle node and has
  been assigned a non-zero value, then examine the
  nodes connected to Current node.
• If the examined node has a value equal to 0,
  assign a value to it equal to one greater than
  Current node and set the Changed flag to TRUE.
  Repeat for each connected node.

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Loop Approach (contd)

• If not the last column in the row, set Current
  node to the node in the next column and repeat
  steps 4 and 5.
• If not the last row, set Current node to the node
  in the first column in the next row and repeat
  steps 4, 5, and 6.
• If the Changed flag is TRUE, repeat steps 2 - 7.
• While wasteful in the fact that many nodes must
  be revisited, this approach ensures successful
  wave propagation around even a very complex
  environment.
• To ease processing, it may help to define a
  border of obstacles around the grid.

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Pros to Using Wavefront

• Simplistic and not very memory intensive.
• Forward moving wave is easy to understand.
• Requires little data for each node.
• Easy to implement a low memory / simple process
  approach.
• Benefit by storing goal location(s) in one array,
  obstacle location(s) in another, and robot
  position in a variable.
• Each time the world grid is reset, traverse
  through each array and reinsert goals, obstacles,
  and robot position into world representation
  array.
• Able to create plans to multiple goals (one at a
  time).
• Allows easy modification of obstacle and goal
  locations in the event the robots sensors detect
  a new one or one is not sensed where it was
  originally mapped to be.

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Cons to Using Wavefront

• Not very efficient in processing time.
• Every node must be visited for optimal path many
  nodes more than once.
• Typically lt10 sec to create a path on a 4 x 6
  usable grid with 2 goals.
• Can only plan a path to one goal at a time.
• When multiple goals are present, plan a path to
  each in turn (set the other goals to empty). Go
  to the closest goal first. If you dont
  necessarily want the closest goal (such as if
  there is goal priority), then it is best to set
  the other goals to obstacles so that the robot
  does not plot a path through them.
• More than one path may result.
• Can use factors such as robots current heading,
  path with least turns, and random choice to
  decide.

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Path PlanningSearch

• The activity of looking for a sequence of actions
  that solves (achieves) the goal (goal state)
• Plan sequence of actions to achieve a goal
• State-Space Search
• Initial State
• Set of Actions
• Goal Test
• Search Tree root is the initial state, each
  successive level is a state expanded from its
  parent by the application of a valid action

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8-Tile Puzzle
(link)
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Search Strategy choosing which state to expand
next.
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Search Strategies

• Uninformed or blind searches
• Breadth First Search, Depth First Search

Systematic, exhaustive search
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Heuristic Search

• Heuristic
• Rule of thumb
• a way to measure good a state is to get to your
  goal
• Examples
• Parking what would be a good heuristic to find
  your car?

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Search Strategies

• Informed or heuristic searches
• Use domain knowledge to determine which state
  looks most promising to expand next
• Heuristic Function
• h(n) estimate of the path cost from state n to
  the goal
• h(n) 0 if and only if n is a goal state

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Informed Search Strategies

• Best First or Greedy Search Expand the state
  that is estimated to be closest to the goal

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Informed Search Strategies

• Branch Bound Expand the state that is
  estimated to be closest to the goal
• f(n) g(n) h(n)
• g(n) actual cost of path going through state n
• f(n) is estimated cost of the cheapest solution
  that goes through state n

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Branch Bound
f(n) g(n) h(n)
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A Search

• Admissible Heuristic Always underestimates the
  actual cost of the path
• A search is Branch Bound with an admissible
  heuristic

• Why is it important for h(n) to underestimate
  the actual cost?

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Search Space Comparison

• Breadth First Search Space
• Shaded region is A Search Space
• The better h(n) estimates the actual cost, the
  smaller the search space
• A and it variations used mostly for navigation

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Search A

• f(n) g(n) h(n)
• g(n) Cost of going from the starting state to
  state n
• h(n) heuristic estimate of the cost of going from
  state n to the goal state
• Guaranteed to find a solution if one exists
• Will find the optimal solution

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Admissible Heuristics for Pathing

• Straight Line Distance
• h(A) sqrt((A.x-goal.x)2 (A.y-goal.y)2)
• Manhattan Distance
• h(A) (abs(A.x-goal.x) abs(A.y-goal.y))
• Use a weighting factor to
• estimate the cost of traversing
• difficult terrain.

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A Primer
Create a node containing the goal state node_goal
Create a node containing the start state
node_start Put node_start on the open list
While the OPEN list is not empty Get the
node off the open list with the lowest f-value
and call it node_current If node_current is the
same state as node_goal we have found the
solution return solution Generate each state
node_successor that can come after node_current
For each node_successor of node_current
        Set the cost of this node to be the cost
of node_current plus the cost to get to
node_successor         If this node is on the
OPEN list but the existing one is better then
discard this successor break         If this
node is on the CLOSED list but the existing one
is better then discard this successor break
         Remove occurrences of this state from
OPEN and CLOSED         Set the parent of
node_successor to node_current         Set
h-value to be the estimated distance to
node_goal         Add this node to the OPEN list
by f-value      Return failure
Do you have to have an OPEN and CLOSED list?
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A Example European Vacation
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On the Road to Bucharest
A Pathing Arad to Bucharest
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Optimal (Shortest) Path

• A chooses which location to expand based on the
  value f(n) g(n) h(n)
• If h(n) is admissible, A will generate all paths
  that underestimate the actual path cost, thereby
  guaranteeing that the solution path found is the
  optimal one.

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Additional Points

• Cost of Travel
• Additional costs associated with path or region.
• Terrain
• Uphill down hill costs
• An efficient data structure is important for
  storing the Open and Close lists.
• Suggestions?
• Variations
• IDA (Iterative Deepening)
• Bi-directional
• D (Dynamic Planning)
• Hierarchical A

A Demo
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Obstacles

• What should the robot do if it cannot complete
  the plan?
• D
• Dijkstras Shortest Path Algorithm

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Other Methods

• Potential Fields
• Occupancy Grids
• Monte Carlo Localization
• http//www.cs.washington.edu/ai/Mobile_Robotics/mc
  l/
• SLAM

(movie)