PRELIMINARY DES IGN OF ONBOARD GUIDANCE S YS TEM US ING DYNAMICALLY DISTRIBUTED GENETIC ALGORITHM FOR EXPERIMENTAL WINGED ROCKET

Masatomo Ichige, Koichi Yonemoto and Takahiro Fujikawa. Department of Mechanical and Control Engineering, Kyushu Institute of Technology, Japan. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History Received: 09 August 2018 Final Accepted: 11 September 2018 Published: October 2018

The authors have been developing the guidance system of winged rocket using dynamically distributed genetic algorithm (DynDGA) for trajectory optimization. DynDGA is an advanced genetic algorithm (GA) wh ich can enhance the variety of trajectories and maintain the trajectory search performance. However, DynDGA requires higher computing power. One of the simple solution for this problem is to reduce the number of individuals and generations, but it also degrades the solution search capability. For the imp lementation, authors need to make a tradeoff between these problems. Evolutionary algorith ms (EAs) have proven successful in a vast number of static applicat ions and the number of papers produced in this area is growing rapidly. However, they also seem to be particularly suitable for dynamic and stochastic optimizat ion problems such as natural selection. The authors performed some simu lations, and the results succeeded to reach the target point. However, at some initial conditions, the simulat ion could not reach near the target point. This paper describes the simu lation results of DynDGA onboard guidance system for experimental winged rocket in dynamic environ ment. The authors have been developing the guidance system using dynamically distributed genetic algorith m (DynDGA 2) ) for trajectory optimization. DynDGA is an advanced genetic algorithm (GA) which can enhance the variety of trajectories and maintain the trajectory search performance. The advantage of adapting DynDGA is obtaining no ndivergent solutions, compared with conventional studies such as SQP methods 3) and numerical methods. From the past studies, the basic algorithm for guidance using DynDGA has been developed. As a next step, the authors have been developing the guidance s ystem for real time implementation. This paper describes the simulat ion results of DynDGA onboard guidance system for experimental winged rocket in dynamic environment.
Dynamically Distributed Genetic Algori thm:-GA is a search heuristic algorith m that imitates the process of natural selection. Figure 2 shows the flowchart of GA. At first, GA creates an initial individual group and calculates their fitness. Fitness is the measure of how well the individual is fitted to the conditions. Next, the GA selects two individuals and their crossover is performed. Finally, GA calculates the individuals' fitness which are generated by the crossover, and selects the individuals that survive to the next generation. Mutation is a process to change the gene values at random with a rate. It makes to escape fro m the local solution. This procedure is repeated many times, and the optimal result is obtained.

Figure2:-Flo wchart of GA
An important feature of this search methodology is the diversity of indiv iduals. In a normal search for an optimal solution, searching is fallen into a local solution. In this situation, escape from the local solution may be achieved by using mutation or the distributed genetic algorith m (DGA 4) ). Figure 3 shows the schematic illustration of the DGA model. Using DGA, Indiv iduals are divided into sets of populations called islands, the search of an optimal solution is conducted in each island independently. For every generation, the DGA trades individuals between islands, which is called migration. This process makes it possible to maintain the variation of individuals and to enhance the search performance. DynDGA is an extension to DGA. Figure 3 shows the model of DynDGA. In DynDGA, the population is distributed into islands based on their dissimilarity, and the number of islands changes dynamically as the optimization proceeds. Hierarchic clustering method 5) is emp loyed to distribute the population into islands. The calculation of the dissimilarity is done using the combinatorial method. Among several approaches, the Ward's method 6) is used in this simu lation. As a result of dynamic clustering, some similar islan ds are merged, and an island is divided into several islands if necessary. By repeating these procedures, some optimized flight trajectories are finally obtained in each island.

Onboard Gui dance S ystem:-Winged rocket model
Kyushu Institute of Technology has been developing reusable space transportation system called WIRES (Winged REusable Sounding rocket, as in Figure 4) since 2005. The objective of this vehicle is to reach 100km altitude and realize the sub-orbital space travel. In the return phase, this rocket glides to a target point using a fully autonomous guidance system based on DynDGA t rajectory optimization.
In this simu lation, the rocket model is a subscale experimental winged rocket called "WIRES#015". The missio n objective of this vehicle is to evaluate the real-time optimal trajectory generation using DynDGA, demonstrate the LOX-Methane propulsion system, reentry attitude control system by gas jet thrusters and recovery by two -stage parachute and airbags. Table 1   DynDGA conditi on Table 2shows the DynDGA condition. Terminat ing generation depends on simulat ion types.
where flight is trajectory length. In short, the objective function is the min imization of the summation of flight time, the difference between the target point and final point in terms of down -range, cross-range, altitude, azimuth, and the flight duration when the obstacle area is violated. However, the obstacle parameter is set to zero because the simu lation doesn't have obstacle area.
For calcu lating the fitness, the guidance system solves the differential equation of motion as in eqs. (7) -(19).
= 1000 e + err + err + obs err = 10 694   sin 2  Figure 5shows a flight area image. Table 3 shows the initial conditions of the first trajectory. Table 4shows the target conditions.  Figure 6shows the outline of simulation flow. In this paper, there are 4 simulat ion patterns. First simu lation pattern is single shot guidance. In this pattern, the guidance system generates an optimal trajectory for every 5 seconds. However, there are no inheriting data to use in the next optimization. Second pattern is continuous optimizat ion. In this pattern, the guidance system continuously generates an optimal trajectory during the simu lation, and it updates the optimal solution for every 100 generations. Third pattern is same as second pattern. In this pattern the guidance system updates the optimal solution for every 800 generations. Final pattern is also similar to second pattern. In this pattern the guidance system updates the optimal solution for every 10 generations.  Table 5 shows the outline of the simu lation results. As the interval between the output solutionsdecreased, the total simulation time also decreasedin the continuous simulation. However, the error of azimuth increases. Fro m the fitness profile, continuous simulation has better fitness than single shot simu lation.

Figure5:-Flight area
In the real time implementation, the guidance system needs to set the interval not for the off springgeneration but for calculation time. Th is is because the calculation time depends on the initial conditions. As a result, the interval time is based on the calculation time which is calculating the 100 generations .

Single shot generati on
The simu lation result is shown in Figure 7. Th is showsall the optimal trajectories produced. The symbol "*" is the initial position at which the trajectory is generated. Each trajectory could reach near the target point. Figure 8 shows the fitness value profile. Each fitness starts with a low value.

Interval of 800 generation
The simulat ion result is shown in Figure 9. Th is shows all the optimal trajectories produced. The symbol "*" is the initial position at which the trajectory is generated. Each trajectory could reach near the target point,however the final trajectory's azimuth has larger error. Figure 10 shows the fitness value profile. Each fitness value starts with a higher fitness value than single shot pattern, however each fitness value terminates with a lower fitness value than single shot pattern.

Interval of 100 generations
The simulation result is shown in Figure 11. This shows all the optimal trajectories produced. The symbol "*" is the initial position at which the trajectory is generated. Each trajectory could reach near the target point. However, the final trajectory's azimuth has larger error. Figure 12 shows the fitness value profile. Each fitness value starts with a higher fitness value than single shot pattern. The final fitness value is less than the single shot pattern. 697

Interval of 10 generati ons
The simulation result is shown in Figure 13. This shows all the optimal trajectories produced. The symbol "*" is the initial position at which the trajectory is generated. Earlier trajectory could not reach near the target point . However, final trajectory could reach near the target. Figure 14 shows the fitness value profile. Each fitness value starts with a higher value than single shot pattern. The final fitness value is less than the single shot pattern.

Conclusion:-
This paper describes the simulat ion results of DynDGA onboard guidance system for experimental winged rocket in dynamic environ ment. Fro m the results, the continuous generation type which has the interval set at 100 generation appears to be optimal than the other generation types. In future, authors continue the simulat ion for real time implementation and validate on the experimental winged rocket.