Add new code

Signed-off-by: Carlos Maiolino <[email protected]>

4 files changed, 1626 insertions, 0 deletions

diff --git a/Arduino/libraries/AccelStepper/src/AccelStepper.cpp b/Arduino/libraries/AccelStepper/src/AccelStepper.cpp
new file mode 100644
index 0000000..54535cc
--- /dev/null
+++ b/Arduino/libraries/AccelStepper/src/AccelStepper.cpp
@@ -0,0 +1,679 @@
+// AccelStepper.cpp
+//
+// Copyright (C) 2009-2020 Mike McCauley
+// $Id: AccelStepper.cpp,v 1.24 2020/04/20 00:15:03 mikem Exp mikem $
+
+#include "AccelStepper.h"
+
+#if 0
+// Some debugging assistance
+void dump(uint8_t* p, int l)
+{
+    int i;
+
+    for (i = 0; i < l; i++)
+    {
+	Serial.print(p[i], HEX);
+	Serial.print(" ");
+    }
+    Serial.println("");
+}
+#endif
+
+void AccelStepper::moveTo(long absolute)
+{
+    if (_targetPos != absolute)
+    {
+	_targetPos = absolute;
+	computeNewSpeed();
+	// compute new n?
+    }
+}
+
+void AccelStepper::move(long relative)
+{
+    moveTo(_currentPos + relative);
+}
+
+// Implements steps according to the current step interval
+// You must call this at least once per step
+// returns true if a step occurred
+boolean AccelStepper::runSpeed()
+{
+    // Dont do anything unless we actually have a step interval
+    if (!_stepInterval)
+	return false;
+
+    unsigned long time = micros();   
+    if (time - _lastStepTime >= _stepInterval)
+    {
+	if (_direction == DIRECTION_CW)
+	{
+	    // Clockwise
+	    _currentPos += 1;
+	}
+	else
+	{
+	    // Anticlockwise  
+	    _currentPos -= 1;
+	}
+	step(_currentPos);
+
+	_lastStepTime = time; // Caution: does not account for costs in step()
+
+	return true;
+    }
+    else
+    {
+	return false;
+    }
+}
+
+long AccelStepper::distanceToGo()
+{
+    return _targetPos - _currentPos;
+}
+
+long AccelStepper::targetPosition()
+{
+    return _targetPos;
+}
+
+long AccelStepper::currentPosition()
+{
+    return _currentPos;
+}
+
+// Useful during initialisations or after initial positioning
+// Sets speed to 0
+void AccelStepper::setCurrentPosition(long position)
+{
+    _targetPos = _currentPos = position;
+    _n = 0;
+    _stepInterval = 0;
+    _speed = 0.0;
+}
+
+// Subclasses can override
+unsigned long AccelStepper::computeNewSpeed()
+{
+    long distanceTo = distanceToGo(); // +ve is clockwise from curent location
+
+    long stepsToStop = (long)((_speed * _speed) / (2.0 * _acceleration)); // Equation 16
+
+    if (distanceTo == 0 && stepsToStop <= 1)
+    {
+	// We are at the target and its time to stop
+	_stepInterval = 0;
+	_speed = 0.0;
+	_n = 0;
+	return _stepInterval;
+    }
+
+    if (distanceTo > 0)
+    {
+	// We are anticlockwise from the target
+	// Need to go clockwise from here, maybe decelerate now
+	if (_n > 0)
+	{
+	    // Currently accelerating, need to decel now? Or maybe going the wrong way?
+	    if ((stepsToStop >= distanceTo) || _direction == DIRECTION_CCW)
+		_n = -stepsToStop; // Start deceleration
+	}
+	else if (_n < 0)
+	{
+	    // Currently decelerating, need to accel again?
+	    if ((stepsToStop < distanceTo) && _direction == DIRECTION_CW)
+		_n = -_n; // Start accceleration
+	}
+    }
+    else if (distanceTo < 0)
+    {
+	// We are clockwise from the target
+	// Need to go anticlockwise from here, maybe decelerate
+	if (_n > 0)
+	{
+	    // Currently accelerating, need to decel now? Or maybe going the wrong way?
+	    if ((stepsToStop >= -distanceTo) || _direction == DIRECTION_CW)
+		_n = -stepsToStop; // Start deceleration
+	}
+	else if (_n < 0)
+	{
+	    // Currently decelerating, need to accel again?
+	    if ((stepsToStop < -distanceTo) && _direction == DIRECTION_CCW)
+		_n = -_n; // Start accceleration
+	}
+    }
+
+    // Need to accelerate or decelerate
+    if (_n == 0)
+    {
+	// First step from stopped
+	_cn = _c0;
+	_direction = (distanceTo > 0) ? DIRECTION_CW : DIRECTION_CCW;
+    }
+    else
+    {
+	// Subsequent step. Works for accel (n is +_ve) and decel (n is -ve).
+	_cn = _cn - ((2.0 * _cn) / ((4.0 * _n) + 1)); // Equation 13
+	_cn = max(_cn, _cmin); 
+    }
+    _n++;
+    _stepInterval = _cn;
+    _speed = 1000000.0 / _cn;
+    if (_direction == DIRECTION_CCW)
+	_speed = -_speed;
+
+#if 0
+    Serial.println(_speed);
+    Serial.println(_acceleration);
+    Serial.println(_cn);
+    Serial.println(_c0);
+    Serial.println(_n);
+    Serial.println(_stepInterval);
+    Serial.println(distanceTo);
+    Serial.println(stepsToStop);
+    Serial.println("-----");
+#endif
+    return _stepInterval;
+}
+
+// Run the motor to implement speed and acceleration in order to proceed to the target position
+// You must call this at least once per step, preferably in your main loop
+// If the motor is in the desired position, the cost is very small
+// returns true if the motor is still running to the target position.
+boolean AccelStepper::run()
+{
+    if (runSpeed())
+	computeNewSpeed();
+    return _speed != 0.0 || distanceToGo() != 0;
+}
+
+AccelStepper::AccelStepper(uint8_t interface, uint8_t pin1, uint8_t pin2, uint8_t pin3, uint8_t pin4, bool enable)
+{
+    _interface = interface;
+    _currentPos = 0;
+    _targetPos = 0;
+    _speed = 0.0;
+    _maxSpeed = 0.0;
+    _acceleration = 0.0;
+    _sqrt_twoa = 1.0;
+    _stepInterval = 0;
+    _minPulseWidth = 1;
+    _enablePin = 0xff;
+    _lastStepTime = 0;
+    _pin[0] = pin1;
+    _pin[1] = pin2;
+    _pin[2] = pin3;
+    _pin[3] = pin4;
+    _enableInverted = false;
+    
+    // NEW
+    _n = 0;
+    _c0 = 0.0;
+    _cn = 0.0;
+    _cmin = 1.0;
+    _direction = DIRECTION_CCW;
+
+    int i;
+    for (i = 0; i < 4; i++)
+	_pinInverted[i] = 0;
+    if (enable)
+	enableOutputs();
+    // Some reasonable default
+    setAcceleration(1);
+    setMaxSpeed(1);
+}
+
+AccelStepper::AccelStepper(void (*forward)(), void (*backward)())
+{
+    _interface = 0;
+    _currentPos = 0;
+    _targetPos = 0;
+    _speed = 0.0;
+    _maxSpeed = 0.0;
+    _acceleration = 0.0;
+    _sqrt_twoa = 1.0;
+    _stepInterval = 0;
+    _minPulseWidth = 1;
+    _enablePin = 0xff;
+    _lastStepTime = 0;
+    _pin[0] = 0;
+    _pin[1] = 0;
+    _pin[2] = 0;
+    _pin[3] = 0;
+    _forward = forward;
+    _backward = backward;
+
+    // NEW
+    _n = 0;
+    _c0 = 0.0;
+    _cn = 0.0;
+    _cmin = 1.0;
+    _direction = DIRECTION_CCW;
+
+    int i;
+    for (i = 0; i < 4; i++)
+	_pinInverted[i] = 0;
+    // Some reasonable default
+    setAcceleration(1);
+    setMaxSpeed(1);
+}
+
+void AccelStepper::setMaxSpeed(float speed)
+{
+    if (speed < 0.0)
+       speed = -speed;
+    if (_maxSpeed != speed)
+    {
+	_maxSpeed = speed;
+	_cmin = 1000000.0 / speed;
+	// Recompute _n from current speed and adjust speed if accelerating or cruising
+	if (_n > 0)
+	{
+	    _n = (long)((_speed * _speed) / (2.0 * _acceleration)); // Equation 16
+	    computeNewSpeed();
+	}
+    }
+}
+
+float   AccelStepper::maxSpeed()
+{
+    return _maxSpeed;
+}
+
+void AccelStepper::setAcceleration(float acceleration)
+{
+    if (acceleration == 0.0)
+	return;
+    if (acceleration < 0.0)
+      acceleration = -acceleration;
+    if (_acceleration != acceleration)
+    {
+	// Recompute _n per Equation 17
+	_n = _n * (_acceleration / acceleration);
+	// New c0 per Equation 7, with correction per Equation 15
+	_c0 = 0.676 * sqrt(2.0 / acceleration) * 1000000.0; // Equation 15
+	_acceleration = acceleration;
+	computeNewSpeed();
+    }
+}
+
+float   AccelStepper::acceleration()
+{
+    return _acceleration;
+}
+
+void AccelStepper::setSpeed(float speed)
+{
+    if (speed == _speed)
+        return;
+    speed = constrain(speed, -_maxSpeed, _maxSpeed);
+    if (speed == 0.0)
+	_stepInterval = 0;
+    else
+    {
+	_stepInterval = fabs(1000000.0 / speed);
+	_direction = (speed > 0.0) ? DIRECTION_CW : DIRECTION_CCW;
+    }
+    _speed = speed;
+}
+
+float AccelStepper::speed()
+{
+    return _speed;
+}
+
+// Subclasses can override
+void AccelStepper::step(long step)
+{
+    switch (_interface)
+    {
+        case FUNCTION:
+            step0(step);
+            break;
+
+	case DRIVER:
+	    step1(step);
+	    break;
+    
+	case FULL2WIRE:
+	    step2(step);
+	    break;
+    
+	case FULL3WIRE:
+	    step3(step);
+	    break;  
+
+	case FULL4WIRE:
+	    step4(step);
+	    break;  
+
+	case HALF3WIRE:
+	    step6(step);
+	    break;  
+		
+	case HALF4WIRE:
+	    step8(step);
+	    break;  
+    }
+}
+
+long AccelStepper::stepForward()
+{
+    // Clockwise
+    _currentPos += 1;
+	step(_currentPos);
+	_lastStepTime = micros();
+    return _currentPos;
+}
+
+long AccelStepper::stepBackward()
+{
+    // Counter-clockwise
+    _currentPos -= 1;
+	step(_currentPos);
+	_lastStepTime = micros();
+    return _currentPos;
+}
+
+// You might want to override this to implement eg serial output
+// bit 0 of the mask corresponds to _pin[0]
+// bit 1 of the mask corresponds to _pin[1]
+// ....
+void AccelStepper::setOutputPins(uint8_t mask)
+{
+    uint8_t numpins = 2;
+    if (_interface == FULL4WIRE || _interface == HALF4WIRE)
+	numpins = 4;
+    else if (_interface == FULL3WIRE || _interface == HALF3WIRE)
+	numpins = 3;
+    uint8_t i;
+    for (i = 0; i < numpins; i++)
+	digitalWrite(_pin[i], (mask & (1 << i)) ? (HIGH ^ _pinInverted[i]) : (LOW ^ _pinInverted[i]));
+}
+
+// 0 pin step function (ie for functional usage)
+void AccelStepper::step0(long step)
+{
+    (void)(step); // Unused
+    if (_speed > 0)
+	_forward();
+    else
+	_backward();
+}
+
+// 1 pin step function (ie for stepper drivers)
+// This is passed the current step number (0 to 7)
+// Subclasses can override
+void AccelStepper::step1(long step)
+{
+    (void)(step); // Unused
+
+    // _pin[0] is step, _pin[1] is direction
+    setOutputPins(_direction ? 0b10 : 0b00); // Set direction first else get rogue pulses
+    setOutputPins(_direction ? 0b11 : 0b01); // step HIGH
+    // Caution 200ns setup time 
+    // Delay the minimum allowed pulse width
+    delayMicroseconds(_minPulseWidth);
+    setOutputPins(_direction ? 0b10 : 0b00); // step LOW
+}
+
+
+// 2 pin step function
+// This is passed the current step number (0 to 7)
+// Subclasses can override
+void AccelStepper::step2(long step)
+{
+    switch (step & 0x3)
+    {
+	case 0: /* 01 */
+	    setOutputPins(0b10);
+	    break;
+
+	case 1: /* 11 */
+	    setOutputPins(0b11);
+	    break;
+
+	case 2: /* 10 */
+	    setOutputPins(0b01);
+	    break;
+
+	case 3: /* 00 */
+	    setOutputPins(0b00);
+	    break;
+    }
+}
+// 3 pin step function
+// This is passed the current step number (0 to 7)
+// Subclasses can override
+void AccelStepper::step3(long step)
+{
+    switch (step % 3)
+    {
+	case 0:    // 100
+	    setOutputPins(0b100);
+	    break;
+
+	case 1:    // 001
+	    setOutputPins(0b001);
+	    break;
+
+	case 2:    //010
+	    setOutputPins(0b010);
+	    break;
+	    
+    }
+}
+
+// 4 pin step function for half stepper
+// This is passed the current step number (0 to 7)
+// Subclasses can override
+void AccelStepper::step4(long step)
+{
+    switch (step & 0x3)
+    {
+	case 0:    // 1010
+	    setOutputPins(0b0101);
+	    break;
+
+	case 1:    // 0110
+	    setOutputPins(0b0110);
+	    break;
+
+	case 2:    //0101
+	    setOutputPins(0b1010);
+	    break;
+
+	case 3:    //1001
+	    setOutputPins(0b1001);
+	    break;
+    }
+}
+
+// 3 pin half step function
+// This is passed the current step number (0 to 7)
+// Subclasses can override
+void AccelStepper::step6(long step)
+{
+    switch (step % 6)
+    {
+	case 0:    // 100
+	    setOutputPins(0b100);
+            break;
+	    
+        case 1:    // 101
+	    setOutputPins(0b101);
+            break;
+	    
+	case 2:    // 001
+	    setOutputPins(0b001);
+            break;
+	    
+        case 3:    // 011
+	    setOutputPins(0b011);
+            break;
+	    
+	case 4:    // 010
+	    setOutputPins(0b010);
+            break;
+	    
+	case 5:    // 011
+	    setOutputPins(0b110);
+            break;
+	    
+    }
+}
+
+// 4 pin half step function
+// This is passed the current step number (0 to 7)
+// Subclasses can override
+void AccelStepper::step8(long step)
+{
+    switch (step & 0x7)
+    {
+	case 0:    // 1000
+	    setOutputPins(0b0001);
+            break;
+	    
+        case 1:    // 1010
+	    setOutputPins(0b0101);
+            break;
+	    
+	case 2:    // 0010
+	    setOutputPins(0b0100);
+            break;
+	    
+        case 3:    // 0110
+	    setOutputPins(0b0110);
+            break;
+	    
+	case 4:    // 0100
+	    setOutputPins(0b0010);
+            break;
+	    
+        case 5:    //0101
+	    setOutputPins(0b1010);
+            break;
+	    
+	case 6:    // 0001
+	    setOutputPins(0b1000);
+            break;
+	    
+        case 7:    //1001
+	    setOutputPins(0b1001);
+            break;
+    }
+}
+    
+// Prevents power consumption on the outputs
+void    AccelStepper::disableOutputs()
+{   
+    if (! _interface) return;
+
+    setOutputPins(0); // Handles inversion automatically
+    if (_enablePin != 0xff)
+    {
+        pinMode(_enablePin, OUTPUT);
+        digitalWrite(_enablePin, LOW ^ _enableInverted);
+    }
+}
+
+void    AccelStepper::enableOutputs()
+{
+    if (! _interface) 
+	return;
+
+    pinMode(_pin[0], OUTPUT);
+    pinMode(_pin[1], OUTPUT);
+    if (_interface == FULL4WIRE || _interface == HALF4WIRE)
+    {
+        pinMode(_pin[2], OUTPUT);
+        pinMode(_pin[3], OUTPUT);
+    }
+    else if (_interface == FULL3WIRE || _interface == HALF3WIRE)
+    {
+        pinMode(_pin[2], OUTPUT);
+    }
+
+    if (_enablePin != 0xff)
+    {
+        pinMode(_enablePin, OUTPUT);
+        digitalWrite(_enablePin, HIGH ^ _enableInverted);
+    }
+}
+
+void AccelStepper::setMinPulseWidth(unsigned int minWidth)
+{
+    _minPulseWidth = minWidth;
+}
+
+void AccelStepper::setEnablePin(uint8_t enablePin)
+{
+    _enablePin = enablePin;
+
+    // This happens after construction, so init pin now.
+    if (_enablePin != 0xff)
+    {
+        pinMode(_enablePin, OUTPUT);
+        digitalWrite(_enablePin, HIGH ^ _enableInverted);
+    }
+}
+
+void AccelStepper::setPinsInverted(bool directionInvert, bool stepInvert, bool enableInvert)
+{
+    _pinInverted[0] = stepInvert;
+    _pinInverted[1] = directionInvert;
+    _enableInverted = enableInvert;
+}
+
+void AccelStepper::setPinsInverted(bool pin1Invert, bool pin2Invert, bool pin3Invert, bool pin4Invert, bool enableInvert)
+{    
+    _pinInverted[0] = pin1Invert;
+    _pinInverted[1] = pin2Invert;
+    _pinInverted[2] = pin3Invert;
+    _pinInverted[3] = pin4Invert;
+    _enableInverted = enableInvert;
+}
+
+// Blocks until the target position is reached and stopped
+void AccelStepper::runToPosition()
+{
+    while (run())
+	YIELD; // Let system housekeeping occur
+}
+
+boolean AccelStepper::runSpeedToPosition()
+{
+    if (_targetPos == _currentPos)
+	return false;
+    if (_targetPos >_currentPos)
+	_direction = DIRECTION_CW;
+    else
+	_direction = DIRECTION_CCW;
+    return runSpeed();
+}
+
+// Blocks until the new target position is reached
+void AccelStepper::runToNewPosition(long position)
+{
+    moveTo(position);
+    runToPosition();
+}
+
+void AccelStepper::stop()
+{
+    if (_speed != 0.0)
+    {    
+	long stepsToStop = (long)((_speed * _speed) / (2.0 * _acceleration)) + 1; // Equation 16 (+integer rounding)
+	if (_speed > 0)
+	    move(stepsToStop);
+	else
+	    move(-stepsToStop);
+    }
+}
+
+bool AccelStepper::isRunning()
+{
+    return !(_speed == 0.0 && _targetPos == _currentPos);
+}
diff --git a/Arduino/libraries/AccelStepper/src/AccelStepper.h b/Arduino/libraries/AccelStepper/src/AccelStepper.h
new file mode 100644
index 0000000..42ee37d
--- /dev/null
+++ b/Arduino/libraries/AccelStepper/src/AccelStepper.h
@@ -0,0 +1,783 @@
+// AccelStepper.h
+//
+/// \mainpage AccelStepper library for Arduino
+///
+/// This is the Arduino AccelStepper library.
+/// It provides an object-oriented interface for 2, 3 or 4 pin stepper motors and motor drivers.
+///
+/// The standard Arduino IDE includes the Stepper library
+/// (http://arduino.cc/en/Reference/Stepper) for stepper motors. It is
+/// perfectly adequate for simple, single motor applications.
+///
+/// AccelStepper significantly improves on the standard Arduino Stepper library in several ways:
+/// \li Supports acceleration and deceleration
+/// \li Supports multiple simultaneous steppers, with independent concurrent stepping on each stepper
+/// \li Most API functions never delay() or block (unless otherwise stated)
+/// \li Supports 2, 3 and 4 wire steppers, plus 3 and 4 wire half steppers.
+/// \li Supports alternate stepping functions to enable support of AFMotor (https://github.com/adafruit/Adafruit-Motor-Shield-library)
+/// \li Supports stepper drivers such as the Sparkfun EasyDriver (based on 3967 driver chip)
+/// \li Very slow speeds are supported
+/// \li Extensive API
+/// \li Subclass support
+///
+/// The latest version of this documentation can be downloaded from 
+/// http://www.airspayce.com/mikem/arduino/AccelStepper
+/// The version of the package that this documentation refers to can be downloaded 
+/// from http://www.airspayce.com/mikem/arduino/AccelStepper/AccelStepper-1.64.zip
+///
+/// Example Arduino programs are included to show the main modes of use.
+///
+/// You can also find online help and discussion at http://groups.google.com/group/accelstepper
+/// Please use that group for all questions and discussions on this topic. 
+/// Do not contact the author directly, unless it is to discuss commercial licensing.
+/// Before asking a question or reporting a bug, please read 
+/// - http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/How_to_ask_a_software_question
+/// - http://www.catb.org/esr/faqs/smart-questions.html
+/// - http://www.chiark.greenend.org.uk/~shgtatham/bugs.html
+///
+/// Beginners to C++ and stepper motors in general may find this helpful:
+/// - https://hackaday.io/project/183279-accelstepper-the-missing-manual
+/// - https://hackaday.io/project/183713-using-the-arduino-accelstepper-library
+///
+/// Tested on Arduino Diecimila and Mega with arduino-0018 & arduino-0021 
+/// on OpenSuSE 11.1 and avr-libc-1.6.1-1.15,
+/// cross-avr-binutils-2.19-9.1, cross-avr-gcc-4.1.3_20080612-26.5.
+/// Tested on Teensy http://www.pjrc.com/teensy including Teensy 3.1 built using Arduino IDE 1.0.5 with 
+/// teensyduino addon 1.18 and later.
+///
+/// \par Installation
+///
+/// Install in the usual way: unzip the distribution zip file to the libraries
+/// sub-folder of your sketchbook. 
+///
+/// \par Theory
+///
+/// This code uses speed calculations as described in 
+/// "Generate stepper-motor speed profiles in real time" by David Austin 
+/// http://fab.cba.mit.edu/classes/MIT/961.09/projects/i0/Stepper_Motor_Speed_Profile.pdf or
+/// http://www.embedded.com/design/mcus-processors-and-socs/4006438/Generate-stepper-motor-speed-profiles-in-real-time or
+/// http://web.archive.org/web/20140705143928/http://fab.cba.mit.edu/classes/MIT/961.09/projects/i0/Stepper_Motor_Speed_Profile.pdf
+/// with the exception that AccelStepper uses steps per second rather than radians per second
+/// (because we dont know the step angle of the motor)
+/// An initial step interval is calculated for the first step, based on the desired acceleration
+/// On subsequent steps, shorter step intervals are calculated based 
+/// on the previous step until max speed is achieved.
+///
+/// \par Adafruit Motor Shield V2
+///
+/// The included examples AFMotor_* are for Adafruit Motor Shield V1 and do not work with Adafruit Motor Shield V2.
+/// See https://github.com/adafruit/Adafruit_Motor_Shield_V2_Library for examples that work with Adafruit Motor Shield V2.
+/// 
+/// \par Donations
+///
+/// This library is offered under a free GPL license for those who want to use it that way. 
+/// We try hard to keep it up to date, fix bugs
+/// and to provide free support. If this library has helped you save time or money, please consider donating at
+/// http://www.airspayce.com or here:
+///
+/// \htmlonly <form action="https://www.paypal.com/cgi-bin/webscr" method="post"><input type="hidden" name="cmd" value="_donations" /> <input type="hidden" name="business" value="[email protected]" /> <input type="hidden" name="lc" value="AU" /> <input type="hidden" name="item_name" value="Airspayce" /> <input type="hidden" name="item_number" value="AccelStepper" /> <input type="hidden" name="currency_code" value="USD" /> <input type="hidden" name="bn" value="PP-DonationsBF:btn_donateCC_LG.gif:NonHosted" /> <input type="image" alt="PayPal — The safer, easier way to pay online." name="submit" src="https://www.paypalobjects.com/en_AU/i/btn/btn_donateCC_LG.gif" /> <img alt="" src="https://www.paypalobjects.com/en_AU/i/scr/pixel.gif" width="1" height="1" border="0" /></form> \endhtmlonly
+/// 
+/// \par Trademarks
+///
+/// AccelStepper is a trademark of AirSpayce Pty Ltd. The AccelStepper mark was first used on April 26 2010 for
+/// international trade, and is used only in relation to motor control hardware and software.
+/// It is not to be confused with any other similar marks covering other goods and services.
+///
+/// \par Copyright
+///
+/// This software is Copyright (C) 2010-2021 Mike McCauley. Use is subject to license
+/// conditions. The main licensing options available are GPL V3 or Commercial:
+///
+/// \par Open Source Licensing GPL V3
+/// This is the appropriate option if you want to share the source code of your
+/// application with everyone you distribute it to, and you also want to give them
+/// the right to share who uses it. If you wish to use this software under Open
+/// Source Licensing, you must contribute all your source code to the open source
+/// community in accordance with the GPL Version 23 when your application is
+/// distributed. See https://www.gnu.org/licenses/gpl-3.0.html
+/// 
+/// \par Commercial Licensing
+/// This is the appropriate option if you are creating proprietary applications
+/// and you are not prepared to distribute and share the source code of your
+/// application. To purchase a commercial license, contact [email protected]
+///
+/// \par Revision History
+/// \version 1.0 Initial release
+///
+/// \version 1.1 Added speed() function to get the current speed.
+/// \version 1.2 Added runSpeedToPosition() submitted by Gunnar Arndt.
+/// \version 1.3 Added support for stepper drivers (ie with Step and Direction inputs) with _pins == 1
+/// \version 1.4 Added functional contructor to support AFMotor, contributed by Limor, with example sketches.
+/// \version 1.5 Improvements contributed by Peter Mousley: Use of microsecond steps and other speed improvements
+///              to increase max stepping speed to about 4kHz. New option for user to set the min allowed pulse width.
+///              Added checks for already running at max speed and skip further calcs if so. 
+/// \version 1.6 Fixed a problem with wrapping of microsecond stepping that could cause stepping to hang. 
+///              Reported by Sandy Noble.
+///              Removed redundant _lastRunTime member.
+/// \version 1.7 Fixed a bug where setCurrentPosition() did not always work as expected. 
+///              Reported by Peter Linhart.
+/// \version 1.8 Added support for 4 pin half-steppers, requested by Harvey Moon
+/// \version 1.9 setCurrentPosition() now also sets motor speed to 0.
+/// \version 1.10 Builds on Arduino 1.0
+/// \version 1.11 Improvments from Michael Ellison:
+///   Added optional enable line support for stepper drivers
+///   Added inversion for step/direction/enable lines for stepper drivers
+/// \version 1.12 Announce Google Group
+/// \version 1.13 Improvements to speed calculation. Cost of calculation is now less in the worst case, 
+///    and more or less constant in all cases. This should result in slightly beter high speed performance, and
+///    reduce anomalous speed glitches when other steppers are accelerating. 
+///    However, its hard to see how to replace the sqrt() required at the very first step from 0 speed.
+/// \version 1.14 Fixed a problem with compiling under arduino 0021 reported by EmbeddedMan
+/// \version 1.15 Fixed a problem with runSpeedToPosition which did not correctly handle
+///    running backwards to a smaller target position. Added examples
+/// \version 1.16 Fixed some cases in the code where abs() was used instead of fabs().
+/// \version 1.17 Added example ProportionalControl
+/// \version 1.18 Fixed a problem: If one calls the funcion runSpeed() when Speed is zero, it makes steps 
+///    without counting. reported by  Friedrich, Klappenbach.
+/// \version 1.19 Added MotorInterfaceType and symbolic names for the number of pins to use
+///               for the motor interface. Updated examples to suit.
+///               Replaced individual pin assignment variables _pin1, _pin2 etc with array _pin[4].
+///               _pins member changed to _interface.
+///               Added _pinInverted array to simplify pin inversion operations.
+///               Added new function setOutputPins() which sets the motor output pins.
+///               It can be overridden in order to provide, say, serial output instead of parallel output
+///               Some refactoring and code size reduction.
+/// \version 1.20 Improved documentation and examples to show need for correctly
+///               specifying AccelStepper::FULL4WIRE and friends.
+/// \version 1.21 Fixed a problem where desiredSpeed could compute the wrong step acceleration
+///               when _speed was small but non-zero. Reported by Brian Schmalz.
+///               Precompute sqrt_twoa to improve performance and max possible stepping speed
+/// \version 1.22 Added Bounce.pde example
+///               Fixed a problem where calling moveTo(), setMaxSpeed(), setAcceleration() more 
+///               frequently than the step time, even
+///               with the same values, would interfere with speed calcs. Now a new speed is computed 
+///               only if there was a change in the set value. Reported by Brian Schmalz.
+/// \version 1.23 Rewrite of the speed algorithms in line with 
+///               http://fab.cba.mit.edu/classes/MIT/961.09/projects/i0/Stepper_Motor_Speed_Profile.pdf
+///               Now expect smoother and more linear accelerations and decelerations. The desiredSpeed()
+///               function was removed.
+/// \version 1.24  Fixed a problem introduced in 1.23: with runToPosition, which did never returned
+/// \version 1.25  Now ignore attempts to set acceleration to 0.0
+/// \version 1.26  Fixed a problem where certina combinations of speed and accelration could cause
+///                oscillation about the target position.
+/// \version 1.27  Added stop() function to stop as fast as possible with current acceleration parameters.
+///                Also added new Quickstop example showing its use.
+/// \version 1.28  Fixed another problem where certain combinations of speed and acceleration could cause
+///                oscillation about the target position.
+///                Added support for 3 wire full and half steppers such as Hard Disk Drive spindle.
+///                Contributed by Yuri Ivatchkovitch.
+/// \version 1.29  Fixed a problem that could cause a DRIVER stepper to continually step
+///                with some sketches. Reported by Vadim.
+/// \version 1.30  Fixed a problem that could cause stepper to back up a few steps at the end of
+///                accelerated travel with certain speeds. Reported and patched by jolo.
+/// \version 1.31  Updated author and distribution location details to airspayce.com
+/// \version 1.32  Fixed a problem with enableOutputs() and setEnablePin on Arduino Due that
+///                prevented the enable pin changing stae correctly. Reported by Duane Bishop.
+/// \version 1.33  Fixed an error in example AFMotor_ConstantSpeed.pde did not setMaxSpeed();
+///                Fixed a problem that caused incorrect pin sequencing of FULL3WIRE and HALF3WIRE.
+///                Unfortunately this meant changing the signature for all step*() functions.
+///                Added example MotorShield, showing how to use AdaFruit Motor Shield to control
+///                a 3 phase motor such as a HDD spindle motor (and without using the AFMotor library.
+/// \version 1.34  Added setPinsInverted(bool pin1Invert, bool pin2Invert, bool pin3Invert, bool pin4Invert, bool enableInvert) 
+///                to allow inversion of 2, 3 and 4 wire stepper pins. Requested by Oleg.
+/// \version 1.35  Removed default args from setPinsInverted(bool, bool, bool, bool, bool) to prevent ambiguity with 
+///                setPinsInverted(bool, bool, bool). Reported by Mac Mac.
+/// \version 1.36  Changed enableOutputs() and disableOutputs() to be virtual so can be overridden.
+///                Added new optional argument 'enable' to constructor, which allows you toi disable the 
+///                automatic enabling of outputs at construction time. Suggested by Guido.
+/// \version 1.37  Fixed a problem with step1 that could cause a rogue step in the 
+///                wrong direction (or not,
+///                depending on the setup-time requirements of the connected hardware). 
+///                Reported by Mark Tillotson.
+/// \version 1.38  run() function incorrectly always returned true. Updated function and doc so it returns true 
+///                if the motor is still running to the target position.
+/// \version 1.39  Updated typos in keywords.txt, courtesey Jon Magill.
+/// \version 1.40  Updated documentation, including testing on Teensy 3.1
+/// \version 1.41  Fixed an error in the acceleration calculations, resulting in acceleration of haldf the intended value
+/// \version 1.42  Improved support for FULL3WIRE and HALF3WIRE output pins. These changes were in Yuri's original
+///                contribution but did not make it into production.<br>
+/// \version 1.43  Added DualMotorShield example. Shows how to use AccelStepper to control 2 x 2 phase steppers using the 
+///                Itead Studio Arduino Dual Stepper Motor Driver Shield model IM120417015.<br>
+/// \version 1.44  examples/DualMotorShield/DualMotorShield.ino examples/DualMotorShield/DualMotorShield.pde
+///                was missing from the distribution.<br>
+/// \version 1.45  Fixed a problem where if setAcceleration was not called, there was no default
+///                acceleration. Reported by Michael Newman.<br>
+/// \version 1.45  Fixed inaccuracy in acceleration rate by using Equation 15, suggested by Sebastian Gracki.<br>
+///                Performance improvements in runSpeed suggested by Jaakko Fagerlund.<br>
+/// \version 1.46  Fixed error in documentation for runToPosition().
+///                Reinstated time calculations in runSpeed() since new version is reported 
+///                not to work correctly under some circumstances. Reported by Oleg V Gavva.<br>
+/// \version 1.48  2015-08-25
+///                Added new class MultiStepper that can manage multiple AccelSteppers, 
+///                and cause them all to move
+///                to selected positions at such a (constant) speed that they all arrive at their
+///                target position at the same time. Suitable for X-Y flatbeds etc.<br>
+///                Added new method maxSpeed() to AccelStepper to return the currently configured maxSpeed.<br>
+/// \version 1.49  2016-01-02
+///                Testing with VID28 series instrument stepper motors and EasyDriver.
+///                OK, although with light pointers
+///                and slow speeds like 180 full steps per second the motor movement can be erratic, 
+///                probably due to some mechanical resonance. Best to accelerate through this speed.<br>
+///                Added isRunning().<br>
+/// \version 1.50 2016-02-25
+///                AccelStepper::disableOutputs now sets the enable pion to OUTPUT mode if the enable pin is defined.
+///                Patch from Piet De Jong.<br>
+///                Added notes about the fact that AFMotor_* examples do not work with Adafruit Motor Shield V2.<br>
+/// \version 1.51 2016-03-24
+///                Fixed a problem reported by gregor: when resetting the stepper motor position using setCurrentPosition() the 
+///                stepper speed is reset by setting _stepInterval to 0, but _speed is not 
+///                reset. this results in the stepper motor not starting again when calling 
+///                setSpeed() with the same speed the stepper was set to before.
+/// \version 1.52 2016-08-09
+///                Added MultiStepper to keywords.txt.
+///                Improvements to efficiency of AccelStepper::runSpeed() as suggested by David Grayson.
+///                Improvements to speed accuracy as suggested by David Grayson.
+/// \version 1.53 2016-08-14
+///                Backed out Improvements to speed accuracy from 1.52 as it did not work correctly.
+/// \version 1.54 2017-01-24
+///                Fixed some warnings about unused arguments.
+/// \version 1.55 2017-01-25
+///                Fixed another warning in MultiStepper.cpp
+/// \version 1.56 2017-02-03
+///                Fixed minor documentation error with DIRECTION_CCW and DIRECTION_CW. Reported by David Mutterer.
+///                Added link to Binpress commercial license purchasing.
+/// \version 1.57 2017-03-28
+///                _direction moved to protected at the request of Rudy Ercek.
+///                setMaxSpeed() and setAcceleration() now correct negative values to be positive.
+/// \version 1.58 2018-04-13
+///                Add initialisation for _enableInverted in constructor.
+/// \version 1.59 2018-08-28
+///                Update commercial licensing, remove binpress.
+/// \version 1.60 2020-03-07
+///                Release under GPL V3
+/// \version 1.61 2020-04-20
+///                Added yield() call in runToPosition(), so that platforms like esp8266 dont hang/crash
+///                during long runs.
+/// \version 1.62 2022-05-22
+///                Added link to AccelStepper - The Missing Manual.<br>
+///                Fixed a problem when setting the maxSpeed to 1.0 due to incomplete initialisation.
+///                Reported by Olivier Pécheux. <br>
+/// \version 1.63 2022-06-30
+///                Added virtual destructor at the request of Jan.<br>
+/// \version 1.64 2022-10-31
+///                Patch courtesy acwest: Changes to make AccelStepper more subclassable. These changes are
+///                largely oriented to implementing new step-scheduling algorithms.
+///
+/// \author  Mike McCauley ([email protected]) DO NOT CONTACT THE AUTHOR DIRECTLY: USE THE GOOGLE GROUP
+// Copyright (C) 2009-2020 Mike McCauley
+// $Id: AccelStepper.h,v 1.28 2020/04/20 00:15:03 mikem Exp mikem $
+
+#ifndef AccelStepper_h
+#define AccelStepper_h
+
+#include <stdlib.h>
+#if ARDUINO >= 100
+#include <Arduino.h>
+#else
+#include <WProgram.h>
+#include <wiring.h>
+#endif
+
+// These defs cause trouble on some versions of Arduino
+#undef round
+
+// Use the system yield() whenever possoible, since some platforms require it for housekeeping, especially
+// ESP8266
+#if (defined(ARDUINO) && ARDUINO >= 155) || defined(ESP8266)
+ #define YIELD yield();
+#else
+ #define YIELD
+#endif
+
+/////////////////////////////////////////////////////////////////////
+/// \class AccelStepper AccelStepper.h <AccelStepper.h>
+/// \brief Support for stepper motors with acceleration etc.
+///
+/// This defines a single 2 or 4 pin stepper motor, or stepper moter with fdriver chip, with optional
+/// acceleration, deceleration, absolute positioning commands etc. Multiple
+/// simultaneous steppers are supported, all moving 
+/// at different speeds and accelerations. 
+///
+/// \par Operation
+/// This module operates by computing a step time in microseconds. The step
+/// time is recomputed after each step and after speed and acceleration
+/// parameters are changed by the caller. The time of each step is recorded in
+/// microseconds. The run() function steps the motor once if a new step is due.
+/// The run() function must be called frequently until the motor is in the
+/// desired position, after which time run() will do nothing.
+///
+/// \par Positioning
+/// Positions are specified by a signed long integer. At
+/// construction time, the current position of the motor is consider to be 0. Positive
+/// positions are clockwise from the initial position; negative positions are
+/// anticlockwise. The current position can be altered for instance after
+/// initialization positioning.
+///
+/// \par Caveats
+/// This is an open loop controller: If the motor stalls or is oversped,
+/// AccelStepper will not have a correct 
+/// idea of where the motor really is (since there is no feedback of the motor's
+/// real position. We only know where we _think_ it is, relative to the
+/// initial starting point).
+///
+/// \par Performance
+/// The fastest motor speed that can be reliably supported is about 4000 steps per
+/// second at a clock frequency of 16 MHz on Arduino such as Uno etc. 
+/// Faster processors can support faster stepping speeds. 
+/// However, any speed less than that
+/// down to very slow speeds (much less than one per second) are also supported,
+/// provided the run() function is called frequently enough to step the motor
+/// whenever required for the speed set.
+/// Calling setAcceleration() is expensive,
+/// since it requires a square root to be calculated.
+///
+/// Gregor Christandl reports that with an Arduino Due and a simple test program, 
+/// he measured 43163 steps per second using runSpeed(), 
+/// and 16214 steps per second using run();
+class AccelStepper
+{
+public:
+    /// \brief Symbolic names for number of pins.
+    /// Use this in the pins argument the AccelStepper constructor to 
+    /// provide a symbolic name for the number of pins
+    /// to use.
+    typedef enum
+    {
+	FUNCTION  = 0, ///< Use the functional interface, implementing your own driver functions (internal use only)
+	DRIVER    = 1, ///< Stepper Driver, 2 driver pins required
+	FULL2WIRE = 2, ///< 2 wire stepper, 2 motor pins required
+	FULL3WIRE = 3, ///< 3 wire stepper, such as HDD spindle, 3 motor pins required
+        FULL4WIRE = 4, ///< 4 wire full stepper, 4 motor pins required
+	HALF3WIRE = 6, ///< 3 wire half stepper, such as HDD spindle, 3 motor pins required
+	HALF4WIRE = 8  ///< 4 wire half stepper, 4 motor pins required
+    } MotorInterfaceType;
+
+    /// Constructor. You can have multiple simultaneous steppers, all moving
+    /// at different speeds and accelerations, provided you call their run()
+    /// functions at frequent enough intervals. Current Position is set to 0, target
+    /// position is set to 0. MaxSpeed and Acceleration default to 1.0.
+    /// The motor pins will be initialised to OUTPUT mode during the
+    /// constructor by a call to enableOutputs().
+    /// \param[in] interface Number of pins to interface to. Integer values are
+    /// supported, but it is preferred to use the \ref MotorInterfaceType symbolic names. 
+    /// AccelStepper::DRIVER (1) means a stepper driver (with Step and Direction pins).
+    /// If an enable line is also needed, call setEnablePin() after construction.
+    /// You may also invert the pins using setPinsInverted().
+    /// Caution: DRIVER implements a blocking delay of minPulseWidth microseconds (default 1us) for each step.
+    /// You can change this with setMinPulseWidth().
+    /// AccelStepper::FULL2WIRE (2) means a 2 wire stepper (2 pins required). 
+    /// AccelStepper::FULL3WIRE (3) means a 3 wire stepper, such as HDD spindle (3 pins required). 
+    /// AccelStepper::FULL4WIRE (4) means a 4 wire stepper (4 pins required). 
+    /// AccelStepper::HALF3WIRE (6) means a 3 wire half stepper, such as HDD spindle (3 pins required)
+    /// AccelStepper::HALF4WIRE (8) means a 4 wire half stepper (4 pins required)
+    /// Defaults to AccelStepper::FULL4WIRE (4) pins.
+    /// \param[in] pin1 Arduino digital pin number for motor pin 1. Defaults
+    /// to pin 2. For a AccelStepper::DRIVER (interface==1), 
+    /// this is the Step input to the driver. Low to high transition means to step)
+    /// \param[in] pin2 Arduino digital pin number for motor pin 2. Defaults
+    /// to pin 3. For a AccelStepper::DRIVER (interface==1), 
+    /// this is the Direction input the driver. High means forward.
+    /// \param[in] pin3 Arduino digital pin number for motor pin 3. Defaults
+    /// to pin 4.
+    /// \param[in] pin4 Arduino digital pin number for motor pin 4. Defaults
+    /// to pin 5.
+    /// \param[in] enable If this is true (the default), enableOutputs() will be called to enable
+    /// the output pins at construction time.
+    AccelStepper(uint8_t interface = AccelStepper::FULL4WIRE, uint8_t pin1 = 2, uint8_t pin2 = 3, uint8_t pin3 = 4, uint8_t pin4 = 5, bool enable = true);
+
+    /// Alternate Constructor which will call your own functions for forward and backward steps. 
+    /// You can have multiple simultaneous steppers, all moving
+    /// at different speeds and accelerations, provided you call their run()
+    /// functions at frequent enough intervals. Current Position is set to 0, target
+    /// position is set to 0. MaxSpeed and Acceleration default to 1.0.
+    /// Any motor initialization should happen before hand, no pins are used or initialized.
+    /// \param[in] forward void-returning procedure that will make a forward step
+    /// \param[in] backward void-returning procedure that will make a backward step
+    AccelStepper(void (*forward)(), void (*backward)());
+    
+    /// Set the target position. The run() function will try to move the motor (at most one step per call)
+    /// from the current position to the target position set by the most
+    /// recent call to this function. Caution: moveTo() also recalculates the speed for the next step. 
+    /// If you are trying to use constant speed movements, you should call setSpeed() after calling moveTo().
+    /// \param[in] absolute The desired absolute position. Negative is
+    /// anticlockwise from the 0 position.
+    void    moveTo(long absolute); 
+
+    /// Set the target position relative to the current position.
+    /// \param[in] relative The desired position relative to the current position. Negative is
+    /// anticlockwise from the current position.
+    void    move(long relative);
+
+    /// Poll the motor and step it if a step is due, implementing
+    /// accelerations and decelerations to achieve the target position. You must call this as
+    /// frequently as possible, but at least once per minimum step time interval,
+    /// preferably in your main loop. Note that each call to run() will make at most one step, and then only when a step is due,
+    /// based on the current speed and the time since the last step.
+    /// \return true if the motor is still running to the target position.
+    boolean run();
+
+    /// Poll the motor and step it if a step is due, implementing a constant
+    /// speed as set by the most recent call to setSpeed(). You must call this as
+    /// frequently as possible, but at least once per step interval,
+    /// \return true if the motor was stepped.
+    boolean runSpeed();
+
+    /// Sets the maximum permitted speed. The run() function will accelerate
+    /// up to the speed set by this function.
+    /// Caution: the maximum speed achievable depends on your processor and clock speed.
+    /// The default maxSpeed is 1.0 steps per second.
+    /// \param[in] speed The desired maximum speed in steps per second. Must
+    /// be > 0. Caution: Speeds that exceed the maximum speed supported by the processor may
+    /// Result in non-linear accelerations and decelerations.
+    void    setMaxSpeed(float speed);
+
+    /// Returns the maximum speed configured for this stepper
+    /// that was previously set by setMaxSpeed();
+    /// \return The currently configured maximum speed
+    float   maxSpeed();
+
+    /// Sets the acceleration/deceleration rate.
+    /// \param[in] acceleration The desired acceleration in steps per second
+    /// per second. Must be > 0.0. This is an expensive call since it requires a square 
+    /// root to be calculated. Dont call more ofthen than needed
+    void    setAcceleration(float acceleration);
+
+    /// Returns the acceleration/deceleration rate configured for this stepper
+    /// that was previously set by setAcceleration();
+    /// \return The currently configured acceleration/deceleration
+    float   acceleration();
+    
+    /// Sets the desired constant speed for use with runSpeed().
+    /// \param[in] speed The desired constant speed in steps per
+    /// second. Positive is clockwise. Speeds of more than 1000 steps per
+    /// second are unreliable. Very slow speeds may be set (eg 0.00027777 for
+    /// once per hour, approximately. Speed accuracy depends on the Arduino
+    /// crystal. Jitter depends on how frequently you call the runSpeed() function.
+    /// The speed will be limited by the current value of setMaxSpeed()
+    void    setSpeed(float speed);
+
+    /// The most recently set speed.
+    /// \return the most recent speed in steps per second
+    float   speed();
+
+    /// The distance from the current position to the target position.
+    /// \return the distance from the current position to the target position
+    /// in steps. Positive is clockwise from the current position.
+    long    distanceToGo();
+
+    /// The most recently set target position.
+    /// \return the target position
+    /// in steps. Positive is clockwise from the 0 position.
+    long    targetPosition();
+
+    /// The current motor position.
+    /// \return the current motor position
+    /// in steps. Positive is clockwise from the 0 position.
+    long    currentPosition();  
+
+    /// Resets the current position of the motor, so that wherever the motor
+    /// happens to be right now is considered to be the new 0 position. Useful
+    /// for setting a zero position on a stepper after an initial hardware
+    /// positioning move.
+    /// Has the side effect of setting the current motor speed to 0.
+    /// \param[in] position The position in steps of wherever the motor
+    /// happens to be right now.
+    void    setCurrentPosition(long position);  
+    
+    /// Moves the motor (with acceleration/deceleration)
+    /// to the target position and blocks until it is at
+    /// position. Dont use this in event loops, since it blocks.
+    void    runToPosition();
+
+    /// Executes runSpeed() unless the targetPosition is reached.
+    /// This function needs to be called often just like runSpeed() or run().
+    /// Will step the motor if a step is required at the currently selected
+    /// speed unless the target position has been reached.
+    /// Does not implement accelerations.
+    /// \return true if it stepped
+    boolean runSpeedToPosition();
+
+    /// Moves the motor (with acceleration/deceleration)
+    /// to the new target position and blocks until it is at
+    /// position. Dont use this in event loops, since it blocks.
+    /// \param[in] position The new target position.
+    void    runToNewPosition(long position);
+
+    /// Sets a new target position that causes the stepper
+    /// to stop as quickly as possible, using the current speed and acceleration parameters.
+    void stop();
+
+    /// Disable motor pin outputs by setting them all LOW
+    /// Depending on the design of your electronics this may turn off
+    /// the power to the motor coils, saving power.
+    /// This is useful to support Arduino low power modes: disable the outputs
+    /// during sleep and then reenable with enableOutputs() before stepping
+    /// again.
+    /// If the enable Pin is defined, sets it to OUTPUT mode and clears the pin to disabled.
+    virtual void    disableOutputs();
+
+    /// Enable motor pin outputs by setting the motor pins to OUTPUT
+    /// mode. Called automatically by the constructor.
+    /// If the enable Pin is defined, sets it to OUTPUT mode and sets the pin to enabled.
+    virtual void    enableOutputs();
+
+    /// Sets the minimum pulse width allowed by the stepper driver. The minimum practical pulse width is 
+    /// approximately 20 microseconds. Times less than 20 microseconds
+    /// will usually result in 20 microseconds or so.
+    /// \param[in] minWidth The minimum pulse width in microseconds. 
+    void    setMinPulseWidth(unsigned int minWidth);
+
+    /// Sets the enable pin number for stepper drivers.
+    /// 0xFF indicates unused (default).
+    /// Otherwise, if a pin is set, the pin will be turned on when 
+    /// enableOutputs() is called and switched off when disableOutputs() 
+    /// is called.
+    /// \param[in] enablePin Arduino digital pin number for motor enable
+    /// \sa setPinsInverted
+    void    setEnablePin(uint8_t enablePin = 0xff);
+
+    /// Sets the inversion for stepper driver pins
+    /// \param[in] directionInvert True for inverted direction pin, false for non-inverted
+    /// \param[in] stepInvert      True for inverted step pin, false for non-inverted
+    /// \param[in] enableInvert    True for inverted enable pin, false (default) for non-inverted
+    void    setPinsInverted(bool directionInvert = false, bool stepInvert = false, bool enableInvert = false);
+
+    /// Sets the inversion for 2, 3 and 4 wire stepper pins
+    /// \param[in] pin1Invert True for inverted pin1, false for non-inverted
+    /// \param[in] pin2Invert True for inverted pin2, false for non-inverted
+    /// \param[in] pin3Invert True for inverted pin3, false for non-inverted
+    /// \param[in] pin4Invert True for inverted pin4, false for non-inverted
+    /// \param[in] enableInvert    True for inverted enable pin, false (default) for non-inverted
+    void    setPinsInverted(bool pin1Invert, bool pin2Invert, bool pin3Invert, bool pin4Invert, bool enableInvert);
+
+    /// Checks to see if the motor is currently running to a target
+    /// \return true if the speed is not zero or not at the target position
+    bool    isRunning();
+
+    /// Virtual destructor to prevent warnings during delete
+    virtual ~AccelStepper() {};
+protected:
+
+    /// \brief Direction indicator
+    /// Symbolic names for the direction the motor is turning
+    typedef enum
+    {
+	DIRECTION_CCW = 0,  ///< Counter-Clockwise
+        DIRECTION_CW  = 1   ///< Clockwise
+    } Direction;
+
+    /// Forces the library to compute a new instantaneous speed and set that as
+    /// the current speed. It is called by
+    /// the library:
+    /// \li  after each step
+    /// \li  after change to maxSpeed through setMaxSpeed()
+    /// \li  after change to acceleration through setAcceleration()
+    /// \li  after change to target position (relative or absolute) through
+    /// move() or moveTo()
+    /// \return the new step interval
+    virtual unsigned long  computeNewSpeed();
+
+    /// Low level function to set the motor output pins
+    /// bit 0 of the mask corresponds to _pin[0]
+    /// bit 1 of the mask corresponds to _pin[1]
+    /// You can override this to impment, for example serial chip output insted of using the
+    /// output pins directly
+    virtual void   setOutputPins(uint8_t mask);
+
+    /// Called to execute a step. Only called when a new step is
+    /// required. Subclasses may override to implement new stepping
+    /// interfaces. The default calls step1(), step2(), step4() or step8() depending on the
+    /// number of pins defined for the stepper.
+    /// \param[in] step The current step phase number (0 to 7)
+    virtual void   step(long step);
+    
+    /// Called to execute a clockwise(+) step. Only called when a new step is
+    /// required. This increments the _currentPos and calls step()
+    /// \return the updated current position
+    long   stepForward();
+
+    /// Called to execute a counter-clockwise(-) step. Only called when a new step is
+    /// required. This decrements the _currentPos and calls step()
+    /// \return the updated current position
+    long   stepBackward();
+
+    /// Called to execute a step using stepper functions (pins = 0) Only called when a new step is
+    /// required. Calls _forward() or _backward() to perform the step
+    /// \param[in] step The current step phase number (0 to 7)
+    virtual void   step0(long step);
+
+    /// Called to execute a step on a stepper driver (ie where pins == 1). Only called when a new step is
+    /// required. Subclasses may override to implement new stepping
+    /// interfaces. The default sets or clears the outputs of Step pin1 to step, 
+    /// and sets the output of _pin2 to the desired direction. The Step pin (_pin1) is pulsed for 1 microsecond
+    /// which is the minimum STEP pulse width for the 3967 driver.
+    /// \param[in] step The current step phase number (0 to 7)
+    virtual void   step1(long step);
+
+    /// Called to execute a step on a 2 pin motor. Only called when a new step is
+    /// required. Subclasses may override to implement new stepping
+    /// interfaces. The default sets or clears the outputs of pin1 and pin2
+    /// \param[in] step The current step phase number (0 to 7)
+    virtual void   step2(long step);
+
+    /// Called to execute a step on a 3 pin motor, such as HDD spindle. Only called when a new step is
+    /// required. Subclasses may override to implement new stepping
+    /// interfaces. The default sets or clears the outputs of pin1, pin2,
+    /// pin3
+    /// \param[in] step The current step phase number (0 to 7)
+    virtual void   step3(long step);
+
+    /// Called to execute a step on a 4 pin motor. Only called when a new step is
+    /// required. Subclasses may override to implement new stepping
+    /// interfaces. The default sets or clears the outputs of pin1, pin2,
+    /// pin3, pin4.
+    /// \param[in] step The current step phase number (0 to 7)
+    virtual void   step4(long step);
+
+    /// Called to execute a step on a 3 pin motor, such as HDD spindle. Only called when a new step is
+    /// required. Subclasses may override to implement new stepping
+    /// interfaces. The default sets or clears the outputs of pin1, pin2,
+    /// pin3
+    /// \param[in] step The current step phase number (0 to 7)
+    virtual void   step6(long step);
+
+    /// Called to execute a step on a 4 pin half-stepper motor. Only called when a new step is
+    /// required. Subclasses may override to implement new stepping
+    /// interfaces. The default sets or clears the outputs of pin1, pin2,
+    /// pin3, pin4.
+    /// \param[in] step The current step phase number (0 to 7)
+    virtual void   step8(long step);
+
+    /// Current direction motor is spinning in
+    /// Protected because some peoples subclasses need it to be so
+    boolean _direction; // 1 == CW
+    
+    /// The current interval between steps in microseconds.
+    /// 0 means the motor is currently stopped with _speed == 0
+    unsigned long  _stepInterval;
+
+private:
+    /// Number of pins on the stepper motor. Permits 2 or 4. 2 pins is a
+    /// bipolar, and 4 pins is a unipolar.
+    uint8_t        _interface;          // 0, 1, 2, 4, 8, See MotorInterfaceType
+
+    /// Arduino pin number assignments for the 2 or 4 pins required to interface to the
+    /// stepper motor or driver
+    uint8_t        _pin[4];
+
+    /// Whether the _pins is inverted or not
+    uint8_t        _pinInverted[4];
+
+    /// The current absolution position in steps.
+    long           _currentPos;    // Steps
+
+    /// The target position in steps. The AccelStepper library will move the
+    /// motor from the _currentPos to the _targetPos, taking into account the
+    /// max speed, acceleration and deceleration
+    long           _targetPos;     // Steps
+
+    /// The current motos speed in steps per second
+    /// Positive is clockwise
+    float          _speed;         // Steps per second
+
+    /// The maximum permitted speed in steps per second. Must be > 0.
+    float          _maxSpeed;
+
+    /// The acceleration to use to accelerate or decelerate the motor in steps
+    /// per second per second. Must be > 0
+    float          _acceleration;
+    float          _sqrt_twoa; // Precomputed sqrt(2*_acceleration)
+
+    /// The last step time in microseconds
+    unsigned long  _lastStepTime;
+
+    /// The minimum allowed pulse width in microseconds
+    unsigned int   _minPulseWidth;
+
+    /// Is the direction pin inverted?
+    ///bool           _dirInverted; /// Moved to _pinInverted[1]
+
+    /// Is the step pin inverted?
+    ///bool           _stepInverted; /// Moved to _pinInverted[0]
+
+    /// Is the enable pin inverted?
+    bool           _enableInverted;
+
+    /// Enable pin for stepper driver, or 0xFF if unused.
+    uint8_t        _enablePin;
+
+    /// The pointer to a forward-step procedure
+    void (*_forward)();
+
+    /// The pointer to a backward-step procedure
+    void (*_backward)();
+
+    /// The step counter for speed calculations
+    long _n;
+
+    /// Initial step size in microseconds
+    float _c0;
+
+    /// Last step size in microseconds
+    float _cn;
+
+    /// Min step size in microseconds based on maxSpeed
+    float _cmin; // at max speed
+
+};
+
+/// @example Random.pde
+/// Make a single stepper perform random changes in speed, position and acceleration
+
+/// @example Overshoot.pde
+///  Check overshoot handling
+/// which sets a new target position and then waits until the stepper has 
+/// achieved it. This is used for testing the handling of overshoots
+
+/// @example MultipleSteppers.pde
+/// Shows how to multiple simultaneous steppers
+/// Runs one stepper forwards and backwards, accelerating and decelerating
+/// at the limits. Runs other steppers at the same time
+
+/// @example ConstantSpeed.pde
+/// Shows how to run AccelStepper in the simplest,
+/// fixed speed mode with no accelerations
+
+/// @example Blocking.pde 
+/// Shows how to use the blocking call runToNewPosition
+/// Which sets a new target position and then waits until the stepper has 
+/// achieved it.
+
+/// @example AFMotor_MultiStepper.pde
+/// Control both Stepper motors at the same time with different speeds
+/// and accelerations. 
+
+/// @example AFMotor_ConstantSpeed.pde
+/// Shows how to run AccelStepper in the simplest,
+/// fixed speed mode with no accelerations
+
+/// @example ProportionalControl.pde
+/// Make a single stepper follow the analog value read from a pot or whatever
+/// The stepper will move at a constant speed to each newly set posiiton, 
+/// depending on the value of the pot.
+
+/// @example Bounce.pde
+/// Make a single stepper bounce from one limit to another, observing
+/// accelrations at each end of travel
+
+/// @example Quickstop.pde
+/// Check stop handling.
+/// Calls stop() while the stepper is travelling at full speed, causing
+/// the stepper to stop as quickly as possible, within the constraints of the
+/// current acceleration.
+
+/// @example MotorShield.pde
+/// Shows how to use AccelStepper to control a 3-phase motor, such as a HDD spindle motor
+/// using the Adafruit Motor Shield http://www.ladyada.net/make/mshield/index.html.
+
+/// @example DualMotorShield.pde
+/// Shows how to use AccelStepper to control 2 x 2 phase steppers using the 
+/// Itead Studio Arduino Dual Stepper Motor Driver Shield
+/// model IM120417015
+
+#endif 
diff --git a/Arduino/libraries/AccelStepper/src/MultiStepper.cpp b/Arduino/libraries/AccelStepper/src/MultiStepper.cpp
new file mode 100644
index 0000000..6a22e11
--- /dev/null
+++ b/Arduino/libraries/AccelStepper/src/MultiStepper.cpp
@@ -0,0 +1,86 @@
+// MultiStepper.cpp
+//
+// Copyright (C) 2015 Mike McCauley
+// $Id: MultiStepper.cpp,v 1.3 2020/04/20 00:15:03 mikem Exp mikem $
+
+#include "MultiStepper.h"
+#include "AccelStepper.h"
+
+MultiStepper::MultiStepper()
+    : _num_steppers(0)
+{
+}
+
+boolean MultiStepper::addStepper(AccelStepper& stepper)
+{
+    if (_num_steppers >= MULTISTEPPER_MAX_STEPPERS)
+	return false; // No room for more
+    _steppers[_num_steppers++] = &stepper;
+    return true;
+}
+
+void MultiStepper::moveTo(long absolute[])
+{
+    // First find the stepper that will take the longest time to move
+    float longestTime = 0.0;
+
+    uint8_t i;
+    for (i = 0; i < _num_steppers; i++)
+    {
+	long thisDistance = absolute[i] - _steppers[i]->currentPosition();
+	float thisTime = abs(thisDistance) / _steppers[i]->maxSpeed();
+
+	if (thisTime > longestTime)
+	    longestTime = thisTime;
+    }
+
+    if (longestTime > 0.0)
+    {
+	// Now work out a new max speed for each stepper so they will all 
+	// arrived at the same time of longestTime
+	for (i = 0; i < _num_steppers; i++)
+	{
+	    long thisDistance = absolute[i] - _steppers[i]->currentPosition();
+	    float thisSpeed = thisDistance / longestTime;
+	    _steppers[i]->moveTo(absolute[i]); // New target position (resets speed)
+	    _steppers[i]->setSpeed(thisSpeed); // New speed
+	}
+    }
+}
+
+// Returns true if any motor is still running to the target position.
+boolean MultiStepper::run()
+{
+    uint8_t i;
+    boolean ret = false;
+    for (i = 0; i < _num_steppers; i++)
+    {
+	if ( _steppers[i]->distanceToGo() != 0)
+	{
+	    _steppers[i]->runSpeed();
+	    ret = true;
+	}
+	// Caution: it has een reported that if any motor is used with acceleration outside of
+	// MultiStepper, this code is necessary, you get 
+	// strange results where it moves in the wrong direction for a while then 
+	// slams back the correct way.
+#if 0
+	else
+	{
+	    // Need to call this to clear _stepInterval, _speed and _n 
+	    otherwise future calls will fail.
+		_steppers[i]->setCurrentPosition(_steppers[i]->currentPosition());
+	}
+#endif
+	
+    }
+    return ret;
+}
+
+// Blocks until all steppers reach their target position and are stopped
+void    MultiStepper::runSpeedToPosition()
+{ 
+    while (run())
+	;
+}
+
diff --git a/Arduino/libraries/AccelStepper/src/MultiStepper.h b/Arduino/libraries/AccelStepper/src/MultiStepper.h
new file mode 100644
index 0000000..d801bb0
--- /dev/null
+++ b/Arduino/libraries/AccelStepper/src/MultiStepper.h
@@ -0,0 +1,78 @@
+// MultiStepper.h
+
+#ifndef MultiStepper_h
+#define MultiStepper_h
+
+#include <stdlib.h>
+#if ARDUINO >= 100
+#include <Arduino.h>
+#else
+#include <WProgram.h>
+#include <wiring.h>
+#endif
+
+#define MULTISTEPPER_MAX_STEPPERS 10
+
+class AccelStepper;
+
+/////////////////////////////////////////////////////////////////////
+/// \class MultiStepper MultiStepper.h <MultiStepper.h>
+/// \brief Operate multiple AccelSteppers in a co-ordinated fashion
+///
+/// This class can manage multiple AccelSteppers (up to MULTISTEPPER_MAX_STEPPERS = 10), 
+/// and cause them all to move
+/// to selected positions at such a (constant) speed that they all arrive at their
+/// target position at the same time. This can be used to support devices with multiple steppers
+/// on say multiple axes to cause linear diagonal motion. Suitable for use with X-Y plotters, flatbeds,
+/// 3D printers etc
+/// to get linear straight line movement between arbitrary 2d (or 3d or ...) positions.
+///
+/// Caution: only constant speed stepper motion is supported: acceleration and deceleration is not supported
+/// All the steppers managed by MultiStepper will step at a constant speed to their
+/// target (albeit perhaps different speeds for each stepper).
+class MultiStepper
+{
+public:
+    /// Constructor
+    MultiStepper();
+
+    /// Add a stepper to the set of managed steppers
+    /// There is an upper limit of MULTISTEPPER_MAX_STEPPERS = 10 to the number of steppers that can be managed
+    /// \param[in] stepper Reference to a stepper to add to the managed list
+    /// \return true if successful. false if the number of managed steppers would exceed MULTISTEPPER_MAX_STEPPERS
+    boolean addStepper(AccelStepper& stepper);
+
+    /// Set the target positions of all managed steppers 
+    /// according to a coordinate array.
+    /// New speeds will be computed for each stepper so they will all arrive at their 
+    /// respective targets at very close to the same time.
+    /// \param[in] absolute An array of desired absolute stepper positions. absolute[0] will be used to set
+    /// the absolute position of the first stepper added by addStepper() etc. The array must be at least as long as 
+    /// the number of steppers that have been added by addStepper, else results are undefined.
+    void moveTo(long absolute[]);
+    
+    /// Calls runSpeed() on all the managed steppers
+    /// that have not acheived their target position.
+    /// \return true if any stepper is still in the process of running to its target position.
+    boolean run();
+
+    /// Runs all managed steppers until they acheived their target position.
+    /// Blocks until all that position is acheived. If you dont
+    /// want blocking consider using run() instead.
+    void    runSpeedToPosition();
+    
+private:
+    /// Array of pointers to the steppers we are controlling.
+    /// Fills from 0 onwards
+    AccelStepper* _steppers[MULTISTEPPER_MAX_STEPPERS];
+
+    /// Number of steppers we are controlling and the number
+    /// of steppers in _steppers[]
+    uint8_t       _num_steppers;
+};
+
+/// @example MultiStepper.pde
+/// Use MultiStepper class to manage multiple steppers and make them all move to 
+/// the same position at the same time for linear 2d (or 3d) motion.
+
+#endif