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.

An investigation of collaboration mechanisms for teams of robots.

What makes robot agents different than agents in other domains, such as the web?Goals:

Carnegie Mellon

Today’s Outline

CollaborationAgent 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

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.

LimitedPerception

ReplaceFaultyRobot

Carnegie Mellon

Cooperative Behavior

The underlying collaboration mechanism makes the total utility increase.

Given a task, a multiple-robotsystem displays cooperativebehavior when:

That is, the system’s performance is higher when robot agents collaborate.

Non-cooperative

Cooperative

Same work, but less effort

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

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

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

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.

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)

Applications:

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

Carnegie Mellon

Features of the Occupancy Grid

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

Advantages of theoccupancy grid:

No need of prior knowledge of the environment.

Incremental discovery procedure.

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.

Po is the probability that the cell is occupied.

1 Pe Po

Distance R

ObstacleSensing Action:

Pe is the probability that the cell is empty.

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)]

sp[r(i) | C(i)=s].p[C(i)=s]

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

=

=

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 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.

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 PerceptionGiven the current map and robot’s position,what are the observations?

Carnegie Mellon

The probability that the robot is at position X’, if it executed actionU at location X.

P(X’ | X,U)

U denotes the control action.

denotes the robot’s location in space.

X O denotes 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 isthe map.

Elementary Models

Robot Motion Robot Perception

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

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.

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

Carnegie Mellon

Experiments

Max likelihood occupancy gridMax likelihood map

Occupancy grid from sonar dataMap from raw data