Electronic Supplementary Material                                                                                                 

ISTC - CNR

Evolving coordinated group behaviors through maximization of mean mutual information

Valerio Sperati, Vito Trianni, Stefano Nolfi

This page contains support material of the paper "Evolving coordinated group behaviors  through maximization of mean mutual information"(2007), submitted to  "Swarm Intelligence: special issue on Swarm Robotics" .                                   

          Experimental Setup

We performed experiments both in simulation and with physical robots. In simulation, a modified version of program Evorobot is used and in reality experiments are performed with the e-Puck robotic platform. The experimental setup involves three wheeled robots situated in a square arena. This team is evolved to maximize the Mutual Information, applied to the motor states of each robot.  Teams characterized by high Mutual Information are expected to produce motor behaviours both structured and coordinated.  In this section the environment, the robot, the neural controller and the evolutionary algorithm are briefly described. For details of all parameters used see the paper.

The Environment

The environment consists of a 100x100 cm arena  surrounded by white walls. In the first experimental condition, a lightbulb is set in the middle of the arena (condition  E_l).  In the second experimental condition this light is removed, leaving the team in the darkness (condition E_d).     

 

The Robot

The robotic platform consist of three e-Puck robots. The robot, which has a diameter of 7.5 cm, is equipped with 2 motors controlling the 2 corresponding wheels, 8 red LEDs located around the robots's body, 8 infrared sensors located around the robot’s body, used both in active mode (proximity sensors), and in passive mode (ambient light sensors), a VGA camera with a field of view of 36° pointing in the direction of forward motion and a wireless Bluetooth interface which can be used to send and receive signals to and from other robots.

 

The Neural Controller

The neural controller of each robot is a fully connected perceptron, provided with 21 sensory neurons (8 infrared, 8 ambient light, 3 vision, 2 communication), and 4 motor neurons (2 wheels, 1 communication, 1 LED). All activations are in the range  [0.0, 1.0] . The input neurons are leaky integrators, that is they are characterized by  time constants.	Figure 1: a snapshot of Neural Controller

Visual and Signal Sensors Activation 

Visual Activation: the straight lines departing from robot X indicate the camera view angle, corresponding to 36º (see Fig. 2). This angle is divided in three perceptual fields, each covering  12º (V1,  V2 and V3 in clockwise order, see Fig. 1). Every receptor is sensible to the presence of another robot, provided that the latter switches on its LEDs (rendered by white circles around the robot's body). The activation of the receptor coincides with the percentage of the receptor field covered by another robot. In this example, robot Z (LEDs on) covers about 50% of robot X's receptor V3, whose activation is about 0.5. On the contrary, robot Y has the LEDs swithced off, and therefore does not activate the receptor V1. The LEDs are switched on  altogether if the activation of output neuron L (see Fig. 1), is higher than an arbitrary threshold equal to 0.9, otherwise they are switched off.  Signal Activation: a robot producing a signal is rendered with a green circle of variable size (see Fig. 2), which represents the amplitude of the emitted signal SO  (see Fig. 1): the thicker the circle, the higher is the signal value. In the above figure, robot Z is not signalling (amplitude is 0.0), robot X is signalling with amplitide 0.5, and robot Y is signalling with the maximum value (1.0). Each robot detects the average team signal through input IS, and one's own signal through input OS (see Fig. 1).

Figure 2: a snapshot of the simulation

 

The Evolutionary Algorithm

The free parameters of the neural controller - the connection weights, the biases of actuators and the time constant of leaky-integrator input neurons - have been adapted through an evolutionary robotics approach using the following parameters: 

	Population size:	100
	Number of generations:	200
	number of trials	10
	trial duration	2000 timesteps (about 200 seconds)
	Genotype:	109 genes/parameters encoded in 8 bits each
	Mutation rate:	4%
	Crossover:	not used
	Selection type:	ranking selection (best 20 are selected)
	Offspring:	5 (with elitism)
	Fitness:	higher Mutual Information applied to motor states
	Number of evolutionary runs:	20 for both experimental conditions El and Ed

Videos of evolved solutions 

 

First experimental condition  E_l: 

On 20 evolutionary runs, we obtained 18 interesting solutions characterized by high values of Mutual Information.  The stretegy adopted by the team is always the same: in order to achieve high behavioural variability and concurrent team coordination, the robots exploit the amplitude of the signal and the lightbulb in the centre of the arena (detected by ambient light sensors). The robots never use the visual information (LEDs are either switched off or never exploited). The following videos refer to evolutionary run 16, which is the best evolved solution. (to see videos of all solutions and download them, click here)

Evolutionary run 16: on left a test performed in simulation ( single random trial corresponding about to 100 seconds). On right, a test performed with physical  robots ( 5 random trials, each one lasting 200 seconds, videos speeded up to 4x). Note that the LEDs in real testing are switched on only to improve video quality.  

 

 

 

 

 

Second experimental condition  E_d: 

On 20 evolutionary runs, we obtained  11 interesting solutions characterized by high values of Mutual Information. In order to achieve high behavioural variability and concurrent team coordination, three different strategies were evolved. For each one we present a video sample (to see videos of all solutions and download them, click here).

 

 

Evolutionary run 6:  a test performed in simulation ( single random trial corresponding about to 100 seconds). Run 6 is an example of the firts strategy (obtained 7 times on 11):  robots exploit signal amplitude, visual information (LEDs are switched on and off), and sometimes infra red information. These replications are generally characterized by spatial pattern symmetry.

 

 

 

Evolutionary run 10: on left a test performed in simulation ( single random trial corresponding about to 100 seconds). On right, a test performed with physical  robots ( 1 random trial lasting 90 seconds, videos speeded up to 2x).Run 10 is an example of the second strategy (obtained 3 times on 11):  robots exploit only signal amplitude (LEDs are always switched off). These replications are not characterized by spatial pattern symmetry.

 

 

 

Evolutionary run 8: on left a test performed in simulation ( single random trial corresponding about to 100 seconds). On right, a test performed with physical  robots ( 1 random trial lasting 7 minutes, videos speeded up to 5x).Run 8 is an example of the third strategy (obtained 1 time on 11): robots exploit signal amplitude and visual information (LEDs are always switched on), but the last one is used as a source of noise (without which the robots remains steady in the same motor state). This replication is not characterized by spatial pattern symmetry.