Archery robot to select arrows: Ohara 2020 study

Seven pages of conference proceedings on a shooting machine built at Osaka City University, second version, with a declared aim: discarding flawed arrows before a competition. No archers, no scores: the machine is the subject.

The problem to solve was the machine itself. The first version weighed 24 kilograms, the string was drawn by turning a handle and the whole assembly vibrated; the left arm was an aluminium tube with a wall a millimetre and a half thick that oscillated; and the bow was not clamped to the hand, so on every shot it came loose and next time the grip landed in a different place. The second version weighs 114.4 kilograms, nearly five times as much, draws the string with a three-mode direct-current motor, uses an iron tube with a two-millimetre wall, and holds the bow in a polyacetal clamp which nonetheless lets it jump forward at the moment of the shot, as happens in an archer's hand.

The most elegant part is the release. The right hand has real fingers, with wires and springs, locked when closed and opened by a solenoid, so as to produce the archer's paradox rather than letting go like a mechanical release. And the release is triggered by the clicker: a microphone hears the click, a filter recognises a sound around 1400 hertz lasting 0.15 seconds, and a Raspberry Pi frees the fingers. So the draw length is always the same, and that is how an archer actually works.

The test fits into one afternoon, 2 October 2019 around four o'clock, a day that was not very windy. A Yamaha α-EX bow, release at 382 millimetres of draw, where 18 kilograms are needed. Seventy metres. Six arrows shot, two of them flawed: one always went right, the other, missing a vane, always went low. With the clicker used as the signal and without it.

The declared result is twofold. The machine would be accurate enough to select arrows at seventy metres with no wind, and the two flawed arrows fall outside a circle of twice the standard deviation while the four good ones stay inside. The second result, however, is built so that it cannot come out otherwise, because that standard deviation is computed on those same four good arrows.

The base is made heavy on purpose, over a hundred kilograms, so that it does not move on the shot, with wheels underneath for moving it and four M24 bolts for fixing it, plus a mechanism for adjusting the angles horizontally and vertically to aim.

The draw: a Maxon direct-current motor driven by a bridge of four transistors, with three modes distinguished by limit switches and managed by the Raspberry Pi. Mode one, rapid drawing, modulation ratio at thirty per cent; mode two, slowing near the clicker, twelve per cent; mode three, the arrow's point reaching the clicker, ten per cent. The switching points between modes can be moved.

The left arm: in the first machine a square aluminium tube with a 1.5-millimetre wall and a 15 by 25 section, which vibrated; in the second an iron tube with a 2-millimetre wall and a 20 by 40 section. The grip is a polyacetal clamp that holds and protects the bow, and that jumps forward from the arm when the shot goes.

The release: the right hand reproduces the structure of the fingers in order to obtain the archer's paradox, with flexion and extension imitated by pulling wires and springs. The fingers lock closed and extend when a solenoid, driven by a power transistor, receives current. The signal starts when the computer recognises the clicker's sound: microphone, preamplifier, capacitor-resistor low-pass filter, first-order low-pass filter, sixth-order high-pass filter, power amplifier, analogue-to-digital converter, Raspberry Pi 3B.

The field test: the machine taken to the range, seventy metres, six arrows, two conditions, with and without the clicker as the release signal. For each impact the horizontal and vertical distances from the centre are measured, and the origin of the graphs is the mean position of the impacts, because aiming was not the objective: the interest was the spread under constant conditions.

As a reference there is a graph from the first machine from an earlier paper, ten shots of the same arrow at eighteen metres with a nine-kilogram bow, because at seventy metres that bow did not reach.

To decide which arrows were abnormal two circles are drawn, one with a radius equal to the standard deviation of the good arrows and one with twice that radius, and one looks at who falls outside. The authors also cite the Smirnov-Grubbs test and Thompson's as alternatives, but do not use them.

The central result cannot come out other than it does, and the reason is written in the article. The abnormal arrows are identified using the standard deviation of the normal arrows, and the normal arrows in that group are four. A circle of twice the standard deviation of four points, centred on their mean, contains them practically always: it is not a result about the four, it is a property of the operation. The real question would be whether the two flawed arrows fall outside an interval estimated on an independent set of good arrows, and that set does not exist.

Add that the two flawed arrows were known beforehand. The article says one always went right and the other always low, and that the latter was missing a vane. So the defect had already been identified by the behaviour the machine is then supposed to reveal, and in one case it was visible to the naked eye. Showing that a hundred-and-fourteen-kilogram machine finds an arrow missing a vane does not measure its ability to find the defects the eye cannot see, which is the problem it was built for.

No numbers. The standard deviation is named as the circle's radius and its value is given nowhere, neither in millimetres nor otherwise; there are no group diameters, there is no numerical comparison between the clicker condition and the other, and the two conclusions about that comparison are "the accuracy is extremely high" and "more clearly". For a work whose purpose is to establish whether the machine is accurate enough, the accuracy is not quantified in the text.

Nor is it clear how many shots lie behind the accuracy measurement. The explicit counts in the text are two, ten shots with the first machine at eighteen metres and six arrows in the selection test at seventy, while the sentence about accuracy speaks of ten arrows inside the 122 millimetres of the ten zone: those ten shots at seventy metres are described nowhere in the text.

The comparison that matters is not made. To select arrows, the machine's variability has to be smaller than the differences between arrows. Here both are measured, the spread of one arrow repeated and the spread of four different arrows, and neither is reported as a number, so a reader cannot know whether the machine resolves the differences it is meant to judge.

One session, one afternoon, one bow, one draw length. No repeat on another day, no remounting of the bow, and the wind described as "not very windy" rather than measured: for a machine that has to tell arrows apart over a few millimetres at seventy metres, wind is the main disturbance and it was not measured. The 382-millimetre draw, moreover, is given without saying where it is counted from, and taken literally it would be far shorter than any archer's draw.

There remains a question of transfer that the article does not address. The clamp holds the bow tightly, and the second machine exists precisely because the first left it loose and the grip did not repeat. An archer's hand, though, does not grip: the bow rests and the hand stays soft. The clamp's forward jump is a good idea in that direction, but a rigid grip behaves differently from a hand with respect to twisting the bow, which is the thing that moves the arrow horizontally most. Arrows ranked by a rigidly gripped machine might not rank the same way in a person's hand.

Finally, the introduction ties the machine to a psychological benefit, that an archer confident of having excluded flawed arrows would be less anxious. It is a motivation, not a datum: in the article nobody measures anxiety, and no archer appears.

For an archer this article is not a result, it is a machine design, and it is worth three ideas that can be taken from it anyway.

The first is the clicker-triggered release. The machine hears the click with a microphone, recognises a sound around 1400 hertz lasting a tenth and a half of a second and only then opens the fingers. The reason is written out: if the draw length changes, the arrows spread vertically. With the clicker as the signal the vertical spread is smaller than without, and this, although shown only as a graph, is the mechanical confirmation of something an archer does by habit, going on the clicker and not before.

The second is the lesson about the grip, and it comes from the first machine's faults. When the bow was not clamped it came loose on every shot and next time the grip landed in a different place, with reduced accuracy. It is not a measurement on a human hand, but it says what a grip that does not repeat costs, and in the crudest possible terms, because here that was the only variable.

The third is mass. A hundred and fourteen kilograms against twenty-four, an iron arm instead of aluminium: almost all this group's work went into taking vibration out of the structure rather than into improving the shot. Anyone building a stand or a support for testing equipment has the pointer here, that the bench weighs more than the method.

What cannot be taken home is the arrow selection. The machine is declared able to discard abnormal arrows, but the test is on six arrows, two of them already known to be flawed, and the exclusion criterion is a circle built on the standard deviation of the four good ones, that is on the same arrows that then come out inside. Without the standard deviation in millimetres and without a comparison between the machine's noise and the differences between arrows, there is no knowing how small a defect this machine finds.

Anyone wanting to try selecting arrows with a machine, their own or a club's, does get from the article the outline of how to do it checkably: measure the spread of the same arrow repeated many times, which is the bench's noise, then the spread between different arrows, and compare the two numbers. Until the first is clearly smaller than the second, the machine is selecting nothing.