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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. Carnegie Mellon 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. Carnegie Mellon 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 Carnegie Mellon 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 Carnegie Mellon 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 Carnegie Mellon 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) Carnegie Mellon 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. Carnegie Mellon 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. Carnegie Mellon 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) Carnegie Mellon 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. Carnegie Mellon 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 Carnegie Mellon 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] Carnegie Mellon An Instance of Occupancy Grid The probabilities The occupancy estimates Carnegie Mellon 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. Carnegie Mellon 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? Carnegie Mellon 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. Carnegie Mellon 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. Carnegie Mellon 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. Carnegie Mellon 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: Carnegie Mellon Experiments Map from raw data Occupancy grid from sonar data Max likelihood map Max likelihood occupancy grid