**Intellectual Evolution Method for Synthesis of Mobile Robot Control System**

**Authors:**

Diveev Askhat

Shmalko Elizaveta

Sofronova Elena

Khamadiyarov Damir

Diveev Askhat

Shmalko Elizaveta

Sofronova Elena

Khamadiyarov Damir

**Some historical facts**

**Network Operator**

The numerical example

Gracias por su atención

Michael O'Neill and

Conor Ryan, 1999

Ivan Zelinka, 2003

John Koza, 1992

Description of the object

An example of the network operator

The Network

Operator Method

Differential equations:

Genetic Programming

Method of Grammatical Evolution

Method of Analytical Programming

Network Operator Method

Askhat Diveev, 2006

**Control Synthesis**

for a Mobile Robot

for a Mobile Robot

Control constraints:

Functionals:

Terminal error:

Time length:

The set of initial values:

Control system:

Set of variables:

Set of parametrs:

Set of unary operations:

Set of binary operations:

The identity operation for unary operations

**Properties of a Network operator**

The graph has no loops

1st step

Finished

2nd step

Spark

Last step

Start

Any non source node has at least one edge from a source node

Any non sink node has at least one edge to a sink node

[X]

[Q]

Every source node corresponds to an element from the set of variables or the set of parameters

O

O

Every node corresponds to a binary operation from the set of binary operations

Every edge corresponds to a unary operation from the set of unary operations

**Rules to calculate the mathematical expression by the network operator**

a) a unary operation is performed only for the edge that comes out from the node with no incoming edges

b) the edge is deleted from the graph once the unary operation is performed

c) a binary operation in the node is performed right after the unary operation of the incoming edge is performed

Unit

element

d) the calculation is terminated when all edges are deleted from the graph

X

1

X

2

1

1

0

0

1

1

1

11

2

4

12

**An example of the network operator**

X

1

X

2

1

1

0

0

1

1

1

11

2

4

12

X

2

1

1

0

0

1

11

2

4

12

Unit

element

X

1

X

2

1

1

0

0

1

1

11

2

4

12

Unit

element

2

1

NOM is based on an

adjacency matrix of a directed graph

X

1

X

2

1

1

0

0

1

1

1

11

2

4

12

1

2

3

4

5

6

The adjacency matrix

**An example of the Network Operator Matrix (NOM)**

The Network Operator Matrix

The vector of nodes

1. Initialize, generate a set of possible solutions

2. Evaluate each possible solution by performance functions

3. Select basic solutions in accordance with Pareto-rank

4. Distribute possible solutions on different bases inversely as Pareto-rank

5. Produce new possible solutions by means of GA’s operators: selection, crossover and mutation

6. Improve the set of possible solutions by replacing bad solutions with new good possible solutions

7. Form new basic solutions as the defined number of loops are repeated

8. Check the stopping criteria that are the defined number of loops are done or the best solution for the problem is found

**The Intellectual evolution method**

The set of network operators:

Basic matrix:

Null-variation:

Set of vectors of variations:

Part of parametrs in a Gray code:

Network operator matrix:

Vector of parameters

New Pareto-set with the solutions, that have zero Pareto-rank

The basic solution

where

q

1

q

2

δ

1

2

1

1

1

0

0

0

0

10

1

1

1

1

1

1

1

1

1

1

1

2

12

6

3

4

7

8

11

16

13

5

The network operators

The network operator matrix

The network operator matrix

of the obtained solution

The obtained solution:

where

Cardinal of initial set of possible solutions: 512

Number of generations: 128

Number of crossovers in one generation: 256

Number of generations between epochs: 32

Number of basic solutions: 5

Probability of mutation: 0.7

The termination conditions are defined: Xf = 0, Yf = 0

The mobile robot starts from the given initial conditions

The robot starts from new initial conditions that differ from those used in synthesis process

Trajectory of robot motion from point to point

Simulation with initial conditions x(0)=1, y(0)=1

Simulation with initial conditions x(0)=-1, y(0)=1

The unit element for binary operations

**Additional requirements for the program notation**

Only unary operations or a digit 1 can be used as arguments of binary operations

**1**

**O**

**1**

**[n]**

**O**

**2**

**[m]**

O

2

[m]

[X]

[Q]

Q

X

i

i

or

Those unary operations, that have the same parameters or variables as arguments cannot be arguments for binary operations

Binary operations or an element from the sets of variables and parameters can be used as arguments for unary operations

**Cybernetics and mechatronics department**

Peoples’ Friendship University of Russia

Peoples’ Friendship University of Russia

**IEEE**

CEC 2013

CEC 2013

1