A Quick Optimization of a Rocket Trajectory Using MCMC Method.

Transcription

1 nd Annual AIAA/USU Conference on Small Satellites A Quick Optimization of a Rocket Trajectory Using MCMC Method. Masashi Miura (The Graduate Univ. for Advanced Studies.) Yohsuke Nambu (Univ. Tokyo.) Masaaki Sugimoto (ISAJ) Hajime Yokota (ISAJ) Akane Uemichi (ISAJ)

2 Introduction Next Generation Space is Convenient. Low Cost, Quick, Adaptable Micro Space Small Satellites Responsive Launchers Standardization Standard Bus Modular LV Scalable Architecture Japan is getting down to above things. Today s presentation Introducing Japanese micro space. Introducing our research concerning technical problems of air launch.

3 Japanese Micro Space Satellites 4 phases of Standardization of Satellite Network-type Satellite Architecture Availability like USB Scalable Architecture Spacewire Network SpaceCube (JAXA, NEC/TOSHIBA) Useful middleware for handling deference on CPU and I/O of hardware.

4 Japanese Micro Space Satellites Advanced Small Satellite Bus Remote Sensing Optical Sensor Remote Sensing SAR Sensor Engineering Test Astronomical Observation NeXT (New exploration X-Ray Telescope) Launched in 011 Size / W950D950H950 Weight / >300kg Payload Power / MAX 300 W Development Term / > year (after ICD fixed) Launched in 013 Weight / 400 kg To study the high-energy nonthermal Universe

5 Japanese Micro Space - Launchers 0 L- 4S M- 4S M- 3C M- 3H M- 3S M- 3SII M- V Total Length 16.5m 3.6m 0.m 3.8m 3.8m 7.8m 30.7m Diameter 0.735m 1.41m 1.41m 1.41m 1.41m 1.41m.5m Seiji Matsuda, AIAA-RS Total 9.4t 43.6t 41.6t 48.7t 48.7t 61t 139t Weight Payload to LEO 6kg 180kg 195kg 300kg 300kg 770kg 1800kg Flight year Rate (s/ l) 1/ 5 3/ 4 3/ 4 3/ 3 4/ 4 7/ 8 6/ 7

6 Technical problems of Air Launch Technical problems of air launch are Vehicle Loading and Deployment Ignition Attitude Stabilization Launch Sequence Inertia Navigation System Initialization etc Initial errors Errors of system parameters Errors by uncertainty of parachute Errors by wind Cause The ignition Attitude may be different from the nominal.

7 Solution to the problem. Hardware Solution Separation device. Control device. Advanced design. Many times experiment. etc Software Solution Trajectory optimization quickly, widely, exactly (Trajectory adjustment) with MCMC method. Real time system identification with Particle Filter. More complicated Systems New method realizes smarter systems. Classical way ex. linearization low calculation cost Improvement of calculation device. high Mathematical statistical way ex. MCMC

8 Optimization Algorithm with MCMC. MCMC Step. 1. Calculating the value of f(x). Here x is the current position.. Generating Δx using random numbers and calculating the value of f(x+ Δx) 3. Calculating the transition probability P from the values of f(x) and f(x+ Δx). 4. Moving from x to x+ Δx at the probability P x-space f(x) 1-p p f(x+δx) P ( x, x + Δ x ) β = 1 n N T 0 T r = 1 e f ( x ) β ( 1) f ( x + Δ x ) 1 [ [ f ( x ) > f ( x ] + Δ x ) f ( x ) β ( 1) f ( x + Δ x ) 1 f ( x ) < f ( x + Δ x ) e ] Searching algorithm in high dimensional space. Useful for multivariate optimization. Able to apply to nonlinear systems.

9 Trajectory Optimization with MCMC. f(x) = f(θ 1, θ,, θ n ; θ 0 ) The objective function target value θ i : Attitude target at each node. θ 0 : Attitude angle at ignition. f h f ( x ) = + f 1000 ( 7 γ ) h f : final altitude γ f : final attitude angle Result after the 17 th step. f(x 17 ) = 0.09 h f = [m] γ f = 6.9 [deg]

10 Motion estimation with Particle Filter To identify system parameters and predict the motion of the rocket exactly at real time with Particle Filter Estimated motion at 3sec after separation. Particle filter corresponds to real time parallel MCMC method.

11 Conclusion Problems specific to Air Launch Attitude unstableness after separation. Ignition attitude error. Trajectory optimization with MCMC Method. Motion estimation with Particle Filter. Software Approaches can smarten systems. New and powerful methods like MCMC or Particle Filter had not been able to be applied to space technologies until calculation devices improved in efficiency, cost and downsizing. These methods should be tools for rockets in next generation. Improvement of calculation device. Classical way low low calculation cost capability no problem high high Mathematical statistical way

12 Objective function. The objective function target value f h f ( x ) = + f 1000 ( 7 γ ) h f γ f : final altitude : final attitude angle h f = h(θ 1, θ,, θ n ; θ 0 ) γ f = γ(θ 1, θ,, θ n ; θ 0 ) f(x) = f(θ 1, θ,, θ n ; θ 0 ) θ i : Attitude target at each node. θ 0 : Attitude angle at ignition.

13 Assumed Air Launch Rocket. Seiji Matsuda, AIAA-RS

14 Particle Filter. A new powerful technique developed in mathematical statistics which provides quick and accurate estimation of high dimensional state vector. The system state is approximated by the distribution of particles. 1.Particles are updated by the governing equation of the system.. For each particle, the likelihood weight is calculated by the sensor data. 3. Particles are resampled at the probability. Advantages can estimate high dimensional state vector exactly and quickly. can estimate system parameters. can be applied to nonlinear systems. easy to design the algorithm.

15 Analysis of internally carried type. Cp 0.47~0.53 The motion of the rocket is different from the nominal for the reason of errors of parameters It is necessary to estimate parameters quickly and exactly after separation. Wind Velocity +10[m]~-10[m]

16 DL 1 = ρ W AC D α Calculation L α Model. M d dt x z = G + L + D T I d dt θ 1 L = ρw 1 D = ρ W G = = l1 L n + l1 D n + l T AC Lα AC R g 0 R + h 1 T = ρ W S 0 C D α p n Entire weight : [kg] Initial condition altitude:10[km] horizontal velocity:43[m/s] initial attitude angle: 5.0[deg] initial pitch rate:10[deg/s]