We will demonstrate the concept of machine athleticism

我們將展示機器運動能力的概念

and the research to achieve it

以及為了實現而進行的研究

with the help of these flying machines called quadrocopters,

靠的是這些飛行機器，叫做「四軸飛行器」 (quadrocopters)

or quads, for short.

簡稱為「四軸」

Quads have been around for a long time.

四軸已經存在很久了

The reason that they're so popular these days

最近很受歡迎的原因

is because they're mechanically simple.

是因為在機械方面很簡單

By controlling the speeds of these four propellers,

只要控制這四個螺旋槳的速度

these machines can roll, pitch, yaw,

這些機器可以側滾，俯仰，偏擺

and accelerate along their common orientation.

以及沿著共同方向加速

On board are also a battery, a computer,

上面還有電池及一台電腦

various sensors and wireless radios.

各種感測器和無線收發器

Quads are extremely agile, but this agility comes at a cost.

四軸極為靈活，但要付出代價

They are inherently unstable, and they need some form

它本質上不穩定，需要某種形式的

of automatic feedback control in order to be able to fly.

自動回饋控制，才可能飛行

So, how did it just do that?

要怎麼做到這點呢？

Cameras on the ceiling and a laptop

天花板上的攝影機和一台筆記型電腦

serve as an indoor global positioning system.

就像是室內的全球定位系統

It's used to locate objects in the space

用來為物體在空間中定位

that have these reflective markers on them.

物體上有這些反光標記

This data is then sent to another laptop

定位資料送到另一台筆記型電腦

that is running estimation and control algorithms,

執行估計與控制的演算法

which in turn sends commands to the quad,

再反過來把命令送到四軸

which is also running estimation and control algorithms.

四軸本身也在執行估計與控制的演算法

The bulk of our research is algorithms.

我們的研究大部分都是演算法

It's the magic that brings these machines to life.

演算法是使這些機器活過來的魔法

So how does one design the algorithms

要怎麼設計演算法

that create a machine athlete?

才能創造出機器運動員？

We use something broadly called model-based design.

我們使用的方法泛稱為模型化基礎設計

We first capture the physics with a mathematical model

我們首先用數學模型捕捉

of how the machines behave.

機器行為的物理法則

We then use a branch of mathematics

然後用數學的一個分支—

called control theory to analyze these models

「控制理論」來分析這些模型

and also to synthesize algorithms for controlling them.

並合成控制的演算法

For example, that's how we can make the quad hover.

例如我們想讓四軸原地懸停

We first captured the dynamics

我們首先捕捉動態

with a set of differential equations.

是一組微分方程式

We then manipulate these equations with the help

然後操縱這些方程式

of control theory to create algorithms that stabilize the quad.

在控制理論建立的演算法幫忙下讓四軸得以穩定

Let me demonstrate the strength of this approach.

讓我展示這種方法的優點

Suppose that we want this quad to not only hover

假設我們希望四軸不止是懸停

but to also balance this pole.

還要讓桿子平衡

With a little bit of practice,

經過一些練習

it's pretty straightforward for a human being to do this,

人類很容易可以做到

although we do have the advantage of having

雖然我們有優勢

two feet on the ground

雙腳可以著地

and the use of our very versatile hands.

還有極為靈活的手

It becomes a little bit more difficult

像這樣就有點困難：

when I only have one foot on the ground

如果只有一腳著地

and when I don't use my hands.

而且不准用手

Notice how this pole has a reflective marker on top,

請注意，桿子頂上有反光標記

which means that it can be located in the space.

表示可在空間中定到它的位置

(Applause)

（掌聲）

You can notice that this quad is making fine adjustments

你可以看到，這架四軸正進行微調

to keep the pole balanced.

以讓桿子保持平衡

How did we design the algorithms to do this?

我們是怎麼設計演算法來做到的？

We added the mathematical model of the pole

我們加入了桿子的數學模型

to that of the quad.

到四軸中

Once we have a model of the combined quad-pole system,

一旦我們有了結合四軸與桿子的模型

we can use control theory to create algorithms for controlling it.

就可以用控制理論建立控制的演算法

Here, you see that it's stable,

這裡，你看，很穩定

and even if I give it little nudges,

就算我輕輕推一下

it goes back to the nice, balanced position.

它仍可回到完全平衡的位置

We can also augment the model to include

我們還可以加強模型，以包括

where we want the quad to be in space.

我們希望四軸在空間的位置

Using this pointer, made out of reflective markers,

用這根有反光標記的指示棒

I can point to where I want the quad to be in space

可以指出我要四軸到的位置

a fixed distance away from me.

和我保持固定的距離

The key to these acrobatic maneuvers is algorithms,

這些特技動作的關鍵是演算法

designed with the help of mathematical models

它的設計要靠數學模型

and control theory.

與控制理論

Let's tell the quad to come back here

我要告訴四軸回來這裡

and let the pole drop,

並讓桿子倒下來

and I will next demonstrate the importance

接下來我要展示

of understanding physical models

了解物理模型、

and the workings of the physical world.

以及實體世界運作的重要性

Notice how the quad lost altitude

注意四軸的高度降低了

when I put this glass of water on it.

我把這杯水放上去

Unlike the balancing pole, I did not include

不像平衡桿，我並未把玻璃杯

the mathematical model of the glass in the system.

的數學模型加到系統裡

In fact, the system doesn't even know that the glass of water is there.

事實上，系統根本不知道有杯水

Like before, I could use the pointer to tell the quad

我一樣可以用指示棒來告訴四軸

where I want it to be in space.

我希望它在空間中的位置

(Applause)

（掌聲）

Okay, you should be asking yourself,

好吧，你應該問自己

why doesn't the water fall out of the glass?

為什麼杯中的水不會灑出來？

Two facts: The first is that gravity acts

兩個事實：第一點是重力

on all objects in the same way.

對所有的物體作用相同

The second is that the propellers are all pointing

第二點是，推進器都指向

in the same direction of the glass, pointing up.

和杯子相同的方向，也就是向上

You put these two things together, the net result

兩個原因加在一起，最終結果是

is that all side forces on the glass are small

玻璃杯各方向的側向力都很小

and are mainly dominated by aerodynamic effects,

還是以空氣動力學效應為主

which as these speeds are negligible.

因此這些速度是微不足道的

And that's why you don't need to model the glass.

這就是為什麼不需要杯子的模型

It naturally doesn't spill no matter what the quad does.

水自然不會灑出來不管四軸怎麼動

(Applause)

（掌聲）

The lesson here is that some high-performance tasks

這裡學到的是，有些高性能任務

are easier than others,

比其他的容易

and that understanding the physics of the problem

還有，理解問題背後的物理

tells you which ones are easy and which ones are hard.

可告訴我們哪些容易、哪些困難

In this instance, carrying a glass of water is easy.

以此為例，載運水很容易

Balancing a pole is hard.

平衡桿子則很困難

We've all heard stories of athletes

我們都聽過運動員的故事

performing feats while physically injured.

雖然身體受傷，仍然完成壯舉

Can a machine also perform

機器可以在

with extreme physical damage?

受重傷的情況下運作嗎？

Conventional wisdom says that you need

傳統觀念認為，你需要

at least four fixed motor propeller pairs in order to fly,

至少四個固定的馬達螺旋槳才能飛

because there are four degrees of freedom to control:

因為有四個自由度要控制：

roll, pitch, yaw and acceleration.

側滾、俯仰、偏擺、加速

Hexacopters and octocopters, with six and eight propellers,

六軸和八軸分別有六和八個螺旋槳

can provide redundancy,

可提供冗餘

but quadrocopters are much more popular

但四軸則普及多了

because they have the minimum number

因為它具有最小數目的

of fixed motor propeller pairs: four.

固定馬達螺旋槳：四個

Or do they?

是這樣嗎？

If we analyze the mathematical model of this machine

我們分析這台機器的數學模型

with only two working propellers,

如果只有兩個螺旋槳可運作

we discover that there's an unconventional way to fly it.

我們發現有種非傳統的方式可飛行

We relinquish control of yaw,

我們放棄控制偏擺

but roll, pitch and acceleration can still be controlled

仍然可以控制側滾、俯仰、加速

with algorithms that exploit this new configuration.

只要演算法能處理這種新配置

Mathematical models tell us exactly when

數學模型告訴我們何時

and why this is possible.

和為何這是可能的

In this instance, this knowledge allows us to design

此例中，這種知識讓我們能設計出

novel machine architectures

新穎的機器架構

or to design clever algorithms that gracefully handle damage,

或優雅應對損害的巧妙演算法

just like human athletes do,

就像人類運動員

instead of building machines with redundancy.

而不必建構具有冗餘的機器

We can't help but hold our breath when we watch

我們不禁屏住呼吸

a diver somersaulting into the water,

當我們看到跳水選手翻個筋斗入水、

or when a vaulter is twisting in the air,

或撐竿跳選手在空中扭轉、

the ground fast approaching.

同時快速接近地面

Will the diver be able to pull off a rip entry?

跳水選手入水時能否成功壓水花？

Will the vaulter stick the landing?

撐竿跳選手能否完美著地？

Suppose we want this quad here

假設我們希望四軸

to perform a triple flip and finish off

表演三轉空翻，並結束在

at the exact same spot that it started.

開始的同一地點

This maneuver is going to happen so quickly

這個動作太快了

that we can't use position feedback to correct the motion during execution.

無法用位置回饋信號糾正執行過程中的動作

There simply isn't enough time.

時間根本不夠

Instead, what the quad can do is perform the maneuver blindly,

相反的，四軸只能盲目進行動作

observe how it finishes the maneuver,

觀察四軸如何完成動作

and then use that information to modify its behavior

再用這些資訊來修改行為

so that the next flip is better.

讓下次空翻更進步

Similar to the diver and the vaulter,

就像跳水選手和撐竿跳選手

it is only through repeated practice

只有通過反覆練習

that the maneuver can be learned and executed

才能學會動作

to the highest standard.

並達到最完美的境界

(Applause)

（掌聲）

Striking a moving ball is a necessary skill in many sports.

打擊移動中的球對許多運動是必要技能

How do we make a machine do

我們如何讓一台機器做出

what an athlete does seemingly without effort?

對運動員看似毫不費力的動作？

(Applause)

（掌聲）

This quad has a racket strapped onto its head

這架四軸頂部綁了個球拍

with a sweet spot roughly the size of an apple, so not too large.

甜蜜點大約一個蘋果大小所以不會太大

The following calculations are made every 20 milliseconds,

以下的計算每二十毫秒執行一次

or 50 times per second.

也就是每秒執行五十次

We first figure out where the ball is going.

我們首先弄清楚球會飛到哪裡

We then next calculate how the quad should hit the ball

然後計算四軸如何擊中球

so that it flies to where it was thrown from.

四軸飛到球丟出的附近

Third, a trajectory is planned that carries the quad

第三，規劃出四軸由目前位置

from its current state to the impact point with the ball.

到擊球位置的軌道

Fourth, we only execute 20 milliseconds' worth of that strategy.

第四，只需執行這戰略二十毫秒

Twenty milliseconds later, the whole process is repeated

二十毫秒過後，再重複整個過程

until the quad strikes the ball.

直到四軸擊中球

(Applause)

（掌聲）

Machines can not only perform dynamic maneuvers on their own,

機器不僅可以自主執行動態操作

they can do it collectively.

還可以互相合作

These three quads are cooperatively carrying a sky net.

這三架四軸合作張開網子

(Applause)

（掌聲）

They perform an extremely dynamic

它們執行的，是非常動態

and collective maneuver

且需要合作的動作

to launch the ball back to me.

把球丟回給我

Notice that, at full extension, these quads are vertical.

請注意的，在完全伸展時這些四軸是垂直的

(Applause)

（掌聲）

In fact, when fully extended,

事實上，在完全伸展時

this is roughly five times greater than what a bungee jumper feels

大約產生五倍於高空彈跳

at the end of their launch.

最低點的力量

The algorithms to do this are very similar

做到這點的演算法非常相似於

to what the single quad used to hit the ball back to me.

單一四軸把球打回我身邊

Mathematical models are used to continuously re-plan

使用數學模型不斷重新規劃

a cooperative strategy 50 times per second.

合作策略，每秒五十次

Everything we have seen so far has been

到目前為止，我們看到的一切

about the machines and their capabilities.

都是關於機器及其功能

What happens when we couple this machine athleticism

我們若把這台機器的運動能力

with that of a human being?

和人結合，會發生什麼事？

What I have in front of me is a commercial gesture sensor

在我面前的是一具商業的人體動作感測器

mainly used in gaming.

主要用於遊戲(Kinect)

It can recognize what my various body parts

可以即時識別我身體

are doing in real time.

各部位的動作

Similar to the pointer that I used earlier,

就像剛才我用指示棒

we can use this as inputs to the system.

我們可用這個作為系統的輸入

We now have a natural way of interacting

我們就有了自然的互動方式

with the raw athleticism of these quads with my gestures.

用我的手勢和四軸的原始運動能力互動

(Applause)

（掌聲）

Interaction doesn't have to be virtual. It can be physical.

互動不一定是虛擬也可以是實體的

Take this quad, for example.

以此四軸為例

It's trying to stay at a fixed point in space.

它試著要待在空間裡固定的一點

If I try to move it out of the way, it fights me,

如果我試著將它移開，它會抵抗

and moves back to where it wants to be.

並移回它想待的地方

We can change this behavior, however.

但我們可以改變這種行為

We can use mathematical models

我們可以用數學模型

to estimate the force that I'm applying to the quad.

估算出我對四軸施力的大小

Once we know this force, we can also change the laws of physics,

一旦知道了力量大小我們也可以改變物理規則

as far as the quad is concerned, of course.

當然是對四軸而言

Here the quad is behaving as if it were

這架四軸的行為就好像它

in a viscous fluid.

在黏性流體中一樣

We now have an intimate way

我們現在有了親密的方式

of interacting with a machine.

可與機器互動

I will use this new capability to position

我要用這新功能把載著相機的四軸

this camera-carrying quad to the appropriate location

定位到適當位置

for filming the remainder of this demonstration.

以拍攝接下來的示範

So we can physically interact with these quads

我們可以與四軸進行實體互動

and we can change the laws of physics.

我們也可以改變物理定律

Let's have a little bit of fun with this.

讓我們來玩一下

For what you will see next, these quads

接下來你會看到這些四軸

will initially behave as if they were on Pluto.

一開始像是在冥王星的引力

As time goes on, gravity will be increased

隨著時間過去，重力逐漸增加

until we're all back on planet Earth,

直到全都回到地球的引力

but I assure you we won't get there.

但我保證不會發生

Okay, here goes.

好的，開始

(Laughter)

（笑聲）

(Laughter)

（笑聲）

(Applause)

（掌聲）

Whew!

呼！

You're all thinking now,

各位現在可能在想

these guys are having way too much fun,

這些傢伙也太愛玩了吧

and you're probably also asking yourself,

你可能也在問自己

why exactly are they building machine athletes?

他們到底為何要建造機械運動員？

Some conjecture that the role of play in the animal kingdom

一個推測是，就像動物王國中遊戲的作用

is to hone skills and develop capabilities.

可以磨練技能和發展能力

Others think that it has more of a social role,

其他人則認為這有更多的社會角色

that it's used to bind the group.

可讓團體聚在一起

Similarly, we use the analogy of sports and athleticism

同樣，我們用運動和運動能力類比

to create new algorithms for machines

來建立機器的新演算法

to push them to their limits.

將其能力推昇到極限

What impact will the speed of machines have on our way of life?

機器的速度會對我們的生活方式產生什麼影響？

Like all our past creations and innovations,

就像我們過去的各種創作及創新