Arnaud VALLEY
Mirror with some correction
Dependencies: mbed FastIO FastPWM USBDevice
Diff: Plunger/rotarySensor.h
- Revision:
- 100:1ff35c07217c
- Child:
- 102:41d49e78c253
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Plunger/rotarySensor.h Thu Nov 28 23:18:23 2019 +0000
@@ -0,0 +1,497 @@
+// Plunger sensor implementation for rotary absolute encoders
+//
+// This implements the plunger interfaces for rotary absolute encoders. A
+// rotary encoder measures the angle of a rotating shaft. For plunger sensing,
+// we can convert the plunger's linear motion into angular motion using a
+// mechanical linkage between the plunger rod and a rotating shaft positioned
+// at a fixed point, somewhere nearby, but off of the plunger's axis:
+//
+// =X=======================|=== <- plunger, X = connector attachment point
+// \
+// \ <- connector between plunger and shaft
+// \
+// * <- rotating shaft, at a fixed position
+//
+// As the plunger moves, the angle of the connector relative to the fixed
+// shaft position changes in a predictable way, so by measuring the rotational
+// position of the shaft at any given time, we can infer the plunger's
+// linear position.
+//
+// (Note that the mechanical diagram is simplified for ASCII art purposes.
+// What's not shown is that the distance between the rotating shaft and the
+// "X" connection point on the plunger varies as the plunger moves, so the
+// mechanical linkage requires some way to accommodate that changing length.
+// One way is to use a spring as the linkage; another is to use a rigid
+// connector with a sliding coupling at one or the other end. We leave
+// these details up to the mechanical design; the software isn't affected
+// as long as the basic relationship between linear and angular motion as
+// shown in the diagram be achieved.)
+//
+//
+// Translating the angle to a linear position
+//
+// There are two complications to translating the angular reading back to
+// a linear plunger position.
+//
+// 1. We have to consider the sensor's zero point to be arbitrary. That means
+// that the zero point could be somewhere within the plunger's travel range,
+// so readings might "wrap" - e.g., we might see a series of readings when
+// the plunger is moving in one direction like 4050, 4070, 4090, 14, 34 (note
+// how we've "wrapped" past the 4096 boundary).
+//
+// To deal with this, we have to make a couple of assumptions:
+//
+// - The park position is at about 1/6 of the overall travel range
+// - The total angular travel range is less than one full revolution
+//
+// With those assumptions in hand, we can bias the raw readings to the
+// park position, and then take them modulo the raw scale. That will
+// ensure that readings wrap properly, regardless of where the raw zero
+// point lies.
+//
+// 2. Going back to the original diagram, you can see that the angle doesn't
+// vary linearly with the plunger position. It actually varies sinusoidally.
+// Let's use the vertical line between the plunger and the rotation point as
+// the zero-degree reference point. To figure the plunger position, then,
+// we need to figure the difference between the raw angle reading and the
+// zero-degree point; call this theta. Let L be the position of the plunger
+// relative to the vertical reference point, let D be the length of the
+// vertical reference point line, and let H by the distance from the rotation
+// point to the plunger connection point. This is a right triangle with
+// hypotenuse H and sides L and D. D is a constant, because the rotation
+// point never moves, and the plunger never moves vertically. Thus we can
+// calculate D = H*cos(theta) and L = H*sin(theta). D is a constant, so
+// we can figure H = D/cos(theta) hence L = D*sin(theta)/cos(theta) or
+// D*tan(theta). If we wanted to know the true position in real-world
+// units, we'd have to know D, but only need arbitrary linear units, so
+// we can choose whatever value for D we find convenient: in particular,
+// a value that gives us the desired range and resolution for the final
+// result.
+//
+// Note that the tangent diverges at +/-90 degrees, but that's not a problem
+// for the mechanical setup we've described, as the motion is inherently
+// limited to stay within this range.
+//
+// There's still one big piece missing here: we somehow have to know where
+// that vertical zero point lies. That's something we can only learn by
+// calibration. Unfortunately, we don't have a good way to detect this
+// directly. We *could* ask the user to look inside the cabinet and press
+// a button when the needle is straight up, but that seems too cumbersome.
+// What we'll do instead is provide some mechanical installation guidelines
+// about where the rotation point should be positioned, and then use the
+// full range to deduce the vertical position.
+//
+// The full range we actually have after calibration consists of the park
+// position and the maximum retracted position. We could in principle also
+// calibrate the maximum forward position, but that can't be read as reliably
+// as the other two, because the barrel spring makes it difficult for the
+// user to be sure they've pushed it all the way forward. Since we can
+// extract the information we need from the park and max retract positions,
+// it's better to rely on those alone and not ask for information that the
+// user can't as easily provide. Given these positions, AND the assumption
+// that the rotation point is at the midpoint of the plunger travel range,
+// we can do some rather grungy trig work to come up with a formula for the
+// angle between the park position and the vertical:
+//
+// let C1 = 1 1/32" (distance from midpoint to park),
+// C2 = 1 17/32" (distance from midpoint to max retract),
+// C = C2/C1 = 1.48484849,
+// alpha = angle from park to vertical,
+// beta = angle from max retract to vertical
+// theta = alpha + beta = angle from park to max retract, known from calibration,
+// T = tan(theta);
+//
+// then
+// alpha = atan(sqrt(4*T*T*C + C^2 + 2*C + 1) - C - 1)/(2*T*C))
+//
+// Did I mention this was grungy? At any rate, everything going into this
+// formula is either constant or known from the calibration, so we can
+// pre-compute alpha and store it after each calibration operation. And
+// knowing alpha, we can translate an angle reading from the sensor to an
+// angle relative to the vertical, which we can plug into D*tan(angle) to
+// get a linear reading.
+//
+// If you're wondering how we derived that ugly formula, read on. Start
+// with the basic relationships D*tan(alpha) = C1 and D*tan(beta) = C2.
+// This lets us write tan(beta) in terms of tan(alpha) as
+// C2/C1*tan(alpha) = C*tan(alpha). We can combine this with an identity
+// for the tan of a sum of angles:
+//
+// tan(alpha + beta) = (tan(alpha) + tan(beta))/(1 - tan(alpha)*tan(beta))
+//
+// to obtain:
+//
+// tan(theta) = tan(alpha + beta) = (1 + C*tan(alpha))/(1 - C*tan^2(alpha))
+//
+// Everything here except alpha is known, so we now have a quadratic equation
+// for tan(alpha). We can solve that by cranking through the normal algorithm
+// for solving a quadratic equation, arriving at the solution above.
+//
+//
+// Choosing an install position
+//
+// There are two competing factors in choosing the optimal "D". On the one
+// hand, you'd like D to be as large as possible, to maximum linearity of the
+// tan function used to translate angle to linear position. Higher linearity
+// gives us greater immunity to variations in the precise centering of the
+// rotation axis in the plunger travel range. tan() is pretty linear within
+// about +/- 30 degrees. On the other hand, you'd like D to be as small as
+// possible so that we get the largest overall angle range. Our sensor has
+// a fixed angular resolution, so the more of the overall circle we use, the
+// more sensor increments we have over the range, and thus the better
+// effective linear resolution.
+//
+// Let's do some calculations for various "D" values (vertical distance
+// between rotation point and plunger rod). For the effective DPI, we'll
+// 12-bit angular resolution, per the AEAT-6012 sensor.
+//
+// D theta(max) eff dpi theta(park)
+// -----------------------------------------------
+// 1 17/32" 45 deg 341 34 deg
+// 2" 37 deg 280 27 deg
+// 2 21/32" 30 deg 228 21 deg
+// 3 1/4" 25 deg 190 17 deg
+// 4 3/16" 20 deg 152 14 deg
+//
+// I'd consider 50 dpi to be the minimum for acceptable performance, 100 dpi
+// to be excellent, and anything above 300 dpi to be diminishing returns. So
+// for a 12-bit sensor, 2" looks like the sweet spot. It doesn't take us far
+// outside of the +/-30 deg zone of tan() linearity, and it achieves almost
+// 300 dpi of effective linear resolution. I'd stop there are not try to
+// push the angular resolution higher with a shorter D; with the 45 deg
+// theta(max) at D = 1-17/32", we'd get a lovely DPI level of 341, but at
+// the cost of getting pretty non-linear around the ends of the plunger
+// travel. Our math corrects for the non-linearity, but the more of that
+// correction we need, the more sensitive the whole contraption becomes to
+// getting the sensor positioning exactly right. The closer we can stay to
+// the linear approximation, the more tolerant we are of inexact sensor
+// positioning.
+//
+//
+// Supported sensors
+//
+// * AEAT-6012-A06. This is a magnetic absolute encoder with 12-bit
+// resolution. It linearly encodes one full (360 degree) rotation in
+// 4096 increments, so each increment represents 360/4096 = .088 degrees.
+//
+// The base class doesn't actually care much about the sensor type; all it
+// needs from the sensor is an angle reading represented on an arbitrary
+// linear scale. ("Linear" in the angle, so that one increment represents
+// a fixed number of degrees of arc. The full scale can represent one full
+// turn but doesn't have to, as long as the scale is linear over the range
+// covered.) To add new sensor types, you just need to add the code to
+// interface to the physical sensor and return its reading on an arbitrary
+// linear scale.
+
+#ifndef _ROTARYSENSOR_H_
+#define _ROTARYSENSOR_H_
+
+#include "FastInterruptIn.h"
+#include "AEAT6012.h"
+
+// The conversion from raw sensor reading to linear position involves a
+// bunch of translations to different scales and unit systems. To help
+// keep things straight, let's give each scale a name:
+//
+// * "Raw" refers to the readings directly from the sensor. These are
+// unsigned ints in the range 0..scaleMax, and represent angles in a
+// unit system where one increment equals 360/scaleMax degrees. The
+// zero point is arbitrary, determined by the physical orientation
+// of the sensor.
+//
+// * "Biased" refers to angular units with a zero point equal to the
+// park position. This uses the same units as the "raw" system, but
+// the zero point is adjusted so that 0 always means the park position.
+// Negative values are forward of the park position. This scale is
+// also adjusted for wrapping, by ensuring that the value lies in the
+// range -(maximum forward excursion) to +(scale max - max fwd excursion).
+// Any values below or above the range are bumped up or down (respectively)
+// to wrap them back into the range.
+//
+// * "Linear" refers to the final linear results, in joystick units, on
+// the abstract integer scale from 0..65535 used by the generic plunger
+// base class.
+//
+class PlungerSensorRotary: public PlungerSensor
+{
+public:
+ PlungerSensorRotary(int scaleMax, float radiansPerSensorUnit) :
+ PlungerSensor(65535),
+ scaleMax(scaleMax),
+ radiansPerSensorUnit(radiansPerSensorUnit)
+ {
+ // start our sample timer with an arbitrary zero point of now
+ timer.start();
+
+ // clear the timing statistics
+ nReads = 0;
+ totalReadTime = 0;
+
+ // Pre-calculate the maximum forward excursion distance, in raw
+ // units. For our reference mechanical setup with "D" in a likely
+ // range, theta(max) is always about 10 degrees higher than
+ // theta(park). 10 degrees is about 1/36 of the overall circle,
+ // which is the same as 1/36 of the sensor scale. To be
+ // conservative, allow for about 3X that, so allow 1/12 of scale
+ // as the maximum forward excursion. For wrapping purposes, we'll
+ // consider any reading outside of the range from -(excursion)
+ // to +(scaleMax - excursion) to be wrapped.
+ maxForwardExcursion = scaleMax/12;
+
+ // reset the calibration counters
+ biasedMinObserved = biasedMaxObserved = 0;
+ }
+
+ // Restore the saved calibration at startup
+ virtual void restoreCalibration(Config &cfg)
+ {
+ // only proceed if there's calibration data to retrieve
+ if (cfg.plunger.cal.calibrated)
+ {
+ // we store the raw park angle in raw0
+ rawParkAngle = cfg.plunger.cal.raw0;
+
+ // we store biased max angle in raw1
+ biasedMax = cfg.plunger.cal.raw1;
+ }
+ else
+ {
+ // Use the current sensor reading as the initial guess at the
+ // park position. The system is usually powered up with the
+ // plunger at the neutral position, so this is a good guess in
+ // most cases. If the plunger has been calibrated, we'll restore
+ // the better guess when we restore the configuration later on in
+ // the initialization process.
+ rawParkAngle = 0;
+ readSensor(rawParkAngle);
+
+ // Set an initial wild guess at a range equal to +/-35 degrees.
+ // Note that this is in the "biased" coordinate system - raw
+ // units, but relative to the park angle. The park angle is
+ // about 25 degrees in this setup.
+ biasedMax = (35 + 25) * scaleMax/360;
+ }
+
+ // recalculate the vertical angle
+ updateAlpha();
+ }
+
+ // Begin calibration
+ virtual void beginCalibration(Config &)
+ {
+ // Calibration starts out with the plunger at the park position, so
+ // we can take the current sensor reading to be the park position.
+ rawParkAngle = 0;
+ readSensor(rawParkAngle);
+
+ // Reset the observed calibration counters
+ biasedMinObserved = biasedMaxObserved = 0;
+ }
+
+ // End calibration
+ virtual void endCalibration(Config &cfg)
+ {
+ // apply the observed maximum angle
+ biasedMax = biasedMaxObserved;
+
+ // recalculate the vertical angle
+ updateAlpha();
+
+ // save our raw configuration data
+ cfg.plunger.cal.raw0 = static_cast<uint16_t>(rawParkAngle);
+ cfg.plunger.cal.raw1 = static_cast<uint16_t>(biasedMax);
+
+ // Refigure the range for the generic code
+ cfg.plunger.cal.min = biasedAngleToLinear(biasedMinObserved);
+ cfg.plunger.cal.max = biasedAngleToLinear(biasedMaxObserved);
+ cfg.plunger.cal.zero = biasedAngleToLinear(0);
+ }
+
+ // figure the average scan time in microseconds
+ virtual uint32_t getAvgScanTime()
+ {
+ return nReads == 0 ? 0 : static_cast<uint32_t>(totalReadTime / nReads);
+ }
+
+ // read the sensor
+ virtual bool readRaw(PlungerReading &r)
+ {
+ // note the starting time for the reading
+ uint32_t t0 = timer.read_us();
+
+ // read the angular position
+ int angle;
+ if (!readSensor(angle))
+ return false;
+
+ // Refigure the angle relative to the raw park position. This
+ // is the "biased" angle.
+ angle -= rawParkAngle;
+
+ // Adjust for wrapping.
+ //
+ // An angular sensor reports the position on a circular scale, for
+ // obvious reasons, so there's some point along the circle where the
+ // angle is zero. One tick before that point reads as the maximum
+ // angle on the scale, so we say that the scale "wraps" at that point.
+ //
+ // To correct for this, we can look to the layout of the mechanical
+ // setup to constrain the values. Consider anything below the maximum
+ // forward exclusion to be wrapped on the low side, and consider
+ // anything outside of the complementary range on the high side to
+ // be wrapped on the high side.
+ if (angle < -maxForwardExcursion)
+ angle += scaleMax;
+ else if (angle >= scaleMax - maxForwardExcursion)
+ angle -= scaleMax;
+
+ // Note if this is the highest/lowest observed reading on the biased
+ // scale since the last calibration started.
+ if (angle > biasedMaxObserved)
+ biasedMaxObserved = angle;
+ if (angle < biasedMinObserved)
+ biasedMinObserved = angle;
+
+ // figure the linear result
+ r.pos = biasedAngleToLinear(angle);
+
+ // Set the timestamp on the reading to right now
+ uint32_t now = timer.read_us();
+ r.t = now;
+
+ // count the read statistics
+ totalReadTime += now - t0;
+ nReads += 1;
+
+ // success
+ return true;
+ }
+
+private:
+ // Read the underlying sensor - implemented by the hardware-specific
+ // subclasses. Returns true on success, false if the sensor can't
+ // be read. The angle is returned in raw sensor units.
+ virtual bool readSensor(int &angle) = 0;
+
+ // Convert a biased angle value to a linear reading
+ int biasedAngleToLinear(int angle)
+ {
+ // Translate to an angle relative to the vertical, in sensor units
+ int angleFromVert = angle - alpha;
+
+ // Translate the angle in sensor units to radians
+ float theta = static_cast<float>(angleFromVert) * radiansPerSensorUnit;
+
+ // Calculate the linear position
+ return static_cast<int>(tanf(theta) * linearScaleFactor);
+ }
+
+ // Update the estimation of the vertical angle, based on the angle
+ // between the park position and maximum retraction point.
+ void updateAlpha()
+ {
+ // See the comments at the top of the file for details on this
+ // formula. This figures the angle between the park position
+ // and the vertical by applying the known constraints of the
+ // mechanical setup: the known length of a standard plunger,
+ // and the requirement that the rotation axis be placed at
+ // roughly the midpoint of the plunger travel.
+ const float C = 1.4848489f; // 1-17/32" / 1-1/32"
+ float T = tanf(biasedMax * radiansPerSensorUnit);
+ float a = atanf((sqrtf(4*T*T*C + C*C + 2*C + 1) - C - 1)/(2*T*C));
+
+ // Convert back to sensor units. Note that alpha represents
+ // a relative angle between two specific points, so it's not
+ // further biased to any absolute point.
+ alpha = static_cast<int>(a / radiansPerSensorUnit);
+
+ // While we're at it, figure the linear conversion factor. The
+ // goal is to use most of the abstract axis range, 0..65535.
+ // To avoid overflow, though, leave a little headroom.
+ const float safeMax = 60000.0f;
+ linearScaleFactor = static_cast<int>(safeMax /
+ tanf(static_cast<float>(biasedMax - alpha) * radiansPerSensorUnit));
+ }
+
+ // Maximum raw angular reading from the sensor. The sensor's readings
+ // will always be on a scale from 0..maxAngle.
+ int scaleMax;
+
+ // Radians per sensor unit. This is a constant for the sensor.
+ float radiansPerSensorUnit;
+
+ // Pre-calculated value of the maximum forward excursion, in raw units.
+ int maxForwardExcursion;
+
+ // Raw reading at the park position. We use this to handle "wrapping",
+ // if the sensor's raw zero reading position is within the plunger travel
+ // range. All readings are taken to be within
+ int rawParkAngle;
+
+ // Biased maximum angle. This is the angle at the maximum retracted
+ // position, in biased units (sensor units, relative to the park angle).
+ int biasedMax;
+
+ // Mininum and maximum angle observed since last calibration start, on
+ // the biased scale
+ int biasedMinObserved;
+ int biasedMaxObserved;
+
+ // The "alpha" angle - the angle between the park position and the
+ // vertical line between the rotation axis and the plunger. This is
+ // represented in sensor units.
+ int alpha;
+
+ // The linear scaling factor, applied in our trig calculation from
+ // angle to linear position. This corresponds to the distance from
+ // the rotation center to the plunger rod, but since the linear result
+ // is in abstract joystick units, this distance is likewise in abstract
+ // units. The value isn't chosen to correspond to any real-world
+ // distance units, but rather to yield a joystick result that takes
+ // advantage of most of the available axis range, to minimize rounding
+ // errors when converting between scales.
+ float linearScaleFactor;
+
+ // timer for input timestamps and read timing measurements
+ Timer timer;
+
+ // read timing statistics
+ uint64_t totalReadTime;
+ uint64_t nReads;
+
+ // Keep track of when calibration is in progress. The calibration
+ // procedure is usually handled by the generic main loop code, but
+ // in this case, we have to keep track of some of the raw sensor
+ // data during calibration for our own internal purposes.
+ bool calibrating;
+};
+
+// Specialization for the AEAT-601X sensors
+template<int nDataBits> class PlungerSensorAEAT601X : public PlungerSensorRotary
+{
+public:
+ PlungerSensorAEAT601X(PinName csPin, PinName clkPin, PinName doPin) :
+ PlungerSensorRotary((1 << nDataBits) - 1, 6.283185f/((1 << nDataBits) - 1)),
+ aeat(csPin, clkPin, doPin)
+ {
+ // Make sure the sensor has had time to finish initializing.
+ // Power-up time (tCF) from the data sheet is 20ms for the 12-bit
+ // version, 50ms for the 10-bit version.
+ wait_ms(nDataBits == 12 ? 20 :
+ nDataBits == 10 ? 50 :
+ 50);
+ }
+
+ // read the angle
+ virtual bool readSensor(int &angle)
+ {
+ angle = aeat.readAngle();
+ return true;
+ }
+
+protected:
+ // physical sensor interface
+ AEAT601X<nDataBits> aeat;
+};
+
+#endif