I'm here today to talk about autonomous flying beach balls.

今天我想要來談一談

(Laughter)

會自動飛行的海灘球。

No, agile aerial robots like this one.

不是啦，是靈巧的飛行機器人，就像這一個。

I'd like to tell you a little bit about the challenges in building these,

我想告訴大家製作這種東西的挑戰性

and some of the terrific opportunities for applying this technology.

以及一些很棒的可能性

So these robots are related to unmanned aerial vehicles.

來運用這種技術。

However, the vehicles you see here are big.

這些機器人

They weigh thousands of pounds, are not by any means agile.

算是一種無人的飛行器。

They're not even autonomous.

不過，如你所見，它們的尺寸都比較大。

In fact, many of these vehicles are operated by flight crews

它們都有幾千磅重，

that can include multiple pilots,

一點都不靈巧。

operators of sensors,

它們甚至並不是自動操作的。

and mission coordinators.

事實上，大部分這些飛行器

What we're interested in is developing robots like this --

是由飛行小組所操作，

and here are two other pictures --

可能有好幾個駕駛員

of robots that you can buy off the shelf.

同時在操控著感應器

So these are helicopters with four rotors,

以及任務協調器。

and they're roughly a meter or so in scale,

我們想要開發的機器人是像這個樣子 --

and weigh several pounds.

左邊這裡另外兩張照片--

And so we retrofit these with sensors and processors,

這些你都可以買到現成的。

and these robots can fly indoors.

這些是一種具有四個螺旋槳的直昇機，

Without GPS.

它們大約是一公尺大小，

The robot I'm holding in my hand

也有好幾磅重。

is this one,

於是我們將它們進行感應器與處理器的改良，

and it's been created by two students,

讓這些機器人能夠在室內

Alex and Daniel.

不靠GPS飛行。

So this weighs a little more than a tenth of a pound.

我手中所拿的這個機器人

It consumes about 15 watts of power.

就是這種飛行器，

And as you can see, it's about eight inches in diameter.

這是由兩位學生所製作的，

So let me give you just a very quick tutorial

Alex 以及 Daniel。

on how these robots work.

它的重量大概是

So it has four rotors.

十分之一磅左右。

If you spin these rotors at the same speed,

它消耗的能量大概是15瓦。

the robot hovers.

如你所見，

If you increase the speed of each of these rotors,

它的直徑大概是8英吋大。

then the robot flies up, it accelerates up.

讓我替大家簡單介紹一下

Of course, if the robot were tilted,

這些機器人的原理。

inclined to the horizontal,

這裡有四個螺旋槳。

then it would accelerate in this direction.

當這四個螺旋槳速度相同時，

So to get it to tilt,

機器人就會懸浮在空中。

there's one of two ways of doing it.

如果這些螺旋槳速度增加，

So in this picture, you see that rotor four is spinning faster

機器人就會飛起來，往上加速。

and rotor two is spinning slower.

當然，如果機器人傾斜了，

And when that happens,

相對於水平線來說，

there's a moment that causes this robot to roll.

它就會往這個方向前進。

And the other way around,

想讓它傾斜的話，這裡有兩種方法可以辦到。

if you increase the speed of rotor three and decrease the speed of rotor one,

在這圖片中，

then the robot pitches forward.

你可以看見4號螺旋槳轉速變快一點，

And then finally,

而2號螺旋槳轉速變慢一點。

if you spin opposite pairs of rotors

當這種情況發生時，

faster than the other pair,

就會讓機器人進行翻轉。

then the robot yaws about the vertical axis.

另一種狀況是，

So an on-board processor

當3號螺旋槳的速度上升，

essentially looks at what motions need to be executed

1號螺旋槳的速度下降時，

and combines these motions,

機器人就會往前傾斜。

and figures out what commands to send to the motors --

而最後一種可能，

600 times a second.

當對角線的兩組螺旋槳

That's basically how this thing operates.

轉得比另外一組快時，

So one of the advantages of this design

機器人就會在垂直方向偏移。

is when you scale things down,

有一個內置處理器

the robot naturally becomes agile.

一直在監控著該進行什麼動作，

So here, R is the characteristic length of the robot.

並且將這些動作進行組合，

It's actually half the diameter.

然後以每秒600次的速度

And there are lots of physical parameters that change as you reduce R.

決定出該對這些螺旋槳下達什麼指令。

The one that's most important is the inertia,

這就是它操作的基本概念。

or the resistance to motion.

這種設計的其中一項優點是，

So it turns out the inertia, which governs angular motion,

當你將它的尺寸縮小時，

scales as a fifth power of R.

機器人自然就會變得很靈巧。

So the smaller you make R,

這邊的 R

the more dramatically the inertia reduces.

代表著機器人特性的長度。

So as a result, the angular acceleration,

事實上是直徑的一半。

denoted by the Greek letter alpha here,

而當你將 R 縮減時，

goes as 1 over R.

許多物理係數就會跟著變動。

It's inversely proportional to R.

其中最重要的

The smaller you make it, the more quickly you can turn.

就是慣性或稱為阻止變動的抵抗力。

So this should be clear in these videos.

結果，

On the bottom right, you see a robot performing a 360-degree flip

控制了角運動的慣性，

in less than half a second.

大小約是 R 的 5 次方。

Multiple flips, a little more time.

所以當 R 變小時，

So here the processes on board

慣性會急遽的下降。

are getting feedback from accelerometers and gyros on board,

結果，角加速度，

and calculating, like I said before,

這裡用希臘字母的 α 表示，

commands at 600 times a second,

變成了 1 / R 。

to stabilize this robot.

它和 R 成反比。

So on the left, you see Daniel throwing this robot up into the air,

當尺寸越小時，它就越容易旋轉。

and it shows you how robust the control is.

用這個影片說明會清楚一點。

No matter how you throw it,

在右下角，你可以看見一個機器人

the robot recovers and comes back to him.

正在進行 360 度翻轉

So why build robots like this?

在不到 1/2 秒的時間內。

Well, robots like this have many applications.

多次的翻轉，只要稍微長一點點的時間。

You can send them inside buildings like this,

在這種狀況下，內置的處理器

as first responders to look for intruders,

接收了加速器

maybe look for biochemical leaks,

以及陀螺儀回傳的資訊，

gaseous leaks.

然後進行計算，如先前所說，

You can also use them for applications like construction.

用每秒600次的速度發出指令，

So here are robots carrying beams, columns

讓機器人保持平衡。

and assembling cube-like structures.

在左下角，Daniel 正將機器人拋向空中。

I'll tell you a little bit more about this.

這會讓你知道它的操控能力有多強大。

The robots can be used for transporting cargo.

不論你怎麼丟，

So one of the problems with these small robots

機器人都能恢復平衡然後回到他的手中。

is their payload-carrying capacity.

為什麼要將機器人設計成這樣呢？

So you might want to have multiple robots carry payloads.

嗯，這種機器人有很多種運用方式。

This is a picture of a recent experiment we did --

你可以將它派遣到這種建築物裡，

actually not so recent anymore --

擔任先遣部隊去找出侵入者，

in Sendai, shortly after the earthquake.

或是去找尋生化物質洩漏，

So robots like this could be sent into collapsed buildings,

或是瓦斯洩漏等。

to assess the damage after natural disasters,

你也可以將它們運用在

or sent into reactor buildings,

例如建築上面。

to map radiation levels.

這裡的機器人正運送著橫梁、柱子，

So one fundamental problem that the robots have to solve

並且組合成立方體形狀的建築物。

if they are to be autonomous,

我再告訴大家詳細一點。

is essentially figuring out how to get from point A to point B.

這些機器人可以用來運送貨櫃。

So this gets a little challenging,

但這些小機器人的困難在於

because the dynamics of this robot are quite complicated.

它們對於重物的負載能力有限。

In fact, they live in a 12-dimensional space.

所以如果你可能會希望能有多一點機器人

So we use a little trick.

一起來搬運這個重物。

We take this curved 12-dimensional space,

這是我們近期實驗的照片 --

and transform it into a flat, four-dimensional space.

事實上已經不算是近期了 --

And that four-dimensional space consists of X, Y, Z,

在地震過後的仙台市(日本)。

and then the yaw angle.

這種機器人可以被派遣進入傾倒的建築物裡面

And so what the robot does,

去評估天災造成的損害，

is it plans what we call a minimum-snap trajectory.

或是派遣到反應爐裡

So to remind you of physics:

去勘查輻射等級。

You have position, derivative, velocity;

如果這些機器人想有自主能力的話，

then acceleration;

它們必須先解決這個問題，

and then comes jerk,

就是必須能夠判斷

and then comes snap.

怎麼從 A 點到達 B 點。

So this robot minimizes snap.

這有一點難度，

So what that effectively does,

因為這個機器人的動力學是相當複雜的。

is produce a smooth and graceful motion.

事實上，它們活在 12 維空間裡。

And it does that avoiding obstacles.

所以我們運用了一些技巧。

So these minimum-snap trajectories in this flat space are then transformed

我們將這個 12 維空間的曲線

back into this complicated 12-dimensional space,

轉換成為

which the robot must do for control and then execution.

一個平面的四維空間。

So let me show you some examples

在這個四維空間之中，

of what these minimum-snap trajectories look like.

包含了 X, Y, Z 還有偏移的角度。

And in the first video,

所以這個機器人所做的是，

you'll see the robot going from point A to point B,

去找出我們所說的最小震盪軌跡。

through an intermediate point.

複習一下物理參數，

(Whirring noise)

我們有位置，接著衍生出速度，

So the robot is obviously capable of executing any curve trajectory.

以及加速度，

So these are circular trajectories,

還有加加速度，

where the robot pulls about two G's.

然後是震盪。

Here you have overhead motion capture cameras on the top

所以機器人將震盪進行最小化。

that tell the robot where it is 100 times a second.

這實際上的結果就是

It also tells the robot where these obstacles are.

產生出柔順且優美的動作。

And the obstacles can be moving.

它還可以用來避開障礙物。

And here, you'll see Daniel throw this hoop into the air,

而這些最小震盪軌跡在這個平面空間中

while the robot is calculating the position of the hoop,

又會被轉換回

and trying to figure out how to best go through the hoop.

這個複雜的 12 維空間，

So as an academic,

才能夠讓機器人去進行

we're always trained to be able to jump through hoops

控制以及執行任務。

to raise funding for our labs,

讓我給大家看一些例子

and we get our robots to do that.

說明這些最小震盪軌跡是什麼樣子。

(Applause)

在第一段影片中，

So another thing the robot can do

你可以看見機器人經過中繼點

is it remembers pieces of trajectory

由 A 點到達 B 點。

that it learns or is pre-programmed.

所以機器人確實可以

So here, you see the robot combining a motion that builds up momentum,

去執行任何曲線軌跡。

and then changes its orientation and then recovers.

這些是環狀軌跡，

So it has to do this because this gap in the window

機器人牽引著大約 2 G 的重力。

is only slightly larger than the width of the robot.

在上面有個置頂動態影像攝影機，

So just like a diver stands on a springboard

它會以每秒100次的速度告訴機器人自己在哪裡。

and then jumps off it to gain momentum,

它也會告訴機器人這些障礙物的位置。

and then does this pirouette, this two and a half somersault through

這些也可以是移動中的障礙物。

and then gracefully recovers,

你將會看見 Daniel 將這個鐵環丟向空中，

this robot is basically doing that.

機器人會計算鐵環的位置，

So it knows how to combine little bits and pieces of trajectories

然後試著去找出穿過鐵環的最佳方式。

to do these fairly difficult tasks.

身為一個學術人員，

So I want change gears.

我們總是被訓練得能夠赴湯蹈火才能籌措研究經費，

So one of the disadvantages of these small robots is its size.

所以我們也要我們的機器人做到。

And I told you earlier

(掌聲)

that we may want to employ lots and lots of robots

這機器人還能做另一件事，

to overcome the limitations of size.

就是去記住軌跡的片段，

So one difficulty is:

不論是它自行發現的或是事先輸入的。

How do you coordinate lots of these robots?

所以你可以看見機器人會去

And so here, we looked to nature.

組合一項動作

So I want to show you a clip of Aphaenogaster desert ants,

讓它產生動量，

in Professor Stephen Pratt's lab, carrying an object.

接著改變自己的行進方向在回復過來。

So this is actually a piece of fig.

它必須這麼做，因為這個窗戶的缺口大小

Actually you take any object coated with fig juice,

只比機器人的寬度稍微大一點。

and the ants will carry it back to the nest.

就像是跳水選手站在跳板上，

So these ants don't have any central coordinator.

接著會跳起來用以產生動量，

They sense their neighbors.

然後快速旋轉，翻轉兩周半進行穿越，

There's no explicit communication.

最後優雅的回復，

But because they sense the neighbors

這就是機器人所做的事。

and because they sense the object,

它懂得如何去結合這些零碎的軌跡

they have implicit coordination across the group.

以達成這些相當困難的任務。

So this is the kind of coordination we want our robots to have.

我想換個話題。

So when we have a robot which is surrounded by neighbors --

這些小機器人的缺點之一就是尺寸。

and let's look at robot I and robot J --

如同先前所提，

what we want the robots to do,

我們想使用大量的機器人

is to monitor the separation between them,

來解決尺寸上的限制。

as they fly in formation.

但有個困難點是

And then you want to make sure

你要如何去協調這些機器人呢？

that this separation is within acceptable levels.

這部份我們觀察了自然界。

So again, the robots monitor this error

我想讓大家看一段影片，

and calculate the control commands 100 times a second,

關於沙漠盤腹蟻

which then translates into motor commands,

在 Stephen Pratt 教授的實驗室裡搬運東西。

600 times a second.

事實上這是一小塊無花果。

So this also has to be done in a decentralized way.

事實上你可以把任何東西沾附一層無花果汁

Again, if you have lots and lots of robots,

螞蟻們就會將它搬回巢穴裡。

it's impossible to coordinate all this information centrally

這些螞蟻並沒有中樞協調者。

fast enough in order for the robots to accomplish the task.

它們能感覺到旁邊的鄰居們。

Plus, the robots have to base their actions only on local information --

不用進行明確的溝通。

what they sense from their neighbors.

但因為它們能感覺到鄰居，

And then finally,

因為它們能感覺到東西，

we insist that the robots be agnostic to who their neighbors are.

它們在團體間有著隱性協調能力。

So this is what we call anonymity.

這種協調能力

So what I want to show you next is a video of 20 of these little robots,

就是我們希望機器人能有的。

flying in formation.

當我們的一個機器人

They're monitoring their neighbors' positions.

被周圍的機器人包圍時 --

They're maintaining formation.

看看機器人 I 和機器人 J --

The formations can change.

我們希望機器人做的事情是

They can be planar formations,

當它們以特定隊形飛行時

they can be three-dimensional formations.

去偵測它們之間的距離。

As you can see here,

你期望能夠確保

they collapse from a three-dimensional formation into planar formation.

這個距離是在可接受的範圍內。

And to fly through obstacles,

於是機器人們偵測著這個誤差值

they can adapt the formations on the fly.

然後以每秒100次的速度

So again, these robots come really close together.

去估算控制指令，

As you can see in this figure-eight flight,

接著以每秒600次的速度對螺旋槳進行動作指令。

they come within inches of each other.

這必須是在

And despite the aerodynamic interactions with these propeller blades,

沒有中央控制的方式下進行。

they're able to maintain stable flight.

當你有許許多多機器人的時候，

(Applause)

想要以中央協調訊息的方式

So once you know how to fly in formation,

快速的讓所有機器人完成任務是不可能的。

you can actually pick up objects cooperatively.

再加上機器人們必須依靠

So this just shows that we can double, triple, quadruple

它們自身去偵測到鄰近機器人

the robots' strength,

以獲得訊息來進行動作。

by just getting them to team with neighbors, as you can see here.

最後，

One of the disadvantages of doing that is, as you scale things up --

我們堅持機器人必須無法預知

so if you have lots of robots carrying the same thing,

鄰近機器人會是誰。

you're essentially increasing the inertia,

也就是匿名的方式。

and therefore you pay a price; they're not as agile.

接下來我將要給大家看

But you do gain in terms of payload-carrying capacity.

一段影片

Another application I want to show you -- again, this is in our lab.

關於20個這些小機器人

This is work done by Quentin Lindsey, who's a graduate student.

以特定隊形進行飛行。

So his algorithm essentially tells these robots