Microsoft PowerPoint - Task Allocation Modeling.ppt [Compatibility Mode] Motivations (ALLIANCE):
Pro: Enables robots to make decisions even when communication breaks down
Con: Must use L-ALLIANCE to set parameters of the system
Negotiation:
Pro: Allows decision process to be made explicit
Con: Does not provide mechanism for robots to recover from communication breakdown
Today’s Paper
“ALLIANCE: An Architecture for Fault Tolerant Multi-Robot Cooperation”, by Parker, IEEE Transactions on Robotics and Automation, 1998.
Presented by Alex Garcia
Challenges of Multi-Robot Cooperation
Fault tolerance:
The ability of the robot team to respond to individual robot failures or failures in communication
Adaptivity:
The ability of the robot team to change its behavior over time in response to a dynamic environment, changes in the team mission, or changes in the team capabilities, to either improve performance or to prevent unnecessary degradation in performance
Reliability:
The dependability of a system, and whether it functions properly and correctly each time it is utilized
Problem Definition, Goal
Solving the problem of multi-robot cooperation for small- to medium-sized teams of heterogeneous robots performing missions composed of independent subtasks that may have ordering constrains
Goal:
Fault tolerant cooperation:
At group level, robots select tasks to ensure that mission is completed by the team as a whole (does not address individual robot fault tolerance)
Assumptions
A robot can detect the actions of other team members
Robots do not lie and are not intentionally adversarial
Communication is not guaranteed to be available
Robots do not possess perfect sensors and effectors
If a robot fails, it cannot necessarily communicate its failure to its teammates
No centralized store of complete world knowledge is available
Overview of ALLIANCE
Utilizes distributed control
Robot failures
Sensor/actuator uncertainties
Dynamic environment
Mission changes
Demonstrated in 8 proof-of-principle applications
Represents current state of the art in multi-robot control for small team sizes
The ALLIANCE Architecture
Higher-level behaviors achieve a task
Behavior set is activated by
motivation levels
Motivational Behaviors
Motivations are designed to allow robot team members to perform tasks only as long as they demonstrate their ability to have the desired effect on the world
Differs from traditional task allocation that begins with task decomposition and then computing the “optimal” robot-to-task mapping
At all times during the mission, each motivational behavior receives input from a number of resources and generates a non-negative number (activation level)
When this level exceeds a given threshold, the corresponding behavior set becomes active
Two Types of Internal Motivations
Motivation is initialized to 0 and increases at a certain rate over time
Impatience:
Enables a robot to handle situations when other robots (outside itself) fail in performing a given task
A robot may be motivated to take over a task from another robot
Fast rate vs. slower rate of impatience
Acquiescence:
Enables a robot to handle situations when itself fails to perform its task
A robot may give up for other tasks because other more capable robots can perform the task or it simply cannot fulfill the task in an acceptable period of time
Action Recognition in ALLIANCE
Issue: How does a robot know what its teammate is doing?
Ideally, prefer passive action recognition
E.g., vision-based interpretation of actions
But, very difficult
ALLIANCE Formal Model
Formal Model: Impatience Impatience rate will be the minimum slow rate, if ri has received communication in the last τi time units, but not for longer than Φij time units
Reset impatience to 0 if ri has just received
its first message from rk
δt = time since last communication check No more than once.
Formal Model: Acquiescence
Give up when: 1) ri has worked on a task for a length of φij time and some other robots has taken over the task
2) ri has worked on a task for a length of λij time
ALLIANCE Formal Model (Con’t.)
This motivation increases at some positive rate unless one of four situations occurs.
Application: “Mock” Hazardous Waste Cleanup
ALLIANCE-Based Control
Application: Adaptive Box Pushing
Box Pushing: Robot Control
Fundamental focus: fault tolerance
Uses motivations (based upon quality metrics) to cause robots to activate tasks
Does not use negotiation
Impatience motivation: Causes robot to become motivated to start a task Fast impatience: if no other robot is performing task
Slow impatience: if some robot is performing task
Acquiescence motivation: Causes robot to give up its task
Task Allocation: Formal Analysis
“A Formal Analysis and Taxonomy of Task Allocation in Multi-Robot Systems”,
by Gerkey and Mataric,
MRTA Problem
Fundamental question: “which robot should execute which task?” in order to cooperatively achieve the global goal.
“Task” a subgoal that can be achieved
independently of other subgoals
Utility (Fitness, Valuation and Cost)
Assumption: each robot internally estimates the value (or the cost) of executing an action
This estimation includes:
Expected quality of task execution, given the method and equipment to be used
Expected resource cost, given the requirement of the task
Given a robot R and a task T, if R is capable of executing T, then the utility can be defined as:
A Taxonomy of MRTA Problems
Three axes for describing MRTA:
Single-task robots (ST) vs. Multi-task robots (MT)
Single-robot tasks (SR) vs. Multi-robot tasks (MR)
Instantaneous assignment (IA) vs. Time- extended assignment (TA)
ST-SR-IA Problems
An instance of the Optimal Assignment Problem
Definition: Given m robots, n prioritized tasks, and utility estimates for
each of the mn possible robot-task pairs, assign at most one task to each robot.
Both centralized and distributed approaches exist to find optimal allocation
Tradeoffs between solution time and communication overhead
Examples: ALLIANCE, MURDOCH, Role-Allocation in Soccer
Algorithm 1 (Greedy Assignment)
1. If any robot remains unassigned, find the robot-task pair (i, j) with the highest utility. Otherwise, quit.
2. Assign robot i to task j and remove them from consideration.
3. Go to step 1.
Reference: BLE Approach by Werger & Mataric (2001)
Algorithm 2 (MURDOCH)
Online assignment:
1. When a new task is introduced, assign it to the most fit robot that is currently available
ST-SR-TA Problems
If there’s a model of how tasks will arrive, then robots’ future utilities for the tasks can be predicted with some accuracy
This problem is one of building a time- extended schedule of tasks for each robot
Problems are NP-hard
Algorithm (Approximation Alg.)
1. Optimally solve the initial mn assignment problem
2. Use the Greedy algorithm to assign the remaining tasks in an online fashion, as the robots become available
ST-MR-IA Problems
Many problems involve tasks that require the combined effort of multiple robots
We must consider combined utilities of groups of robots, which are in general not sums over individual utilities
In multi-agent community, the ST-MR-IA problem is referred to as coalition formation
It is equivalent to a Set Partitioning Problem (SPP), which is NP-hard
Approach: It may be necessary to enumerate a set of feasible
coalition-task combinations
In the case that the combination space is very large, there’s a need to prune
ST-MR-TA Problems
This problem includes both coalition formation and scheduling
Example, delivering a number of packages of various sizes from a single distribution center to different destinations
To produce an optimal solution, all possible schedules for all possible coalitions must be considered, which is NP-hard