Programming Exercise - Artificial Intelligence for Robotics Udacity English Japanese

Programming Exercise - Artificial Intelligence for RoboticsYouTube↗ IA↗(long shot)
Education 35.6K views 144 likes 6 dislikes 23 Feb 2015

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Let's now come to our programming exercise

ではプログラミングの練習問題です

I want you to program exactly what we just talked about.

これまでに学んだことを正確にプログラミングしてください

We're given a two-dimensional world

二次元の世界があるとします

where we observe in 2D measurements of a moving object

移動する対象に関して二次元の観測で観察します

with an unknown but fixed velocity.

速度は不明ですが一定です

Using a state vector of this type, I'd like you to implement the Kalman filter.

このタイプの状態ベクトルを使いカルマンフィルタを実装してください

Now, this Kalman filter now has 4 state variables

このカルマンフィルタは状態変数が4つあります

whereas the one we used before had 2 state variables.

以前使ったものは2つでした

I will give you the entire code for the Kalman filter,

カルマンフィルタの全体的なコードは教えます

but I want you to set up the state vector x, the motion u, P, F, H, R, and I,

皆さんに設定してほしいのは状態ベクトルxです動作u、P、F、H、R、Iをそれぞれ設定してください

which are all those variables that define the Kalman filter.

これらはすべてカルマンフィルタを定義する変数です

Start with the assignment that we had in 2D

二次元の課題から始めてください

and make it work in 4D.

それを拡張して四次元で機能するようにします

Here is exactly the same matrix class that I wrote you before.

以前書いたものとまったく同じ行列がこれです

Here is the Kalman filter procedure.

ここにカルマンフィルタの手順があります

We'll go through our measurements and apply the Kalman filter equations.

観測結果をカルマンフィルタの方程式に適用します

I should point out there's a slight difference to the code I gave you previously

以前のコードと少し違うことを指摘しておきます

where I insert a zeta transpose.

Z．transposeを加えたためです

It makes it a little bit easier to work with multidimensional measurements than how I had it before.

これで多次元の観測が前よりも少し扱いやすくなりました

But you don't have to pay attention to this. It's just fixed. There was a kind of a bug before.

ですがあまり気にしないでください以前あったバグを修正した程度のことです

As I scroll down, the output of the Kalman filter routine will be an x and a P.

下の方を見るとカルマンフィルタのルーチンの出力がxとPになっています

In our example, the measurements will be a sequence of measurements

この例のmeasurementsは一連の観測です

in two-dimensional spaces now--in x and y.

二次元空間なのでxとyの結果です

Look at the x's 5, 6, 7, 8, 9, and 10.

xは5、6、7、8、9、10で

The y's go 10, 8, 6, 4, and 2.

yは10、8、6、4、2です

You can imagine what the regularity is and what the velocity is.

規則性や速度が想像できますね

We assume a dt of 0.1.

dtを0．1とします

That means when it goes from 5 to 6 the velocity is actually 10, not 1.

これは5から6へ変わる時に速度が1ではなく10であることを意味します

We won't tell the system, but we will tell the system our initial x,y location, which is 4.

システムには初期位置のみを入力します

That goes nicely into 5, 6, 7, and it's 12. That blends nicely into 10, 8, and 6.

xは4です　これは5、6、7にうまくつながりますまたyは12なので10、8、6とつながります

Our initial state vector I have already given you, which is the initial x and y.

すでにお渡しした初期状態ベクトルは初期値がx、yであり

and 0, 0 for the two unknown velocities.

2つの未知の速度は0、0となります

The motion vector, just for completeness, will just be 0, 0, 0, 0.

動作ベクトルは完備性のために 0、0、0、0とします

We have no external motion.

外部動作はありません

That's a bit confusing, because there is actually motion in the system itself,

少し混乱するところですシステム自体の動作はありますが

but this will be more like an external change of the motion as if someone hit the object with an external force.

これは誰かが外力を対象に加えるような動作の外的な変化のことです

So it's 0, 0, 0, 0--please don't change it.

そのためここは0、0、0、0なのです変えないでください

P is the initial uncertainty,

Pは初期の不確実性です

and I want you to initialize it so that the uncertainty for the x,y coordinates is zero,

x、y座標の不確実性をゼロにするために初期化してください

but the covariance term for the velocities is 1000,

速度の共分散の項は1，000です

indicating that we really don't know the initial velocity. We just know the initial position.

初期速度を本当に知らないという意味です初期位置を知っているだけです

I want you to plug in the f matrix.

行列Fを入力してください

I want you to design an H matrix that's a projection matrix from 4-dimensional state space to 2 dimensions,

四次元の状態空間から二次元への射影行列である行列Hを設計してください

reflecting the fact that we can only observe the first two state variables--x and y-- but not the velocities.

最初の2つの状態変数x、yのみ観測でき速度は観測できません

I want you to define the measurement uncertainty matrix, which now is a 2 x 2

主対角線の0．1を観測ノイズとした観測の不確実性の行列を

that has 0.1 as the main diagonal as measurement noise.

2×2の行列で定義してください

This is an identity matrix over here.

これは単位行列です

Once you design all those, you should get the following output.

これらをすべて設計すると次の出力を得ます

So when I run this, I get as an output

では実行して出力を確認しましょう

for my 4-dimensional example the x coordinates 10 and 0.

私の四次元の例の結果ではxの座標が10、0です

This makes sense given that these sequences over here

この値はすでに設定された一連のmeasurementsが

has a final measurement 10 and 0--5, 6, 7, 8, 9, 10--10, 8, 6, 4, 2, 0.

最終的に10と0になることと一致しますつまり5、6、7、8、9、10、及び10、8、6、4、2、0のようにです

The interesting thing that I want your program to produce is the velocities.

このプログラミングで興味深い点は速度が算出されることです

They are approximately 10, which makes sense given out delta-t of 0.1

速度は約10ですがこれはΔtを0．1としたことと一致します

gives us per time step a 10 divided by 10 equals 1 increment over here.

時間あたりのステップ10を10で割るとこの増分の1になります

The second velocity is -20 multiplied by 0.1 gives us a -2.

2つ目の速度は－20で0．1を掛けると－2になります

You can see it over here--10, 8, 6, 4, and 2.

この部分の10、8、6、4、2です

I also want you to output the covariance matrix,

共分散行列Pも出力してください

which has certain elements that are still 0, like these guys over here.

ここにあるように要素は0のままです

We find that along the main diagonal our uncertainty has shrunk substantially.

主対角線を見ると不確実性はかなり減っています

It's 0.03 for the coordinate estimates and 0.1 for the velocity estimates.

座標の推定値は0．03で速度の推定値は0．1です

Remember, this number over here was 1000 before.

この数値が以前は1，000だったことを思い出してください

Here is a second example where we have an initial coordinate of -4 and 8.

2つ目の例は初期座標が－4と8です

We can see the measurements 1, 6, 11, 16.

measurementsは1、6、11、16となっています

It seems the increments are in x direction 5.

x方向の増分は5のようです

In the y direction they are -4--8, 4, 0, -4, -8.

y方向では4ずつ減少し 8、4、0、－4、－8となります

If I now run this, I get for my x vector approximately 16--the number over here,

これを実行するとxベクトルが約16となりこの数値と一致します

approximately -8--the number over here.

yは約－8でここと同じです

These are velocities--50 and -40 in approximation,

こちらが速度で約50と約－40です

which multiplied with 0.1 is our plus 5 and our -4.

それぞれ0．1を掛けると増分5と－4です

Here is yet another example. Initial state 1 and 19.

さらに他の例も見てみます　初期状態が1と19です

You can see the first coordinate doesn't change at all. You should get a velocity of 0.

最初の座標がまったく変わらないので速度は0だと分かります

The second coordinate goes 19, 17, 15, 13, and 11.

2つ目の座標は19、17、15、13、11と変化します

Running it gives us 1--unchanged--and 11.

実行すると変化のない1と11を得ます

Velocities are 0 and -20 for the decrements of -2.

速度は0と2ずつ減少する－20です

Going into the covariance, we see values along the main diagonals--

共分散を見ると速度に対する主対角線の値が

0.05, 0.05, 0.33, and 0.33 for the velocities.

0．05、0．05、0．33、0．33となっています

There are certain off-diagonal elements.

いくつか非対角要素があります

Make sure those all match what your code produces.

今の結果があなたのコードの結果と合うか確かめてください

I can now change some of these measurements to make a noisy measurement.

ではこのmeasurementsのいくつかをノイズのある観測に変えましょう

One way to do this is to set an oscillating measurement between 2 and 0.

方法の1つは2と0の間で振動する観測を設定することです

Remember that this Kalman filter assumes a fixed velocity.

カルマンフィルタは一定の速度を仮定すると思い出してください

There is no way to explain these measurements with a fixed velocity,

これらのmeasurementsは一定の速度では説明することができません

so there has to be measurement noise. We can run the Kalman filter again.

観測ノイズが必要ですカルマンフィルタを再実行しましょう

Your filter should output the following values:

フィルタは以下の値を出力するはずです

0.7 for the current state, 11 as before, and here are our two velocity estimates.

現在の状態として0．7 前のように11がありここにも速度の推定値が2つあります

It actually believes there is a slight velocity of -0.66

実際にはx方向にわずかな速度の－0．66があるとしますこれはノイズのあるセンサ入力を行ったためです

in the x direction where we had noisy sensor input. The covariance matrix would look exactly as before,

共分散行列Pは前回と同じになるでしょう

because it's not affected by the measurements themselves.

measurementsによる影響を受けないためです

Your job is to fill in these various matrices. Good luck.

さてこれらの行列を埋めることが課題です頑張ってください

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