1. Optimization Of Robot Motion Planning Using Genetic AlgorithmBy
Ali Talib Oudah
University Of Baghdad/ Al-khwarizmi College Of Engineering/
Mechatronics Engineering Department

2. Abstract
Autonomous motion planning is an important area of robotics research. This type of planning relieves the human operator from the tedious job of motion planning. This reduces the possibility of human error and increase efficiency of the whole process. By conventional methods, it is difficult to decide how the robot moves from point to point in the workspace with specific requirements
Since several years, artificial intelligence played the main role to solve this type of problems which require multi-objective solution. Genetic algorithm is one of the most promising techniques for solving such large optimization problems. It is robust search and optimization strategy based on principle of natural genetics and survival of the fitness.
In this work, genetic algorithm has been used to optimize the point to point motion planning for 2-link (and 3-link) planar robot arm. The objective function is to minimize traveling time and traveling space (joint space and Cartesian space), while not exceeding a maximum pre-defined torque, without collision with any obstacle in the workspace. Quadrinomial and quintic polynomial are used to describe the segments that connect the initial, intermediate and final point in joint space.
Verification case study has been executed for 2-link robot arm to move from point-to-point in free workspace. It has been found that there was a large decrement in the amount of total traveling time (71.32%) and a little decrement in the amount of the Cartesian trajectory length (3.03%), but there was (28.6%) increment in the amount of the total joint traveling distance. The amount of traveling time decrement is more than the amount of joint traveling distance increment. Therefore, the result of the new proposed approach is satisfied.
The proposed multi-objective optimization using GA has been tested successfully to generate point to point motion planning for 2 and 3 link robot arm with existence and absence of obstacles in the workspace.

3. Aims Of The Research
Point to point motion planning has been tested for 2 and 3-link robot using quadrinomial and quintic polynomial as motion planning strategy.
The motion planning has been optimized by genetic algorithm. The objective functions used are these minimizing traveling time and traveling space (joint space and Cartesian space), while not exceeding a maximum pre-defined torque. New criteria indices have been proposed for the GA fitness function
Testing the ability of the proposed optimization process to make the robot to avoid the obstacle collision as well as performing the other objective functions for motion planning process.

4. Motion Planning Strategy
The supposed point to point trajectory is connected (for each robot joint) by two segments with continuous acceleration at the intermediate via point. the intermediate point can be given as a particular point that should be passed through.
intermediate point
quintic polynomial
quadrinomial
final point
Initial point

5. Motion Planning Strategy (contd.)
So:
&
Should be given.
Initial point
final point
intermediate point
&
Can be optimized.
Can be determined using
the above parameters.

6. Genetic Algorithm As Optimization Tool
Genetic algorithm: is a search and an optimization technique based on Darwin’s Principle of Natural Selection and survival of the fittest.
Genetic algorithm maintains a population of structure with following main operators during each generation:
Selection
Crossover
mutation

7. GA Operators And Parameters

8. 1.Encoding
The process of representation the solution in the form of a string that conveys the necessary information.
Just as in a chromosome, each gene controls a particular characteristics of the individual, similarly, each bit in the string represents a characteristic of the solution.
Real number coding has been proposed, in which each variable being optimized is represented as a conventional floating-point number as shown below:
Chromosome
1.235  5.323  0.454  2.321  2.402

9. 2. Fitness Function
A fitness function quantifies the optimality of a solution (chromosome) so that the particular solution may be ranked against all the other solution.
A fitness value is assigned to each solution depending on how close it actually is to solving the problem.

10. 3.Selection
Each current string in the population has a slot assigned to it which is in proportion to it’s fitness.
Strings that are fitter are assigned a larger slot and hence have a better chance of appearing in the new population.
5-tournament selection has been proposed in this work.

11. 4.Crossover
It is the process in which two chromosomes (string) combine their genetic material (bits) to produce a new offspring which possesses both their characteristics.
Two strings are picked from the mating pool at random to crossover.
Crossover probability (pc): determine how often the chromosome will be crossover.
Then, the number of crossover chromosome at each generation = pc*population size
Single point crossover has been proposed in this work.

12. 5.Mutation
Is the process by which a string is deliberately changed with specific criteria so as to maintain diversity in the population set.
mutation probability pm: determines how often the part of chromosome will be mutated.
Then, the number of mutated genes at each generation=pm*population size*chromosome length

13. The GA Motion Planning Scheme
The GA planning scheme renders an optimized trajectory having:
Minimum space (Joint & Cartesian).
Minimum time.
Not exceeding a maximum pre-defined joint torque.
Without colliding with any obstacle in the workspace.
The motion planning adopts direct kinematics to avoid singularity problems. The trajectory parameters are encoded directly, using real codification as chromosome to be used by GA.

14. The GA Motion Planning Scheme For 2-link Robot
=?,?
=?,?
=0,0
=0,0
=0,0
=?,?
=0,0
So:
chromosome

15. The GA Motion Planning Scheme For 3-link Robot
=?,?,? =?
=?,?,?
=0,0,0
=0,0,0
=0,0,0
=?,?
=0,0,0
So:
chromosome

16. Case Studies One verification case study.
Three case studies for 2-link robot (for both free and obstacle existence workspace).
Three case studies for 3-link redundant robot (for both free and obstacle existence workspace).

17. Verification Case Study
The proposed work is compared with the work proposed with another approach. The total trajectory traveling distance, total Cartesian trajectory length, and total traveling time have been computed to make a comparison and verify the efficiency of the new proposed work, as figure below:
The parameter
Intermediate configurations method[30]
Polynomial method
Percentage change
Joint traveling
distance (rad)
2.01
2.585
Cartesian trajectory length (m)
2.94
2.851
-3.027
Total traveling
time (s) 9
2.581

18. Case Study For 3-link Robot Motion
This case consist on moving 3-link robot
Starting point
Final point
With obstacle position

19. Case Study Demo

20. Case Study Results Motion planning in obstacle existence workspace
Motion planning in Free workspace

21. Conclusions:
Since the proposed motion planning is based on the joint space, the total traveling time depends only on the joint traveling distance.
Kinematics redundancy for the final configuration was considered as a motion planning variable.
The joint torque of the robot did not exceed its maximum pre-defined torque in both free and obstacle existence workspace case.
Obstacle avoidance objective function has been achieved efficiently by the proposed GA.
The proposed fitness function of the GA resulted in an economic execution time when used in motion planning.