Robotics by yurtgc548

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									Carnegie Mellon



                  Mobile Robot Agents




          Eduardo Camponogara




          18-879, Special Topics in Systems and Control: Agents
          Electrical & Computer Engineering
Carnegie Mellon



                   Report Goals

                  A study of the specifics of robotic
                  agents.
                    What makes robot agents different
                    than agents in other domains,
 Goals:             such as     the web?



                  An investigation of collaboration
                         mechanisms for teams of robots.
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                      Today’s Outline

                                   Agent Perception        Mapping
            Collaboration
                                          Navigation       Planning

 “Collaborative Mobile Robotics:   “Sensor-Based Real-World
     Antecedents & Directions,”        Mapping & Navigation,” 1987
     1998 by Uny Cao et al.            by Elfes.

                                   “Using Occupancy Grid for Mobile
                                       Robot Perception &
                                       Navigation,” 1989 by Elfes.

                                   “A Probabilistic Approach to
                                       Concurrent Mapping and
                                       Localization for Mobile
                                       Robots,” 1998 by Thrun.
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                  Multiple-Robot Systems

             The motivations for the intense interest in
              designing systems of multiple robots:


Tasks may be complex.              The efficiency of scale. Building
A robot is limited in the space    simple robots is easier, cheaper
it covers and perceives.           and more flexible.



                                                               Replace
Limited                                                        Faulty
Perceptio                                                      Robot
n
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                  Cooperative Behavior
                                            Non-cooperative
 Given a task, a multiple-robot
 system displays cooperative
 behavior when:
         The underlying collaboration
         mechanism makes the total
                                              Cooperative
         utility increase.
 That is, the system’s
 performance is higher when
 robot agents collaborate.
                          Same work,
                          but less effort
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                  Cooperative Behavior

 Observation:      Most of the research has focused
                     on cooperation mechanisms.

                                                       Environment
 The design        Given a) a team of robots,
 problem:                 b) an environment, and
                          c) a task,
                   Find a cooperation mechanism.

 Research:         Along the axes, or elements,       Robots
                          of the design space
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          The Axes of the Design Space

                                Organization          Centralized/Decentralized
           Architecture         Differentiation       Homogeneous/Heterog

                                Model Other Ags.

           Resource Conflicts   Space Sharing         Restricted /Multiple Paths
                                                      Autonomous /Centralized
                                Innate (Insects)
           CooperationOrigin
                                Motivated (Utility)

           Learning                                   Find control parameters

                                                      Sensing (Vision, Radar)
           Communications                             Explicit (Wireless Net)
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                      Two Relevant Points

 1.) Does the scaling property of decentralization offset
      the coordinative advantage of centralized systems?
             Neither empirical, nor theoretical, work that addresses
               this question in mobile robotics has been published yet.

 2.) Agent perception and localization are usually
     taken for granted in the software domain?

                         In Robotics, perception and localization define
                           research sub-fields.

 Distinguishing          Simulated results may be inconclusive without
  characteristic of        adequate modeling of error and uncertainty
  robot agents             in perception and location.
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 Perception & Location In Robot Agents

 To accomplish its task,
                                                        Where am I?
    the autonomous robot must plan.

 To conceive a plan,
    the autonomous robot needs a description of
     the “world” and should know its location.

        How does the robot agent represent its world?

        How does the agent map the unknown environment, while
            accounting for uncertainty in perception & location?

        The questions define:           The Mapping Problem.
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                  Representing the World
                                                  y
     Occupancy Grid

 The grid stores the
  probability p(x,y) that                                              x
  cell c(x,y) is occupied.

                                               p(x,y)

 Applications:      Given the occupancy grid and landmarks, the
                     agent can come up with a plan to accomplish
                     its tasks. (e.g., drop cans into a garbage bin)
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        Features of the Occupancy Grid

 Traditional approaches, to representing the world,
  rely on recovery and manipulation of geometric models.


                               No need of prior knowledge of the
                                 environment.

 Advantages of the             Incremental discovery procedure.
 occupancy grid:
                               Explicit handling of uncertainties.

                               Ease to combine data from multiple
                                 sensors.
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              Sensing the Surroundings

 Sensing Procedure:         The robot agent
                              a) senses its surroundings,
                              b) process the signals, and
                              c) computes the occupancy estimate r(i),
                                 {OCC, EMP, UNK}, of cell i.


   Sensing Action:                                                 Obstacle

         Pe is the probability that
            the cell is empty.
                                           1     Pe     Po
         Po is the probability that
            the cell is occupied.
                                                      Distance R
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           Updating the Occupancy Grid
                                                OCC - occupied
The robot computes the
  occupancy estimate of cell i,                 EMP - empty
r(i),
  at time t.
                                                UNK - unknown

 We want to compute the probability that cell i is occupied at time t,
   p[C(i)=OCC | r(i)], given the observation r(i).

 Assuming that the process is markovian in space and time,
   p[C(i)=OCC | r(i)] can be computed with Bayes rule as follows:

        p[C(i)=OCC| r(i)] = p[r(i) | C(i)=OCC].p[C(i)=OCC]/p[r(i)]

                                  p[r(i) | C(i)=OCC].p[C(i)=OCC]
        p[C(i)=OCC| r(i)] =
                                  å ("s) p[r(i) | C(i)=s].p[C(i)=s]
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         An Instance of Occupancy Grid


                        The probabilities




     The occupancy
      estimates
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   Weakness of the Updating Procedure

 Reminder:        Map building is the problem of
                   determining the location of the entities of interest,
                   relative to a global frame of reference.

 Example:         Determine obstacles relative to the cartesian frame.



           To determine the                          The robot agent needs to
           location of these entities                know its location



  Weaknesses of          Sensitive to error/uncertainty in the agent’s location.
  the previous
  approach:              It does not account for past sensor readings.
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 Improving Quality of Occupancy Grids
 New Approach:        Formulate the mapping problem (updating) as a
                      maximum-likelihood estimation problem such that:
                        a) The location of the landmarks are estimated,
                        b) The robot’s position is estimated, and
                        c) All past sensor readings are considered

                                               Given the current position
                      Robot Motion              and control input,
                                               what is the next position?
 Elementary Models:

                                              Given the current map and
                      Robot Perception         robot’s position,
                                              what are the observations?
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                    Elementary Models

             Robot Motion                       Robot Perception

 X     denotes the robot’s location     O    denotes the landmark
       in space.                             observation (e.g., obstacle).

 U      denotes the control action.     M    denotes the map of the
                                             environment (occup. grid).

                                        P(O | X,M)
 P(X’ | X,U)                            The probability of making
 The probability that the robot is at   observation O, given that the
 position X’, if it executed actionU    robot is at location X and M is
 at location X.                         the map.
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                              The Data

 The data is a sequence of control actions, u(t), and observations, o(t).



 d ={o(1),u(1),…,o(n-1),u(n-1),o(n)}



 The model is a HMM (Hidden Markov Model)

                  1) The agent does not know the location at time t,
 Hidden
                  x(t).
 Variables
                  2) It does not know the map m either.
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            Finding the Most Likely Map

             P(m|d) be the likelihood of map m given data d.

             P(d|m) be the likelihood of data d given map m.
 Let:
             P(d) be the probability of observing data d.

             P(m) be the prior probability of map m.

                                                            P(d|m) . P(m)
 The most likely map:         m* = ArgMax P(m|d) =
                                                               P(d)

                              The Expectation-Maximization Alg (EM)
 Problem Solution:             for HMMs, together with some tricks,
                               can compute m* efficiently.
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        The Outline of the EM Algorithm

     Step 1.             Set t=0 and guess a map m(0).

     Step 2. (E-step)    Fix the model m(t) and estimate the
                           probabilities.

     Step 3. (M-step)    Find model m(t+1) of maximum
                           likelihood.

     Step 4.             Make t=t+1 and go to step 2.


     It works like a
                               Estimate the
       steepest decent                                   Take a step
                               gradient
       algorithm:
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                       Experiments
   Map from raw data       Occupancy grid from sonar data




  Max likelihood map       Max likelihood occupancy grid

								
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