Task Allocation: Motivation-Based. Dr. Daisy Tang

Transcription

1 Task Allocation: Motivation-Based Dr. Daisy Tang

2 Outline Motivation-based task allocation (modeling) Formal analysis of task allocation

3 Motivations vs. Negotiation in MRTA 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

4 Today s Paper ALLIANCE: An Architecture for Fault Tolerant Multi-Robot Cooperation, by Parker, IEEE Transactions on Robotics and Automation, Presented by Alex Garcia

5 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 changeits behavior over time in response to a dynamic environment, changes in the team mission, or changes in the team capabilities, to either improve performanceor to prevent unnecessary degradation in performance Reliability: The dependability of a system, and whether it functions properly and correctly each time it is utilized

6 Problem Definition, Goal The Problem: Solving the problem of multi-robot cooperation for small-to medium-sized teams of heterogeneousrobots performing missions composed of independentsubtasks that may have ordering constrains Goal: Adaptive, fault tolerant cooperative action selection in multi-robot teams 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)

7 Assumptions Robots can detect the effect of their own actions 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

8 Overview of ALLIANCE ALLIANCE developed for heterogeneousmulti-robot cooperation Utilizes distributed control Focuses on adaptiveresponse to off-normal events amidst: 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

9 The ALLIANCE Architecture Higher-level behaviors achieve a task Behavior set is activated by motivation levels Lower-level behaviors can be inhibited by higher-levels

10 Motivational Behaviors Motivations are designed to allow robot team members to perform tasks only as long as they demonstrate their abilityto 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

11 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

12 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 As substitute, ALLIANCE uses periodic, lowbandwidth broadcastcommunications to inform teammates of current actions

13 ALLIANCE Formal Model

14 Formal Model: Impatience Impatience rate will be the minimum slow rate, if r i has received communication in the last τ i time units, but not for longer than Φ ij time units Reset impatience to 0 if r i has just received its first message from r k δt = time since last communication check No more than once.

15 Formal Model: Acquiescence Give up when: 1) r i has worked on a task for a length of φ ij time and some other robots has taken over the task 2) r i has worked on a task for a length of λ ij time

16 ALLIANCE Formal Model (Con t.) This motivation increases at some positive rate unless one of four situations occurs.

17 Application: Mock Hazardous Waste Cleanup

18 ALLIANCE-Based Control

19 Application: Mock Hazardous Waste Cleanup Part I

20 Application: Mock Hazardous Waste Cleanup Part II

21 Application: Mock Hazardous Waste Cleanup Part III

22 Application: Adaptive Box Pushing

23 Box Pushing: Robot Control

24 Summary of ALLIANCE Fundamental focus: fault tolerance Uses motivations(based upon quality metrics) to cause robots to activate tasks Does not use negotiation Impatiencemotivation: 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 Acquiescencemotivation: Causes robot to give up its task

25 Task Allocation: Formal Analysis A Formal Analysis and Taxonomy of Task Allocation in Multi-Robot Systems, by Gerkey and Mataric, in Intl. Journal of Robotics Research, 2004.

26 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 Approaches: Intentional cooperation (ALLIANCE) Negotiation-based (CNP, MURDOCH) Emergent approaches

27 Utility (Fitness, Valuation and Cost) Assumption: each robot internally estimates the value (or the cost) of executing an action This estimation includes: Expected qualityof 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:

28 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. Timeextended assignment (TA)

29 ST-SR-IA Problems An instance of the Optimal Assignment Problem Definition: Given mrobots, nprioritized tasks, and utility estimates for each of the mnpossible 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

30 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)

31 Algorithm 2 (MURDOCH) Online assignment: 1. When a new task is introduced, assign it to the most fit robot that is currently available

32 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 timeextended schedule of tasks for each robot Problems are NP-hard

33 Algorithm (Approximation Alg.) 1. Optimally solve the initial mnassignment problem 2. Use the Greedy algorithm to assign the remaining tasks in an online fashion, as the robots become available

34 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

35 ST-MR-TA Problems This problem includes both coalition formationand 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 If coalitions are given, with no more than one coalition allowed for each task, the result in an instance of a multiprocessor scheduling problem, still NP-hard