Modeling of task planning for multirobot system is developed from two parts: task decomposition and task allocation. In the part of task decomposition, the conditions and processes of decomposition are elaborated. In the part of task allocation, the collaboration strategy, the framework of reputation mechanism, and three types of reputations are defined in detail, which include robot individual reputation, robot group reputation, and robot direct reputation. A time calibration function and a group calibration function are designed to improve the effectiveness of the proposed method and proved that they have the characteristics of time attenuation, historical experience related, and newly joined robot reward. Tasks attempt to be assigned to the robot with higher overall reputation, which can help to increase the success rate of the mandate implementation, thereby reducing the time of task recovery and redistribution. Player/Stage is used as the simulation platform, and three biped-robots are established as the experimental apparatus. The experimental results of task planning are compared with the other allocation methods. Simulation and experiment results illustrate the effectiveness of the proposed method for multi-robot collaboration system.
The field of distributed robotics started in the late 1980s, when several researchers began investigating issues in multiple mobile robot systems. Prior to this time, researches had concentrated on either single robot systems or distributed problem-solving systems that did not involve robotic components [
In recent years, multirobot systems research has made great progress in many areas [
Collaboration is an important characteristic and a major evaluation indicator for multirobot systems [
Task planning includes two aspects [
In the task decomposition and distribution research, there are several traditional methods: Contract Net Mechanism [
The traditional task allocation is mainly based on contract net protocol (CNP) [
Gerkey applied the market algorithm in multirobot system to deal with dynamic task allocation problem named MURDOCH [
However, the task allocation methods have their limitations to some extent. Behavior-based task allocation mechanism does not take into account the influence of collaboration history, while market-mechanism-based task allocation does not fully consider the impact of the time factor, leading to poor robustness.
In addition, the topics of multirobot search and rescue, cooperative localization, motion coordination, and formation control attract a lot of researchers in the fields of robot collaboration system [
In this paper, a task planning method based on reputation mechanism is proposed. Reputation plays an important role in the collaboration among people. In many cases, task allocation is based on someone’s reputation, which is gained from the evaluation of the completion of historical tasks. Reputation theory is attracting interest from industrial and academic research communities and increasingly being integrated with online services and applications, especially in network computing system.
Reputation of robots is the overall assessment and the summary of past actions observed from one robot to another through the gradual dynamic capabilities in a continuous interactive process. The assessment can be used to guide further actions of the robot. Reputation includes five attributes:
The rest of the paper is organized into four sections as follows: the system structure and basic concepts are presented in Section
Task planning consists of two parts: decomposition and allocation. Task allocation in the multirobot system is divided into two categories: direct allocation and delegation allocation. Direct allocation is to assign a task to robot that can provide collaboration directly. If the robot cannot complete the assigned task, the assigned task can be delegated to other robots. The task can be further delegated if needed.
The periodical constraint is utilized to guarantee the time effectiveness of task allocation. (
Robot collaboration system.
In Figure
In the robot reputation system, robot reputation level (RRL) is proposed to quantify the reputation of each robot, which is based on the historical experience and the overall evaluation of the system. “0” and “1” are used to quantize the reputation value. “0” represents the lowest reputation and “1” represents the highest reputation. The symbol of robots group is indicated as
Reputation of the robot collaboration system.
In Figure
In this section, task planning is divided into two parts: task decomposition and task allocation. Firstly, the condition and process of the task decomposition are presented. Secondly, task allocation using reputation mechanism is defined and presented in detail.
A task can be decomposed if it meets certain conditions. Four task decomposition conditions are given in [
An automata is a tuple
The parallel composition of
The natural projections of
Formal linear temporal logic language is used to present the whole tasks of the robot system, which is almost the same with the natural language in structure.
Several temporal operators of task decomposition are presented as follows [ next state “ until “ eventually “ always “
The reachability while avoiding some events: Sequence: Coverage: Recurrence:
The equivalent task automata
The negotiation process of the robot collaboration system is presented, which mainly is concerned about how to build partnerships between the collaborative robots according to the reputation mechanism.
The robot initialization set
A collaboration strategy is defined as a quintuple
Giving that
Giving that
Giving that
Giving that
If the cooperative system is composed by
Giving that
If the robot does not take any assigned task, its reputation will diminish as the time went on. The coefficients is satisfied with
The curve, when
Giving that
If
Typical group parameters.
Loyalty | Honesty | Improvement | Randomization | |
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0–0.1 | 0.1–0.2 | 0.2–0.3 | 0.4–0.6 |
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0.9–0.99 | 0.8–0.9 | 0.7–0.8 | 0.5–0.7 |
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||||
Concealment | Tricky | Corruption | Deceivement | |
|
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0.6–0.7 | 0.7–0.8 | 0.8–0.9 | 0.9–0.99 |
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0.4–0.5 | 0.2–0.3 | 0.1–0.2 | 0–0.1 |
Many simulation platforms can be used for multirobot systems [
Three robots
Robot
However, if
Task automata.
The assigned task is to push the boxes to area 3. The local event set of each robot is presented as follows:
Checking that the decomposition conditions
DTM presents the direct reputation relationships among robots. Three robots in the collaboration system named from
The reputation in the matrix is updated after each step of the collaboration. Box moving is simulated by the approach, shown in Figure
Simulation process of the approach.
Initialization
Taking the assignment
Pushing boxes
Waiting for next assignment
Two typical allocation algorithms are used to make contrast and evaluate the performance of the proposed method, which are sequence allocation and auction allocation. The simulation has seven robots in area 1 and 14 boxes in area 2, without obstacles between them.
In the case of the sequence allocations, the results of
The simulation of sequence allocation.
Initialization
Taking the assignments
Pushing boxes
Completing assignment
In the case of the auction allocation, the bidding is lauched at the beginning by the auctioneer. The best bid is picked out by the predetermined standard. The task will be assigned to the winner of the auction. The winner of the auction is chosen by the auctioneer giving the highest bid.
The bid matrix is used to store the value of robot biding for each assignment. A typical bid matrix in the simulation is presented as
The tasks are performed in the following sequence:
Simulation of auction allocation.
Initialization
Taking the assignment
Pushing boxes
Completing the assignment
In the case of the task allocation by reputation, the initial reputation value of the system is the following matrix:
The value of DRM is updated after each process of collaboration. If successfully finished the assigned task, the value of direct reputation between the robots increases by 0.01, otherwise reduces 0.05. In the simulation process, if the assigned task failed, the moving trajectory of the robot is the same to facilitate the performance comparison. The process of performing tasks is shown in Figure
Process of task allocation by reputation.
Every experiment is simulated six times to get a reasonable performance assessment. The ultimate results are the arithmetic average of the six times.
The order allocation needs about 635.71
Comparison of the three allocation method.
The biped-robot apparatus are utilized as the experimental platform. The shape parameters of the robot are with upright height 33.3 cm, width 9.9 cm, arm length 15.9 cm, arms stretched flat horizontal length 41.7 cm, upper high 13.9 cm, waist high 19.4 cm, and weight 1 kg, as shown in Figure
Biped-robot experimental apparatus.
The wireless sensor module is used to send and receive commands, which are coded as the standard serial data and sent to the assigned robot. The effective transmission distance is about 30 m. The experimental parameters of task allocation are shown in Table
The experimental parameters.
Parameters | Value |
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|
|
|
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own | 0 |
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0.6, 0.5 |
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1/3, 1/3, 1/3 |
Four task allocation methods are engaged to evaluate the efficiency. In addition to the proposed method, the other three methods are random allocation, order distribution, and simultaneous allocation.
A nonnumbered box with the size 8 cm3 is arranged to be moved to the destination. The moving distance is set to be 0.6 m. After receiving the task assignment, the robot moves to the side of the box, pick it up, move it, and put it down at the destination. The processes of picking up and putting down are done manually; other actions are done automatically.
For the case of task allocation using order distribution algorithm, the results of
For the case of task allocation using random distribution, the random number set
The tasks numbered
Comparison of small number of arranged tasks.
With the number of tasks increasing to
Comparison of medium number of tasks.
According to the practical application, the robots with relatively high-speed capability are allocated more tasks and the efficiency of the task allocation by reputation is 4.35% higher than the second high method.
When the number of tasks continues to increase to
Comparison of large number of tasks.
In the case of large number of tasks, the efficiency of task allocation by reputation is 3.57% higher than the second high method.
The experimental results show that the task allocation using reputation mechanism can effectively increase the performance and prevent a robot from a delay in the case of the individual robot failure.
Task planning is developed by two parts: task decomposition and task allocation. The processes of the task decomposition and task allocation using reputation mechanism, are presented. The robot collaboration strategy, the framework of reputation mechanism, and three reputations are defined in detail, which includes robot individual reputation, robot group reputation, and robot direct reputation. Time calibration function and group calibration function are designed to improve the effectiveness of the method, which are proved to be with characteristics of time attenuation, historical experience related, and newly joined robot reward. The success rate of collaboration is enhanced and the time of recovery and redistribution of the task are reduced.
Player/Stage is used as the simulation platform, and three biped-robots are established as the experimental apparatus. In the simulation, task decomposition is studied, and the result of task allocation is compared with the sequence and auction allocation methods. The biped-robots are used in the experiments, and four task allocation methods are engaged to evaluate the efficiency. The simulation and experimental results show that the approach can provide an effective performance for multirobot system.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is jointly supported by NSFC under Grant no. 60903067, Beijing Natural Science Foundation under Grant no. 4122049, Funding Project for Beijing Excellent Talents Training under Grant no. 2011D009006000004, and Beijing Higher Education Young Elite Teacher, and the Fundamental Research Funds for the Central Universities (FRF-JX-12-002, FRF-TP-12-083A).