Antoine Ligot^{1},
Jonas Kuckling^{1},
Darko Bozhinoski^{1},
Mauro Birattari^{1} (December 2018)
^{1}IRIDIA, Université Libre de Bruxelles, Brussels, Belgium
Table of Contents |
In this page, you will find supplementary information about the three studies conducted. In the following, Sections 1, 2, and 3 are dedicated to Study 1, 2, and 3, respectively.
All the results obtained in the three studies are available for download here.
The source code used to generate the control software are available here: Maple, Chocolate, EvoStick
You can import them in R using read.csv("resultsAll.csv"). In these Sections you will find videos of robot experiments, images of the instances of control software generated by the design methods, and p-values tables. In Section 4, we illustrate the two instances of dummy control software. In Section 5, we illustrate behavior trees and finite-state machines that encodes an elaborate strategy for the Foraging mission.
In a p-values table, we report the p-values resulting of the assessment of Wilcoxon rank-sum tests in the left-hand part (all the cells (i, j) with j < i), and the corresponding relation between the two variables compared in th e right-hand part (that is, all the cells (i, j) with i < j). In some cases, the comparison between performances are not meaningfull: for example, comparing performance of two different design methods, one assessed in simulation, and the other one in reality. In these cases, we did not apply the Wilcoxon rank-sum test, and the corresponding cells contains the characters "NA". In the right-hand part, a cell can be empty, or have one of the following character: ">" or "<". If a cell (i, j) with i < j is empty, the corresponding p-value in cell (j, i) is greater than 0.05. If a cell (i, j) with i < j contains the character ">", the p-value in cell (j, i) is less than 0.05, and the variable of the i-th row is significantly greater than the variable of the j-th column. Similarly, if a cell (i, j) with i < j contains the character "<", the p-value in cell (j, i) is less than 0.05, and the variable of the i-th raw is significantly smaller than the variable of the j-th column. For example, in the p-values table of Study 1: Foraging, the cell (1, 2) contains ">", which means that the performance of Maple in simulation is significantly greater than the one of Maple in reality. Indeed, the corresponding p-value, reported in cell (2, 1), is equal to 4.66e-02, which is smaller than 0.05.
The arena contains two source areas (black circles) and a nest (white area). A light is placed behind the nest to help the robots to navigate. In this idealized version of foraging, a robot is deemed to retrieve an object when it enters a source and then the nest. The goal of the swarm is to retrieve as many objects as possible.
Examples of experimental runs with robots, and examples of typical instances of control software, are displayed below. All videas and images of the control software are available for download: videos and control software.
AutoMoDe-Maple |
AutoMoDe-Chocolate |
EvoStick |
AutoMoDe-Maple |
AutoMoDe-Chocolate |
P-values table |
The swarm must select one of the two black areas and aggregate there. The objective function is computed at the end of the experimental run, and is maximized when all robots are either on the left or the right area.
Examples of experimental runs with robots, and examples of typical instances of control software, are displaye d below. All videas and images of the control software are available for download: videos and control software.
AutoMoDe-Maple |
AutoMoDe-Chocolate |
EvoStick |
AutoMoDe-Maple |
AutoMoDe-Chocolate |
P-values table |
In a p-values table, we report the p-values resulting of the assessment of Wilcoxon rank-sum tests in the left-hand part (all the cells (i, j) with j < i), and the corresponding relation between the two variables compared in the right-hand part (that is, all the cells (i, j) with i < j). In the right-hand part, a cell can be empty, or have one of the following character: ">" or "<". If a cell (i, j) with i < j is empty, the corresponding p-value in cell (j, i) is greater than 0.05. If a cell (i, j) with i < j contains the character ">", the p-value in cell (j, i) is less than 0.05, and the variable of the i-th row is significantly greater than the variable of the j-th column. Similarly, if a cell (i, j) with i < j contains the character "<", the p-value in cell (j, i) is less than 0.05, and the variable of the i-th raw is significantly smaller than the variable of the j-th column. For example, in the p-values table of Foraging, the cell (4, 5) contains "<", which means that Chocolate-1k is significantly worse thant Maple-5k. Indeed, the corresponding p-value, reported in cell (5, 4), is equal to 2.65e-03, which is smaller than 0.05.
P-values table Foraging |
P-values table Aggregation |
Variant →*(→) |
Variant ?*(?) |
Variant →(?) |
Variant ?*(→) |
Variant →*(→|?) |
Variant ?*(→|?) |
Variant FL (free leaves) |
Variant ND (negation decorator) |
P-values table Foraging |
P-values table Aggregation |
Foraging |
Aggregation |
Illustrations of behavior trees and finite-state machines that encodes the following individual behavior: the robot explores the gray area to find the food sources. Once a food source is found, the robot goes towards the light placed behind the nest using the phototaxis low-level behavior. If the robot enters the nest, it directly leaves it using the anti-phototaxis low-level behavior.
In the illustrations of behavior trees, the parameter p is the success probability (the probability that an action node return success). In Maple and all other variants with the exception of SP, the success probability is fixed to 0.
Finite-state machine |
Behavior tree variant ND (negation decorator) |
Behavior tree variant CFN (control-flow node) |