Drum Shape Design and Optimization Using Genetic Algorithms

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1 Drum Shape Design and Optimization Using Genetic Algorithms Team RioBotz João Luiz Almeida de Souza Ramos Marco Antônio Meggilaro, Ph.D.

2 Introduction This work regards the mechanical design and optimization of a spinning steel drum used as a combat robot weapon. Finding the best solution is not always possible or it is too complex to be found analytically. Genetic Algorithms are numerical methods inspired in the natural evolution process to find a locally optimal solution for a given problem. Team RioBotz 2

3 Design Principles There are mainly five things that need to be taken into account when designing a spinning weapon: It s inertia It s strength The number of teeth attached to it The teeth height The weapon and robots speed Team RioBotz 3

4 Design Principles The tooth bite d is the overlap between a robot weapon and the opponent before hitting it. Number of teeth Angular velocity Relative translational speed Team RioBotz 4

5 Design Principles If the weapon spins to fast or if there are to many teeth, the spinner chew out the opponent instead of grabbing it to deliver a full blow. The best solution for the greatest tooth bite is a single toothed drum. Team RioBotz 5

6 Previous Solution Team RioBotz 6

7 Previous Solution The disadvantages: High cost of Tungsten alloys Low strength of Tungsten alloys The need for attaching mechanisms, such as bolts and weld, that would make weak spots on the drum. The problem was to design a perfectly balanced drum with no need for counterweights and with the greatest tooth bite. Team RioBotz 7

8 The Genetic Algorithm The so called chromosomes contain all the characteristics of an individual and they can mutate and/or be transmitted to their heirs in the chain of evolution. They are chosen to represent each individual. In the current case, the n discrete radius of the drum-individual. Team RioBotz 8

9 The Genetic Algorithm Team RioBotz 9

10 The Genetic Algorithm To evaluate how fit an individual is, it is defined the so called fitness function, which weights all the demanded characteristics that should be minimized. The w1, w2 and w3 are user-specified weights factors that define the importance of, respectively, the tooth bite (h), the drum balancing (Cx and Cy), and its convexity (c). Team RioBotz 10

11 The Genetic Algorithm The crossover function specify how to combine two individuals, or parents, to form a crossover child for the next generation (ex: scattered, single point, two point, heuristic). Single Point crossover on bit coded individual Team RioBotz 11

12 The Genetic Algorithm The mutation function specify how to make small random changes in the individuals in the population to create mutation children (ex: uniform, Gaussian). Random bit inversion on bit coded individual Team RioBotz 12

13 The Evolution Process In order to simulate the evolution of the population, it is necessary to define the parameters: number of sides of the polygonal drum (n); maximum drum radius (Rmax); minimum value of each chromosome (Rmin); number of generations in the evolution process (N); size of the population of each generation (np); number of best individuals that are chosen to survive without any mutation (elite count, ne); crossover fraction (cf) and function; mutation function; and values of the weight factors (wi). Team RioBotz 13

14 The Evolution Process Initial population: 100 individuals of unbalanced linear spirals from 0.7 to 1. Parameter Value Drum regions (n) 18 Maximum radius (Rmax) 1 Minimum radius (Rmin) 0.75 Number of generations (N) 10,000 Number of individuals in each generation (np) 100 Elite count (ne) 5 Crossover fraction (cf) 0.7 Weight factors (w1, w2 and w3) 2, 15 and 30 Initial Individual, the linear spiral drum, have the following chromosomes for 18 sectors (19 different radius): X = [ ] Team RioBotz 14

15 The Evolution Process Team RioBotz 15

16 The Evolution Process After generations the initial random population evolved to a balanced solution. Team RioBotz 16

17 Matheck s Notch The final best individual was then later re-evaluated to include the tooth notch for optimized strength. Based on tree geometry optimization to reduce stress concetration. Team RioBotz 17

18 The Snail Drum The resulted drum was finally baptized as Snail Drum. Team RioBotz 18

19 Future Works Include the calculation of the continuous (nonpolygonal) version of the Snail Drum, with Baud s notch, even better then Matheck s. Notch based on the liquid profile flowing through an opening. Team RioBotz 19

20 Future Works Continuous Snail Drum: Like Water Coming Soon RoboGames 2013 Team RioBotz 20

21 Thank you! João Luiz Ramos Marco Antônio Meggiolaro Team RioBotz 21

Heuristic Optimisation

Heuristic Optimisation Part 10: Genetic Algorithm Basics Sándor Zoltán Németh http://web.mat.bham.ac.uk/s.z.nemeth s.nemeth@bham.ac.uk University of Birmingham S Z Németh (s.nemeth@bham.ac.uk) Heuristic