How does the hopping mechanism of the Minerva II rovers work?

Question

The Minerva II rovers deployed to Ryugu by Hayabusa 2 have gotten a lot of news coverage for their hopping method of locomotion. Is there public information on exactly how this works? I seem to recall reading that it was some kind of off-center weight that can be made to rotate, but I'm surprised I haven't been able to find any popular coverage that gave any more detail than that. Is that basic idea right? Are there any cutaway diagrams available to the public? Are there details about rate of rotation and average velocity during a hop? How big, and how massive, is the mechanism compared to the rest of the rover?

Answer 1

They do this by moving a "torquer" in their interior, which rests atop a disk-shaped turntable.

"By rotating the torquer, a reaction force against the asteroid surface makes the rover hop with a significant horizontal velocity," a team of researchers led by JAXA's Tetsuo Yoshimitsu wrote in a 2012 study outlining the concept. "After hopp[ing] into the free space, it moves ballistically. With this mechanism, by changing the magnitude of torque, the hopping speed can be altered, so as not to exceed … the escape velocity from the asteroid surface."

The MINERVA-II rovers control the direction of their hops by manipulating the orientation of the turntable, the scientists added. These hops can last for 15 minutes and cover about 50 feet (15 m) of horizontal distance.

source

source (This paper is about MINERVA, not MINERVA II, and I am not sure if they are exactly the same)

Answer 2

MINERVA-II consisted of three rovers: MINERVA-II1, a pair of rovers developed by JAXA, and MINERVA-II2, a single rover developed by a consortium of Japanese universities. MINERVA-II1 and MINERVA-II2 used completely different mechanisms for hopping. The only real details I could find about either mechanism are in Japanese; in the rest of my answer, I include some quotes from Japanese sources, followed by my own English translations.

MINERVA-II1

The MINERVA-II1 hopping mechanism is described in the 2016 article 車輪なしでどうやって移動する？ローバー「ミネルバ2」の仕組み (How do you move without wheels? MINERVA-II rover design):

原理は非常にシンプルだ。まず本体内部に、重り（アルミ製の円板）を付けたDCモーターを搭載する。このモーターを回転させると、逆向きに回転しようとする力が発生する。回転椅子に座って、伸ばした腕を左に回すと、体が右に回るのと原理は同じだ。この力により、地面を蹴ってジャンプする。

初代ミネルバの場合、ホッピング用のDCモーターをターンテーブルに乗せて、ホップする方向を変えられるようになっていた。ただ、ターンテーブルは仕組みが複雑になり、重くなってしまうという欠点がある。そのため、ミネルバ2では、DCモーター×2セットを直交配置し、それぞれの回転数を調整して、任意の方向に移動する方式が考えられていた。

　ところが、開発が進むにつれ、ミネルバ2の重量オーバーが深刻化。最終的に、DCモーターを1つに減らすことが決まった。こうすると、前後方向にしか移動できなくなってしまうが、ローバーを1台にして2自由度を維持するよりも、たとえ1自由度になったとしてもローバーを2台にしたいという判断だろう。

なお、重力が小さいとは言っても、初代ミネルバが行ったイトカワに比べると、ミネルバ2のリュウグウは2倍ほど大きく、重力もそれだけ強い。そのため、DCモーターはより大きなものを搭載しているそうだ。

　このDCモーターをフル回転させたとき、発生したトルクにより、秒速10cm程度の速度で飛び上がることが可能。水平方向の速度は、地面との摩擦の大きさや地形次第であるが、もし45°くらいの角度でホップした場合には、一気に10mくらい移動できるという。微小重力環境での実験はドイツで行い、正常に動作することを確認した。

The idea is extremely simple. Inside the body of the rover is a weight (an aluminum disc) attached to a DC motor. When the motor turns, a force is generated that tries to rotate the rover in the opposite direction. You can see the same principle in action when you sit in a swivel chair: if you stretch out your arms and swing them to the left, your body rotates to the right. This force causes the rover to kick the ground and jump up.

With the first-generation MINERVA rover, the motor was placed on a turntable; by rotating the turntable, the direction of the hops could be changed. However, a turntable has the weakness that it makes the construction heavier and more complex. An alternative idea was to use a set of two orthogonal DC motors; by adjusting the number of rotations of each motor, the rover could move in any arbitrary direction.

However, as development progressed, MINERVA-II ran into weight limitations. Ultimately, it was decided to use only a single DC motor per rover. This limited the rovers to moving only forward and backward, but apparently the designers wanted to use two rovers even if each had only one degree of freedom, rather than a single rover with two degrees of freedom.

Furthermore, even though MINERVA-II's target asteroid Ryugu has low gravity, Ryugu is roughly double the size of MINERVA's target Itokawa, so the gravity is stronger. Therefore, MINERVA-II was equipped with a larger DC motor than MINERVA.

When the motor makes a full rotation, the generated torque can cause the rover to jump at up to 10 cm/s. The horizontal speed depends on the terrain and the amount of friction with the ground, but in the case of a 45° hop, it could move about 10 m at a time.

This article is the second in a series about MINERVA-II1 (part one is here) based on discussions the author had with Tetsuo Yoshimitsu, who led development of both MINERVA and MINERVA-II1.

The 2012 paper Advanced robotic system of hopping rovers for small solar system bodies (English) describes the abandoned orthogonal motor proposal mentioned in the previous article. The authors even created a prototype and did microgravity testing on it using a drop tower. The paper includes some photos of the prototype where you can see the motors and their size relative to the prototype body (see especially Figure 1b). Even though this design wasn't used in the final MINERVA-II1 rovers, I'm guessing the physical size of the motors wasn't drastically different.

MINERVA-II2

MINERVA-II2 actually had four distinct hopping mechanisms, each developed by a different university. The 2019 article はやぶさ2搭載の小型ローバー「MINERVA-II2」に不具合、復旧は困難か (Recovery may be difficult after malfunction in Hayabusa2's MINERVA-II2 rover) has a good overview:

山形大学の「環境依存型座屈機構」は、熱膨張率が異なる2種類の金属を組み合わせ、バネのように伸びたり縮んだりできる仕組み。昼と夜の温度変化により2つの状態が切り替わるため、動作に電力が不要なことが大きな特徴だ。

大阪大学の「板バネを用いた弾性エネルギー解放型撃力発生機構」は、板バネを凹んだ状態で搭載しておき、凸状に解放したときの反動を利用する。解放にはロック機構を利用するが、形状を戻す仕組みはないため、1回動作したら終わりだ。

東京電機大学の「永久磁石型撃力発生機構」は、金属の重りが永久磁石にくっつくときの衝突力を利用する。駆動にはDCモーターを利用しており、電力があれば何度でも動かすことは可能だ。

東北大学の「偏心モーター型マイクロホップ機構」のみ、偏った重りを回転させてトルクを発生させるが、MINERVA初号機などと違い大きくホップするのではなく、スマホがバイブで振動するように、微小なホップを連続して小惑星表面をなぞるように移動する。

The "environment-dependent buckling mechanism" developed by Yamagata University combines two metals with different rates of thermal expansion, which stretch and shrink like springs. This mechanism is distinct because it requires no electric power; it switches between its two states due to temperature changes between day and night.

Osaka University's "leaf spring elastic energy release impulsive force mechanism" uses the recoil generated when compressed leaf springs are released. The spring release is controlled by a locking mechanism, but there is no way to re-compress the springs, so this mechanism can only be used once.

Tokyo Denki University's "permanent magnet impulsive force mechanism" uses the impact force of a metal weight sticking to a permanent magnet. It uses a DC motor so as long as there is power, it can be used over and over again.

Tohoku University's "eccentric motor microhop mechanism" is the only one to use the rotation of an off-center weight to generate torque, but unlike the original MINERVA, it doesn't make large hops; instead, like a vibrating cell phone, it uses a series of microhops to move along the surface of the asteroid.

The third photo in the article shows diagrams of all four mechanisms: clockwise from top-left, they are Yamagata University's bimetal mechanism, Tohoku University's eccentric motor microhop mechanism, Tokyo Denki University's magnet mechanism, and Osaka University's leaf spring mechanism.

The Mineta Lab at Yamagata University has a more detailed description of their bimetal mechanism on their website:

日照の有無によって生まれる大きな温度差を利用しバイメタルをアクチュエータに用いた環境温度駆動型の移動機構を考案して作製しました。バイメタル（膨張率の異なる2種類の合金の積層板）は温度変化によって曲がろうとし、限界点を超えると瞬間的に反対側に反る座屈型（峯田研）と、磁石から外れて瞬間的に反る磁気ラッチ型（妻木研）の2種類を搭載しています。それぞれ高温域と低温域に動作温度をずらして設計し、MINERUVA-II-2の投下位置や周囲状況によって環境温度が変わっても、どちらかが対応できる可能性を高めました。小惑星リュウグウの自転周期は約８時間であり、朝夕に相当する4時間ごとにランダムな方向へホッピング動作する構想です。

We designed and built a movement mechanism driven by ambient temperature; it uses a bimetal as an actuator and relies on the large temperature difference that arises with the presence or absence of sunlight. A bimetal (two metals with different rates of expansion layered together) bends with changes in temperature. MINERVA-II-2 is equipped with two types of bimetal mechanism: a buckling type that instantaneously warps in the opposite direction when its threshold temperature is exceeded (Mineta Lab), and a magnetic latch type that instantaneously warps when the bimetal disconnects from a magnet (Tsumaki Lab). Each was designed with its own high and low activation temperature staggered from the other, so even if the ambient temperature varies depending on MINERVA-II-2's drop location and its surroundings, there is a higher likelihood that one of the two will be suitable. The rotational period of asteroid Ryugu is about eight hours, so the idea is for the rover to hop in a random direction every four hours, in the morning and the evening.

There is a photo of the mechanism on that page showing both types integrated into a single component, with the magnetic type toward the bottom edge of the photo and the buckling type toward the top edge.

The Osaka University Engineering Department website has an article describing their leaf spring mechanism:

3章のような設計指針をもとに阪大チームでは、飛 び移り座屈方式を採用することにしたが、今回はその 第一ステップということで、最も単純な駆動装置を開 発することにした。

図 8 に最終的に制作した「飛び移り座屈ユニット」 を示す。

この図の下面の W 字型をしている部分が飛び移り 座屈部で、写真はテグス（糸）で押さえられている。 この状態で目的の小惑星までいき、あるタイミングで テグスを熱で切る。そうすると座屈現象が発生しジャ ンプするようになっている。

このユニットを 2 セット MINERVA-II-2 に搭載し た。その様子を図 9 に示す。

Based on the design principles in Section 3, the Osaka University team decided to use the snap-through buckling method, but since this was a first step, we decided to develop the simplest driving mechanism possible.

Figure 8 shows the snap-through buckling unit that we ultimately produced.

The W-shaped piece at the bottom of the image is the part that buckles; it is shown being compressed with a piece of thread. It travels to the target asteroid in this state, until at some point the thread is cut using heat. This triggers the buckling phenomenon and makes the rover jump.

MINERVA-II-2 is equipped with two of these units, which are pictured in Figure 9.

Figures 8 and 9 are on the last page of the article. In Figure 9, you can see the internals of MINERVA-II2. The label on the bottom right points to Yamagata University's bimetal mechanism; the label above it indicates Osaka University's two leaf spring devices.