Simulation of Obstacle Avoiding Autonomous Robots Controlled by Neuro-Evolution

Wolfgang Wagner


Lots of research is currently being done in the development of control systems for autonomous robots [Links]. The basic capability of these robots is to walk around in an unknown environment and to fulfil various tasks (e.g. avoiding obstacles) without the presence of any human remote control. They could be used in different fields, like acting in dangerous environments, cleaning waste pipes, exploring other planets and many more.
It is easy for human beings or even insects to act autonomously in known or unknown environments, but for computer controlled robots it is still a great challenge. Although the requirements are easy to define the capability of reacting to unexpected situations requires complex algorithms and data structures.
One way to implement client control systems is to take living creatures as a model and to use neural nets (NNs) like our brain. Artificial neural nets (ANNs) have already proved to be a useful and flexible mechanism for controlling different kinds of technical devices [Ri94]. But knowing their structure, and the capability of simulating their behavior on a computer is not enough. Like in real life they have to learn in order to solve  problems. Although the way how living creatures (or in fact their brains) learn has not been completely investigated, several learning strategies for ANNs have already been developed. One of these strategies is neuro-evolution (NE) . It uses the evolutionary algorithm that was developed from the results of the exploration of natural evolution and applies it to ANNs. Although the combination of NNs and evolution does not exist in nature, it has already been proved to be a useful learning strategy for ANNs.
The following paper describes a computer simulation that allows one to verify that NE can be used for the breeding of control systems of autonomous robots.

Just to be Precise

In the following chapters the expression 'robot' is used whenever the robot's control system is meant; just like in every days life we don't speak about someone's brain if we mean someone. In the chapter about the genetic algorithm the term robot is replaced by creature because it better matches the other terms concerning genetic evolution.
robot's control system <- robot <- creature.

The Simulation

In order to test the capability of NE for the development of robot's control systems, simulated robots and a simulated environment in which they can move around have to be defined. The environment has to be somehow hostile for robots in order to be able to distinguish between good and bad adapted behavior.
Two tasks have been defined that our (simulated) robots have to meet. They have to: These two demands force the robots to take decisions in different situations depending on their current local environment. The capability to take the right decision at the right moment is the fitness of the robot.
In order for robots to react to their environment some kind of sensor interface has to be defined that gives a picture of the local environment.
These sensors are defined by the following rules:
The robot can distinguish between other robots and obstacles. It can determine the distance of each of these objects within a certain scope. Objects which are out of scope cannot be recognized. The local environment of robots is divided into octants. In each of these octants the number of other robots is counted and weighted by the distance of the particular object. The same is done for obstacles. This leads to a vector of 16 values, which represents the distribution of robots and obstacles around a robot.

In addition to the sensors, there has to be an effectors interface that allows one to control the movements of the robots. This interface is composed of the steer heading of the robot and of its velocity. The steer heading can be set to a value between 0 and 7 where 0 means 0 o, 1 means 45 o, 2 means 90o , ... 7 means 315o. The velocity can be set between 0 and a maximum value of 50 pixels per simulation step. Any value within this range can be chosen, independent of the current value.
With the definition of the sensor - and the effector interface we can imagine a control system (that does not necessarily have to be an ANN) which guides the movements of a robot according to the values of the sensor interface.

The Genetic Algorithm

Genetic algorithms can be seen as search algorithms that can be used to find nearly optimal solutions in arbitrarily formed search spaces. In natural genetics this search space is the set of all combinations of DNA strings of a certain species. An optimal DNA string (genotype) is one that creates fit creatures (phenotypes). In order to ascertain which pheno- or genotype is fitter than others, they have to be comparable in a certain way. In real life they are compared by the capability of their phenotypes to survive and to propagate. Creatures well adapted to their environment will live longer and will by that have a greater chance of meeting partners than poorly adapted ones. If two creatures meet each other they can propagate, where the genotype of the children by crossing over the parents genes.
Applying repeated crossover to a final population creates relatively identical genotypes in a short period of time. This would be the end of progress for the evolutionary process, and even worse; a population like this would loose the ability to adapt to a changing environment. To always ensure a certain variance of behavior inside a population there has to be a mechanism to change the genotype randomly. Variance is introduced through gene mutation.
The above described rules lead to the simple genetic algorithm [Go89 ] witch consists of three key operations. These general rules where implemented in our simulation in the following way: To start the genetic algorithm we have to generate a hostile environment for our creatures. This is done by adding obstacles that walk around controlled by a random walk algorithm. Then the simulation is initialized with a certain amount of creatures. As the parameters for these "first generation creatures" are random values, the result is a kind of random walk. Whenever one of them touches an obstacle it dies immediately. These conditions result in a population of very quickly dying creatures. If the number of creatures is less than a minimum, new "random creatures" are generated. For a certain amount of time the simulation remains in the state of just generating "random creatures" which don't show any sensible. If a creature shows by chance an environmentally adapted allowing it to survive long enough, and if at the same time another one fulfils the same preconditions and if those two manage to come somehow close together, the first crossover takes place. E.g. the first child of the simulation is born.
This "birth" means that one or more (twins) new creatures are created whose control systems are generated by applying the crossover and mutation operation on the parents genotypes. If the creatures, generated by the genetic operation, show the same, or an even better adaptation to their environment as their parents, they also have the chance to produce children in the same way as their parents did.
This creates a population of well behaving creatures after a relatively short time. The number of creatures would explode if it was not limited by an upper limit. If this limit is exceeded the whole population gets temporarily infertile. Two creatures meet in this infertile period don't get children even if all necessary conditions are fulfilled. If a creature survives for a maximum time it dies because of old age. This natural death lowers the population size and after a while the creatures get fertile again.
Whenever a child is born, the mutation operation is applied to its genotype. No mutation takes place during the lifetime of creatures.

The Artificial Neuronal Network (ANN)

In the above chapters the phenotype of creatures/robots was often mentioned without an explanation of what this phenotype should be. One possible implementation is with the use of an ANN. It has already been demonstrated that they have the capability of controlling mobile robots [Links].
For this project a feed forward net with 4 layers was chosen. The input layer consists of 16 and the output layer of 8 neurons. The in-between layers have 11 and 13 neurons. Every neuron, except the neurons of the input layer, is connected with every neuron of the previous layer with one weighted connection. The structure of the connections is fixed. The only parameters that can be varied are the weights of the connections.

The Neurons

The net is built from neurons which are represented by a simple mathematically model [Ri94]. Every neuron has an integer value representing the degree of stimulation. This integer value can be in the interval (-a, a) where 'a' has the value of 1000. Every connection between neurons contains a weight also represented by an integer out of the interval (-b,  b) without 0. The value of 'b' is 100 in our net. The value of a neuron is calculated in the following way: Given that the values of the preceding neurons are calculated, the values of the input neurons are then preprocessed by applying the weights of the corresponding synaptic connections using the formula:
v1 = v0 DIV w
v1 ... pre-processed value
v0 ... value of the preceding neuron
w  ... weight of the synaptic connection
Beware that using the DIV function results in a highly non-linear behavior when forwarding activation to succeeding layers. It seems as if this non-linearity has no negative consequences on the behavior of the net. If ratio of the maximum value of weights (b) to the maximum value of stimulation (a) is too large, we easily get into the situation where all values get pre-processed to zero. The ratio of 100 to 1000 seems to be a good assumption for our net. These pre-processed values are then summarized and evaluated by the so called transfer function.
vs = T (SUM (v11 ... v1n))
v1i ... Pre-processed values of the synaptic connections
T   ... Transfer function
As a transfer function the sigmoid function was chosen
v = a * (2 / (1 + EXP (-vs * s)) - 1)
a ... maximum value of stimulation
vs ... sum of pre-processed values
s  ... constant stretch factor of the sigmoid function (0.01 in our net)

Genetic Operations on ANNs

When working with ANNs to control our robots and using a genetic algorithm to search for a nearly optimal control system, we have to define how to apply the basic genetic operations (selection, crossover and mutation) to the ANN. Selection does not have to be defined for ANNs separately, as it is independent of the control system. Crossover and Mutation are dependant on the structure of the control system.


In nature, crossover is applied to (two) DNA strings each of which represents a code containing all the properties of the corresponding creature. The result is a new code from which a new creature is formed that has to prove its fitness in its environment. Applying crossover to ANNs means finding a code which contains the values of all parameters of the ANN so that we can apply the crossover operation on it. The parameters of our ANN are its weights since we have defined the structure to be constant. One possible representation of the above mentioned code is a binary string. Mapping the weights to a binary string is easy as the values are already integer values. Defining an order to the weights and concatenating the binary represented integer values generates automatically a binary string.

If you have (two) binary strings, created by the above mentioned mapping algorithm the crossover operation can be applied to them to create a new string from which a new ANN can be generated later. You start with one of the parent strings and copy it to the child string. After a random number of bits you switch to the other parent and so on.  As the structure of the ANNs is always the same they also have the same number of weights and their strings always have the same length. To speed up the crossover process, crossover points are only allowed at the border of weights. The consequence of this is that the binary string does not really have to be created. The child net's weights can be created from the weights of its parent by just iterating through the weights of the parents nets in the above described order.



Mutation in conventional genetic algorithms, based on binary strings, is implemented by iterating all bits and switching the value of each by chance. The probability of changing one bit is called the mutation rate. Taking the above mentioned mapping from ANNs to binary string in consideration, changing of randomly chosen bits would lead to random changes of the values of weights. If we presume that the mutation rate is small, mutation will mostly result in changing one bit in some weights. Changing one bit in a value represented by an eight bit integer number can have a very small or a very large impact depending on what bit was changed. Almost the same effect can be achieved by simply setting the values of the effected weights to a random value. So, the mutation rate in our case is defined as the probability of changing a weight to a random value.


The above described algorithm was implemented as a computer program in OberonII [Links]. In this implementation the robots where called Nepros. The name was derived from Repros as they have the capability of reproduction. As Repros are controlled by neuronal nets the name was changed to Nepros.
The application includes a graphical user interface where the movements of Nepros and obstacles can be easily observed. This visually shows how the initial random walk of Nepros is turned into a controlled obstacle avoiding behavior.
In order to qualify the results of the learning process a parameter has to be defined that can be easily observed. There are two ways in which Nepros can die. They may be destroyed by touching an obstacle, or they die because of exceeding a certain age. We might call these two kinds of death; violent and natural death. Many creatures dying violently indicate a badly adapted population whereas many natural deaths indicate a well adapted population. Counting the total number of deaths in a certain period of time in relation to the number of violent deaths in the same period defines the killrate.
k = v / (v + n)
k ... Kill rate
v ... Violent deaths in p
n ... Natural deaths in p
Exploring the kill rate for a typical simulation results in the following diagrams.

Three phases can be observed. The first phase is the random phase. This means that the current population consists mainly of creatures which randomly generated nets. They are usually very badly adapted and die quickly. The kill rate of this phase is almost 100%. In the above diagram the random phase lasts for about the first 500 steps of the simulation. If by chance, two of the randomly created creatures have the capability to survive long enough, the learning phase is entered. In the learning phase almost no more random creatures are produced. New creatures are the result of the above described genetic algorithm. The learning phase in the above diagram continues from step 500 to about step 5000. I presume that in the learning phase crossover is the most important operation for the development of the nets. The so called stable phase follows the learning phase. In this phase the population has reached its maximum fitness. In our example simulation the kill rate fluctuates between 60% and 30%. The final kill rate does not say a lot about the absolute fitness of Nepros as it is strongly dependant on the density of obstacles. In this phase it is probably mutation that causes the oscillation of the kill rate. Even if you simulate for a long time, the fitness of creatures never gets much better than after the learning phase. The following diagram shows the same simulation as the one above but on a different time scale.


Future Work

The exploration of the above described algorithms and its simulation lead to various questions that could be answered by exploring the results in more detail or by adding new concepts.
One interesting parameter of evolution is the genetic diversity within the population. At the moment I can only guess that the diversity is high in the random phase, decreasing in the learning phase and small in the stable phase. After exploring the diversity it would be interesting to explore how the diversity could be influenced and what effects could be produced by artificially increasing it. Two or more populations could develop independent of each other. Mixing these populations after a while could result in fitter creatures.
Another interesting field of research could be the ANN itself. In our simulation the most simple net was used. It can only react to the current state of the simulation but does not know anything of the past. So it cannot make any assumptions about the movements of other objects. The easiest extension would be to not only feed the current state of the environment into a creatures net, but to somehow remembered previous states and feed these together with the current state into the net. This would give the net the possibility of interpolating from the past to the future and, by this means (perhaps) react in a better way.
How would recurrent nets behave in our simulation?
What if the genetic algorithm not only changes the weights of the neurons but also optimizes the topology of the net?
Another nice idea would be to also add "intelligence" to obstacles. This would extend the simulation to a predator-prey behavior.
I am sure that anyone who tries fiddling with the simulation (changing parameters and watching what happens) would find lots of open questions or come up with ideas that would be worthwhile answering or trying out. But who has the time.


The implementation of the above described algorithm has proved that neuro-evolution using the above described GA and ANN leads to creatures / robots that adapt to their environment in a very short time. The behavior is not excellent in the since that robots do not avoid obstacles 100% of the time, but it generates stable populations that can survive for a long time.
It seems as if the genetic algorithm does not optimize the individual creatures / robots but rather searches for an optimal population. Like in real life, this optimal population does not consist of a collection of optimal individuals.


[Ri94] Rigoll Gerhard; Neuronale Netze. Eine Einführung für Ingeneure; Informatiker und Naturwissenschaftler; Renninger-Malmsheim: Expert-Verlag 1994.

[Go89] Goldberg; Genetic Algorithms in Search Optimization and Machine Learning; Addison-Wesley._


The Nepros Homepage
Neural Nets Research Groups
The Oberon Homepage (V4)

Thanks to

Ed and Walter who helped me a lot with this article.