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Intellectual Evolution Method for Synthesis of Mobile Robot Control System

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Damir Damir

on 21 June 2013

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

Intellectual Evolution Method for Synthesis of Mobile Robot Control System
Authors:
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

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

IEEE
CEC 2013

1
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