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Mobile Robot Agents

Mobile Robot Agents. Eduardo Camponogara 18-879, Special Topics in Systems and Control: Agents Electrical & Computer Engineering. Report Goals. A study of the specifics of robotic agents. What makes robot agents different than agents in other domains, such as the web?. Goals:.

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Mobile Robot Agents

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  1. Mobile Robot Agents • Eduardo Camponogara • 18-879, Special Topics in Systems and Control: Agents • Electrical & Computer Engineering

  2. Report Goals A study of the specifics of robotic agents. What makes robot agents different than agents in other domains, such as the web? Goals: An investigation of collaboration mechanisms for teams of robots.

  3. Today’s Outline Collaboration Agent Perception Mapping Navigation Planning “Collaborative Mobile Robotics: Antecedents & Directions,” 1998 by Uny Cao et al. “Sensor-Based Real-World Mapping & Navigation,” 1987 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.

  4. Multiple-Robot Systems The motivations for the intense interest in designing systems of multiple robots: Tasks may be complex. A robot is limited in the space it covers and perceives. The efficiency of scale. Building simple robots is easier, cheaper and more flexible. Replace Faulty Robot Limited Perception

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

  6. Cooperative Behavior Observation: Most of the research has focused on cooperation mechanisms. Environment The design problem: Given a) a team of robots, b) an environment, and c) a task, Find a cooperation mechanism. Research: Along the axes, or elements, of the design space Robots

  7. 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)

  8. 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 characteristic of robot agents Simulated results may be inconclusive without adequate modeling of error and uncertainty in perception and location.

  9. 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.

  10. y x Representing the World Occupancy Grid The grid stores the probability p(x,y) that 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)

  11. 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. Incremental discovery procedure. Advantages of the occupancy grid: Explicit handling of uncertainties. Ease to combine data from multiple sensors.

  12. 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

  13. Updating the Occupancy Grid OCC - occupied The robot computes the occupancy estimate of cell i, r(i), at time t. EMP - empty 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]

  14. An Instance of Occupancy Grid The probabilities The occupancy estimates

  15. 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 location of these entities The robot agent needs to know its location Weaknesses of the previous approach: Sensitive to error/uncertainty in the agent’s location. It does not account for past sensor readings.

  16. 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 and control input, what is the next position? Robot Motion Elementary Models: Given the current map and robot’s position, what are the observations? Robot Perception

  17. Elementary Models Robot Motion Robot Perception X denotes the robot’s location in space. O denotes the landmark 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 observation O, given that the robot is at location X and M is the map. The probability that the robot is at position X’, if it executed actionU at location X.

  18. 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, x(t). Hidden Variables 2) It does not know the map m either.

  19. 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) for HMMs, together with some tricks, can compute m* efficiently. Problem Solution:

  20. 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 steepest decent algorithm: Estimate the gradient Take a step

  21. Experiments Map from raw data Occupancy grid from sonar data Max likelihood map Max likelihood occupancy grid

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