Stochastic Motion - Artificial Intelligence for Robotics Udacity English Japanese

Stochastic Motion - Artificial Intelligence for RoboticsYouTube↗ IA↗(long shot)
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[Sebastian:] Let me talk about dynamic programming with stochastic actions.

確率論的動作によるダイナミック・プログラミングを紹介します

At the end of this assignment, you'll be able to program this.

課題の終わりにはプログラミングできるようになっているでしょう

The motivation to study this is as follows:

学習の動機づけは次のとおりです

suppose we have a robot, and we have an obstacle and a goal state.

あるロボットがいて障害とゴールの状態があると仮定します

Then this robot might be tempted to scratch the wall over here and head towards the goal.

ロボットが壁をこすってゴールへ向かうように動かされることもあるかもしれませんが

In practice this is a bad idea, because robots that get really close to obstacles are frightening.

ロボットが障害に接近しすぎるのは危険なので実際にはよくないアイデアです

In fact, if their actions aren't quite perfect they might actually hit the obstacle, which is no good.

もっと言えば動作が完璧でなければロボットが障害にぶつかってしまうこともあります

In practice, what we tend to do is we go more like this.

なのでこのような経路をとって

We maintain a certain clearance to obstacles.

障害から一定の距離を保ちます

Now we're going to modify our dynamic programming planner to do just that--

ではダイナミック・プログラミングのプランナを修正して

to find paths that are a little bit safer and lead a little bit away from obstacles.

もう少し安全で障害からも距離をとるような経路を探索します

The way we will do this is we will model actions as stochastic,

そのためには動作を確率論としてモデル化しますが

and we have not done this before, but you'll learn how to do it.

まだこれまでにやったことがないので方法を教えましょう

Take the action of going north from the from the cell over here.

このセルから北へ向かう動作をします

In a deterministic action, it obviously succeeds, unless of course we run into a wall.

決定論的動作の場合は壁に衝突しない限り成功します

In the stochastic case, it succeeds with a certain probability--say 50%--

確率論的動作の場合は約50％の一定の確率で成功します

whereas with 25% chance, it might accidentally go left or right even though we commanded it to go up.

一方25％の確率で上に進むように命令しても誤って左か右に進んでしまう可能性があります

This is a stochastic action, and it's exactly the type of action I want you to program later on.

これが後ほどプログラミングしてもらう確率論的動作というのものです

If, for example, there was a wall over here and the robot decided to go up,

例えばここに壁があってロボットが上へ移動しようとした時に

there'd be a 25% chance it would hit the wall, which is not good.

壁にぶつかる確率が 25％あるというのはまずいので

So staying away from the wall is a good idea in a stochastic situation.

確率論的な状況で壁から離れる方がいいのです

I will now show you how the backup works without asking or quizzes.

では質問や小テストは抜きにしてバックアップの仕組みを説明します

Suppose we study the action of going up over here, and we have a 50% of success.

ここから上に進む動作を調べて 50％の確率で成功することが分かったとします

Suppose at the time we do the backup, the value over here is 10, 20 over here, and 40 on the right.

バックアップする時点での値はそれぞれ10、20、40です

Then the value of the state for the action "go up" would be obtained as follows.

上に進む動作の状態値は次のように求めます

It's a 50% chance times 10, 25% times 20, and 25% chance times 40 plus 1,

50％の確率×10、25％の確率×20 そして25％の確率×40に動作コストの1を足します

which is our motion cost, which together gives me 5 plus 5 plus 10 plus 1 equals 21.

これを計算すると 5＋5＋10＋1＝21となります

That is the backed up value over here for the action go up,

これが上に進む動作のバックアップの値です

and you can do the same with go right, go left, go down.

同様に右、左、下の場合も求められます

The interesting case in your implementation is the one for an action

実装による面白いケースは

that either runs off the grid or into a wall.

グリッドからはみ出たり壁に衝突したりする動作です

Let's study the case of going north from this cell over here

ではこのセルから北へ進む場合を見てみましょう

where there is a 25% chance of falling off the grid.

25％の確率でグリッドから落ちてしまいます

Then the value for the cell and the action of going north is 50% times 20, which is 10, 25% chance times 40, which is also 10,

セルの値と北へ進む動作の値は 50％×20＝10と 25％×40＝10になります

and then we have this case where we fall off the wall.

壁から落ちるケースもあります

Let's define the penalty for falling off the grid or for hitting an obstacle as 100.

グリッドから落ちたり障害に衝突したりした場合のペナルティを100と定義しましょう

So we add 25% chance times 100 plus 1, 1,

25％の確率×100＋1を加えるので

hence the new value is 10 plus 10 plus 25 plus, which is 46.

新しい値は10＋10＋25＋1＝46です

I want your update to produce for the cell over here 46 for this specific action of going up.

上に進むという特定の動作においてこのセルが46になるように更新してください

Of course, the value might be smaller because there might be a better action like the action of going right.

より適切な右に進むという動作があるのでこの値は小さくなる可能性もあります

But for this specific calculation you should receive 46.

しかしこの計算では46になるはずです

Your programming assignment looks as follows. I will give you a grid.

プログラミングの課題は次のとおりです私がグリッドを提示します

In this case it's a grid that's entirely unoccupied.

このケースではグリッドはすべて空の状態です

As before, I give you a goal state and a set of actions.

前回のように私がゴールの状態と動作のセットを指定します

I want you to program dynamic programming all the way to the end,

ダイナミック・プログラミングを最後まで完成させてください

so when I run it, the values I get are 0 for the goal state,

私が実行する時に得る値はゴールの状態がゼロで

37 for the 2 adjacent states, and 44, 16, and 63.

2つが隣接する状態が 37、44、16、63となります

If I go right to the goal, there is a 50% chance of hitting the goal, in which case my cost is just one, which is the cost of motion.

真っすぐゴールに到達する確率は50％でこの場合のコストは動作コストの1になります

There is 25% chance of running into the wall,

壁に衝突する確率は25％で

which costs me 100 plus, of course, 1 for the robot motion,

このコストは100に動作コストの1を足したものです

and there's a 25% chance I find myself down here, which costs us 44.

そしてこの場所にいる確率は25％でコストは44です

If I put this into mathematics, we get 50% chance for reaching the goal,

計算するとゴールにたどり着く確率は50％

25% for hitting a wall, which costs me 100,

壁に衝突する確立は25%でコストが100

25% for going south, and the value here is 44.77 plus the cost of motion is 1.

南へ進む確率が25％で値が44．77ですそれに動作コストの1を足します

If you add this all up, you get exactly the 37.193 that this value over here constitutes.

合計すると37．193になりますこの値になります

After conversions for this grid, I want the value function to look just like this.

グリッドを変換するとこのような価値関数が出るようにしてください

Here is the corresponding policy.

これが対応するポリシーです

If I modify the grid to insert an obstacle over here, then I get a value function like this. One thousand is my initial value for each cell.

グリッドを修正してここに障害を挿入する場合はこのような価値関数になります 1，000は各セルの初期値です

It's unmodified for the obstacle cell, and these are the values I receive--

障害のセルは変更されておらず

94, 86, 73, and 44.

得られる値は94、86、73、44です

You can check whether these values are correct.

これらの値が正しいかどうかはチェックできます

Let me pick a slightly bigger grid

もう少し大きいグリッドを見てみましょう

with a goal position in the top right corner and two obstacles down here--size 4 x 4.

ゴールは右上の角でここに2つの障害がありサイズは4×4です

Here is my output for the value function. I can read those values.

これが価値関数の出力ですこれらの値を読むことができます

They happen to be 1000 for the two obstacles.

2つの障害は1，000です

What's remarkable is the policy.

注目すべきはポリシーです

When I'm close to the wall, you can see that I'm being pulled away

壁に近づいた時は壁の要素から引き離され

from those wall elements to stay in free space.

自由空間にとどまります

I will eventually reach the goal, but I never am willing to drive in a way

最終的にはゴールに着きますが

that crashes me into a wall if it's not avoidable.

衝突が避けられない場合でも壁に突っ込むような運転は絶対にしません

What you have to do with the code we provide is to modify

このコード内の決定論的動作を前提としたダイナミック・プログラミングのルーチンを

the dynamic programming routine that assumes a deterministic action with the one for a stochastic action.

確率論的動作のルーチンに変更してください

Specifically, what this routine should do is it should incorporate the probability of successful action and the collision costs.

具体的に言うとこのルーチンは動作が成功する確率と衝突コストを組み込む必要があります

For example, if I modify the probability of success into a deterministic function,

例えば成功する確率を決定論的関数に修正すると

then my value function will look as follows.

価値関数はこのようになります

It's just a number of steps in the usual way--1, 2, 3--as before, and the policy drives me straight to the goal as shown over here.

通常と変わらない1、2、3というステップの数字でポリシーによって真っすぐゴールまで運ばれます

In your final submission, please exclude any printouts

最終的に提出する際は出力部分を全て削除してください

so we can modify the grid and these values for success probabiilty and collision cost,

グリッド、成功する確率、衝突コストの値を変更して

and we can see what your code generates.

コードの生成結果を確認します

In the initial value function, please initialize your value function with 1000.

最初の価値関数は値を1，000で初期化してください

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