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

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

3. Carnegie Mellon Today’s Outline Collaboration Agent Perception “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. PlanningNavigation Mapping

4. Carnegie Mellon 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. Limited Perception Replace Faulty Robot

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

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

7. Carnegie Mellon The Axes of the Design Space Explicit (Wireless Net) Sensing (Vision, Radar) Find control parameters Architecture Restricted /Multiple Paths Homogeneous/Heterog Centralized/DecentralizedOrganization Differentiation Model Other Ags. Space Sharing Autonomous /Centralized Innate (Insects) Motivated (Utility) Learning Communications Resource Conflicts CooperationOrigin

8. Carnegie Mellon Two Relevant Points 1.) Does the scaling property of decentralization offset the coordinative advantage of centralized systems? 2.) Agent perception and localization are usually taken for granted in the software domain? Neither empirical, nor theoretical, work that addresses this question in mobile robotics has been published yet. In Robotics, perception and localization define research sub-fields. Simulated results may be inconclusive without adequate modeling of error and uncertainty in perception and location. Distinguishing characteristic of robot agents

9. Carnegie Mellon Perception & Location In Robot Agents To accomplish its task, the autonomous robot needs a description of the “world” and should know its location. To conceive a plan, the autonomous robot must plan. How does the robot agent represent its world? How does the agent map the unknown environment, while accounting for uncertainty in perception & location? Where am I? The questions define:The Mapping Problem.

10. Carnegie Mellon Representing the World x y Occupancy Grid 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) p(x,y)p(x,y) Applications: The grid stores the probability p(x,y) that cell c(x,y) is occupied.

11. Carnegie Mellon Features of the Occupancy Grid Traditional approaches, to representing the world, rely on recovery and manipulation of geometric models. Advantages of the occupancy grid: No need of prior knowledge of the environment. Incremental discovery procedure. Explicit handling of uncertainties. Ease to combine data from multiple sensors.

12. 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. Po is the probability that the cell is occupied. 1 PePo Distance R Obstacle Sensing Action: Pe is the probability that the cell is empty.

13. Carnegie Mellon Updating the Occupancy Grid The robot computes the occupancy estimate of cell i, r(i), at time t. OCC - occupied 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[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)]  s  p[r(i) | C(i)=s].p[C(i)=s] p[C(i)=OCC| r(i)] = =

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

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

17. Carnegie Mellon The probability that the robot is at position X’, if it executed actionU at location X. P(X’ | X,U) Udenotes the control action. denotes the robot’s location in space. XOdenotes the landmark observation (e.g., obstacle). denotes the map of the environment (occup. grid). M P(O | X,M) The probability of making observation O, given that the robot is at location X and M is the map. Elementary Models Robot MotionRobot Perception

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

19. Carnegie Mellon Finding the Most Likely Map Let: P(m|d) be the likelihood of map m given data d. P(d|m) be the likelihood of data d given map m. P(d) be the probability of observing data d. P(m) be the prior probability of map m. The most likely map: P(d|m). P(m) P(d) m* = ArgMax P(m|d)= Problem Solution: The Expectation-Maximization Alg (EM) for HMMs, together with some tricks, can compute m* efficiently.

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

21. Carnegie Mellon Experiments Max likelihood occupancy gridMax likelihood map Occupancy grid from sonar dataMap from raw data