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/*
* ScaraKinematics.cpp
*
* Created on: 24 Apr 2017
* Author: David
*/
#include "ScaraKinematics.h"
#if SUPPORT_SCARA
#include <Platform/RepRap.h>
#include <Platform/Platform.h>
#include <Storage/MassStorage.h>
#include <GCodes/GCodeBuffer/GCodeBuffer.h>
#include <Movement/DDA.h>
#include <limits>
#if SUPPORT_OBJECT_MODEL
// Object model table and functions
// Note: if using GCC version 7.3.1 20180622 and lambda functions are used in this table, you must compile this file with option -std=gnu++17.
// Otherwise the table will be allocated in RAM instead of flash, which wastes too much RAM.
// Macro to build a standard lambda function that includes the necessary type conversions
#define OBJECT_MODEL_FUNC(...) OBJECT_MODEL_FUNC_BODY(ScaraKinematics, __VA_ARGS__)
constexpr ObjectModelTableEntry ScaraKinematics::objectModelTable[] =
{
// Within each group, these entries must be in alphabetical order
// 0. kinematics members
{ "name", OBJECT_MODEL_FUNC(self->GetName(true)), ObjectModelEntryFlags::none },
};
constexpr uint8_t ScaraKinematics::objectModelTableDescriptor[] = { 1, 1 };
DEFINE_GET_OBJECT_MODEL_TABLE_WITH_PARENT(ScaraKinematics, ZLeadscrewKinematics)
#endif
ScaraKinematics::ScaraKinematics() noexcept
: ZLeadscrewKinematics(KinematicsType::scara, SegmentationType(true, false, false)),
proximalArmLength(DefaultProximalArmLength), distalArmLength(DefaultDistalArmLength), xOffset(0.0), yOffset(0.0)
{
thetaLimits[0] = DefaultMinTheta;
thetaLimits[1] = DefaultMaxTheta;
psiLimits[0] = DefaultMinPsi;
psiLimits[1] = DefaultMaxPsi;
crosstalk[0] = crosstalk[1] = crosstalk[2] = requestedMinRadius = 0.0;
Recalc();
}
// Return the name of the current kinematics
const char *ScaraKinematics::GetName(bool forStatusReport) const noexcept
{
return "Scara";
}
// Calculate theta, psi and the new arm mode from a target position.
// If the position is not reachable because it is out of radius limits, set theta and psi to NaN and return false.
// Otherwise set theta and psi to the required values and return true if they are in range.
// Note: theta and psi are now returned in degrees.
bool ScaraKinematics::CalculateThetaAndPsi(const float machinePos[], bool isCoordinated, float& theta, float& psi, bool& armMode) const noexcept
{
const float x = machinePos[X_AXIS] + xOffset;
const float y = machinePos[Y_AXIS] + yOffset;
const float cosPsi = (fsquare(x) + fsquare(y) - proximalArmLengthSquared - distalArmLengthSquared) / twoPd;
// SCARA position is undefined if abs(SCARA_C2) >= 1. In reality abs(SCARA_C2) >0.95 can be problematic.
const float square = 1.0 - fsquare(cosPsi);
if (square < 0.01)
{
theta = psi = std::numeric_limits<float>::quiet_NaN();
return false; // not reachable
}
psi = acosf(cosPsi) * RadiansToDegrees;
const float sinPsi = fastSqrtf(square);
const float SCARA_K1 = proximalArmLength + distalArmLength * cosPsi;
const float SCARA_K2 = distalArmLength * sinPsi;
// Try the current arm mode, then the other one
bool switchedMode = false;
for (;;)
{
if (armMode != switchedMode)
{
// The following equations choose arm mode 0 i.e. distal arm rotated anticlockwise relative to proximal arm
if (supportsContinuousRotation[1] || (psi >= psiLimits[0] && psi <= psiLimits[1]))
{
theta = atan2f(SCARA_K1 * y - SCARA_K2 * x, SCARA_K1 * x + SCARA_K2 * y) * RadiansToDegrees;
if (supportsContinuousRotation[0] || (theta >= thetaLimits[0] && theta <= thetaLimits[1]))
{
break;
}
}
}
else
{
// The following equations choose arm mode 1 i.e. distal arm rotated clockwise relative to proximal arm
if (supportsContinuousRotation[1] || ((-psi) >= psiLimits[0] && (-psi) <= psiLimits[1]))
{
theta = atan2f(SCARA_K1 * y + SCARA_K2 * x, SCARA_K1 * x - SCARA_K2 * y) * RadiansToDegrees;
if (supportsContinuousRotation[0] || (theta >= thetaLimits[0] && theta <= thetaLimits[1]))
{
psi = -psi;
break;
}
}
}
if (isCoordinated || switchedMode)
{
return false; // not reachable
}
switchedMode = true;
}
// Now that we know we are going to do the move, update the arm mode
if (switchedMode)
{
armMode = !armMode;
}
// Save the original and transformed coordinates so that we don't need to calculate them again if we are commanded to move to this position
cachedX = machinePos[0];
cachedY = machinePos[1];
cachedTheta = theta;
cachedPsi = psi;
cachedArmMode = armMode;
return true;
}
// Convert Cartesian coordinates to motor coordinates, returning true if successful
// In the following, theta is the proximal arm angle relative to the X axis, psi is the distal arm angle relative to the proximal arm
bool ScaraKinematics::CartesianToMotorSteps(const float machinePos[], const float stepsPerMm[], size_t numVisibleAxes, size_t numTotalAxes, int32_t motorPos[], bool isCoordinated) const noexcept
{
float theta, psi;
if (machinePos[0] == cachedX && machinePos[1] == cachedY)
{
theta = cachedTheta;
psi = cachedPsi;
currentArmMode = cachedArmMode;
}
else
{
bool armMode = currentArmMode;
if (!CalculateThetaAndPsi(machinePos, isCoordinated, theta, psi, armMode))
{
return false;
}
currentArmMode = armMode;
}
//debugPrintf("psi = %.2f, theta = %.2f\n", psi * RadiansToDegrees, theta * RadiansToDegrees);
motorPos[X_AXIS] = lrintf(theta * stepsPerMm[X_AXIS]);
motorPos[Y_AXIS] = lrintf((psi - (crosstalk[0] * theta)) * stepsPerMm[Y_AXIS]);
motorPos[Z_AXIS] = lrintf((machinePos[Z_AXIS] - (crosstalk[1] * theta) - (crosstalk[2] * psi)) * stepsPerMm[Z_AXIS]);
// Transform any additional axes linearly
for (size_t axis = XYZ_AXES; axis < numVisibleAxes; ++axis)
{
motorPos[axis] = lrintf(machinePos[axis] * stepsPerMm[axis]);
}
return true;
}
// Convert motor coordinates to machine coordinates. Used after homing and after individual motor moves.
// For Scara, the X and Y components of stepsPerMm are actually steps per degree angle.
void ScaraKinematics::MotorStepsToCartesian(const int32_t motorPos[], const float stepsPerMm[], size_t numVisibleAxes, size_t numTotalAxes, float machinePos[]) const noexcept
{
const float theta = ((float)motorPos[X_AXIS]/stepsPerMm[X_AXIS]);
const float psi = ((float)motorPos[Y_AXIS]/stepsPerMm[Y_AXIS]) + (crosstalk[0] * theta);
// Cache the current values so that a Z probe at this position won't fail due to rounding error when transforming the XY coordinates back
currentArmMode = cachedArmMode = (motorPos[Y_AXIS] >= 0);
cachedTheta = theta;
cachedPsi = psi;
cachedX = machinePos[X_AXIS] = (cosf(theta * DegreesToRadians) * proximalArmLength + cosf((psi + theta) * DegreesToRadians) * distalArmLength) - xOffset;
cachedY = machinePos[Y_AXIS] = (sinf(theta * DegreesToRadians) * proximalArmLength + sinf((psi + theta) * DegreesToRadians) * distalArmLength) - yOffset;
// On some machines (e.g. Helios), the X and/or Y arm motors also affect the Z height
machinePos[Z_AXIS] = ((float)motorPos[Z_AXIS]/stepsPerMm[Z_AXIS]) + (crosstalk[1] * theta) + (crosstalk[2] * psi);
// Convert any additional axes linearly
for (size_t drive = XYZ_AXES; drive < numVisibleAxes; ++drive)
{
machinePos[drive] = motorPos[drive]/stepsPerMm[drive];
}
}
// Set the parameters from a M665, M666 or M669 command
// Return true if we changed any parameters that affect the geometry. Set 'error' true if there was an error, otherwise leave it alone.
bool ScaraKinematics::Configure(unsigned int mCode, GCodeBuffer& gb, const StringRef& reply, bool& error) THROWS(GCodeException) /*override*/
{
if (mCode == 669)
{
const bool seenNonGeometry = TryConfigureSegmentation(gb);
bool seen = false;
gb.TryGetFValue('P', proximalArmLength, seen);
gb.TryGetFValue('D', distalArmLength, seen);
gb.TryGetFValue('X', xOffset, seen);
gb.TryGetFValue('Y', yOffset, seen);
if (gb.TryGetFloatArray('A', 2, thetaLimits, reply, seen))
{
error = true;
return true;
}
if (gb.TryGetFloatArray('B', 2, psiLimits, reply, seen))
{
error = true;
return true;
}
if (gb.TryGetFloatArray('C', 3, crosstalk, reply, seen))
{
error = true;
return true;
}
gb.TryGetFValue('R', requestedMinRadius, seen);
if (seen)
{
Recalc();
}
else if (!seenNonGeometry && !gb.Seen('K'))
{
Kinematics::Configure(mCode, gb, reply, error);
reply.printf(", proximal arm %.2fmm range %.1f to %.1f" DEGREE_SYMBOL
"%s, distal arm %.2fmm range %.1f to %.1f" DEGREE_SYMBOL "%s, crosstalk %.1f:%.1f:%.1f, bed origin (%.1f, %.1f)",
(double)proximalArmLength, (double)thetaLimits[0], (double)thetaLimits[1], (supportsContinuousRotation[0]) ? " (continuous)" : "",
(double)distalArmLength, (double)psiLimits[0], (double)psiLimits[1], (supportsContinuousRotation[0]) ? " (continuous)" : "",
(double)crosstalk[0], (double)crosstalk[1], (double)crosstalk[2],
(double)xOffset, (double)yOffset);
}
return seen;
}
else
{
return ZLeadscrewKinematics::Configure(mCode, gb, reply, error);
}
}
// Return true if the specified XY position is reachable by the print head reference point
bool ScaraKinematics::IsReachable(float axesCoords[MaxAxes], AxesBitmap axes) const noexcept
{
if (axes.IsBitSet(X_AXIS) && axes.IsBitSet(Y_AXIS))
{
// See if we can transform the position
float coords[2] = {axesCoords[X_AXIS], axesCoords[Y_AXIS]};
float theta, psi;
bool armMode = currentArmMode;
if (!CalculateThetaAndPsi(coords, false, theta, psi, armMode))
{
return false;
}
}
axes.ClearBit(X_AXIS);
axes.ClearBit(Y_AXIS);
return Kinematics::IsReachable(axesCoords, axes);
}
// Limit the Cartesian position that the user wants to move to, returning true if any coordinates were changed
LimitPositionResult ScaraKinematics::LimitPosition(float finalCoords[], const float * null initialCoords,
size_t numVisibleAxes, AxesBitmap axesToLimit, bool isCoordinated, bool applyM208Limits) const noexcept
{
// First limit all axes according to M208
bool limited = applyM208Limits && Kinematics::LimitPositionFromAxis(finalCoords, 0, numVisibleAxes, axesToLimit);
// Now check whether the arms can reach the final position
float theta, psi;
bool armMode = currentArmMode;
if (!CalculateThetaAndPsi(finalCoords, isCoordinated, theta, psi, armMode))
{
// The requested position was not reachable
limited = true;
if (std::isnan(theta))
{
// We are radius-limited
float x = finalCoords[X_AXIS] + xOffset;
float y = finalCoords[Y_AXIS] + yOffset;
const float r = fastSqrtf(fsquare(x) + fsquare(y));
if (r < minRadius)
{
// Radius is too small. The user may have specified x=0 y=0 so allow for this.
if (r < 1.0)
{
x = minRadius;
y = 0.0;
}
else
{
x *= minRadius/r;
y *= minRadius/r;
}
}
else
{
// Radius must be too large
x *= maxRadius/r;
y *= maxRadius/r;
}
finalCoords[X_AXIS] = x - xOffset;
finalCoords[Y_AXIS] = y - yOffset;
}
// Recalculate theta and psi, but don't allow arm mode changes this time
if (!CalculateThetaAndPsi(finalCoords, true, theta, psi, armMode) && !std::isnan(theta))
{
// Radius is in range but at least one arm angle isn't
cachedTheta = theta = constrain<float>(theta, thetaLimits[0], thetaLimits[1]);
cachedPsi = psi = constrain<float>(psi, psiLimits[0], psiLimits[1]);
cachedX = finalCoords[X_AXIS] = (cosf(theta * DegreesToRadians) * proximalArmLength + cosf((psi + theta) * DegreesToRadians) * distalArmLength) - xOffset;
cachedY = finalCoords[Y_AXIS] = (sinf(theta * DegreesToRadians) * proximalArmLength + sinf((psi + theta) * DegreesToRadians) * distalArmLength) - yOffset;
cachedArmMode = currentArmMode;
}
}
// The final position is now reachable. Check that we can get there from the initial position.
if (isCoordinated && initialCoords != nullptr)
{
// Calculate how far along the line the closest point of approach to the distal axis is
// From maxima, t = -(y0(y1-y0)+x0(x1-x0))/L^2, d^2=((x0y1-x1y0)^2)/L^2
// where t is how far from along the line from x0y0 to x1y1 the closest point of approach is (0..1), d is the closest approach distance, and L^2= (x1-x0)^2+(y1-y0)^2
const float xdiff = finalCoords[0] - initialCoords[0];
const float ydiff = finalCoords[1] - initialCoords[1];
const float sumOfSquares = fsquare(xdiff) + fsquare(ydiff);
const float p = -(xdiff * (initialCoords[0] + xOffset) + ydiff * (initialCoords[1] + yOffset));
if (p > 0.0 && p < sumOfSquares)
{
// The closest point of approach to the distal axis is between the start and end points, so calculate the distance
const float cpa2 = fsquare((finalCoords[0] + xOffset) * (initialCoords[1] + yOffset) - (finalCoords[1] + yOffset) * (initialCoords[0] + xOffset));
if (cpa2 < minRadiusSquared * sumOfSquares)
{
return (limited) ? LimitPositionResult::adjustedAndIntermediateUnreachable : LimitPositionResult::intermediateUnreachable;
}
}
}
return (limited) ? LimitPositionResult::adjusted : LimitPositionResult::ok;
}
// Return the initial Cartesian coordinates we assume after switching to this kinematics
void ScaraKinematics::GetAssumedInitialPosition(size_t numAxes, float positions[]) const noexcept
{
positions[X_AXIS] = maxRadius - xOffset;
positions[Y_AXIS] = -yOffset;
for (size_t i = Z_AXIS; i < numAxes; ++i)
{
positions[i] = 0.0;
}
}
// Return the axes that we can assume are homed after executing a G92 command to set the specified axis coordinates
AxesBitmap ScaraKinematics::AxesAssumedHomed(AxesBitmap g92Axes) const noexcept
{
// If both X and Y have been specified then we know the positions of both arm motors, otherwise we don't
if ((g92Axes & XyAxes) != XyAxes)
{
g92Axes &= ~XyAxes;
}
return g92Axes;
}
// Return the set of axes that must be homed prior to regular movement of the specified axes
AxesBitmap ScaraKinematics::MustBeHomedAxes(AxesBitmap axesMoving, bool disallowMovesBeforeHoming) const noexcept
{
if (axesMoving.Intersects(XyAxes))
{
axesMoving |= XyAxes;
}
return axesMoving;
}
// This function is called when a request is made to home the axes in 'toBeHomed' and the axes in 'alreadyHomed' have already been homed.
// If we can proceed with homing some axes, return the name of the homing file to be called.
// If we can't proceed because other axes need to be homed first, return nullptr and pass those axes back in 'mustBeHomedFirst'.
AxesBitmap ScaraKinematics::GetHomingFileName(AxesBitmap toBeHomed, AxesBitmap alreadyHomed, size_t numVisibleAxes, const StringRef& filename) const noexcept
{
// Ask the base class which homing file we should call first
const AxesBitmap ret = Kinematics::GetHomingFileName(toBeHomed, alreadyHomed, numVisibleAxes, filename);
if (ret.IsEmpty())
{
// Change the returned name if it is X or Y
if (StringEqualsIgnoreCase(filename.c_str(), "homex.g"))
{
filename.copy(HomeProximalFileName);
}
else if (StringEqualsIgnoreCase(filename.c_str(), "homey.g"))
{
filename.copy(HomeDistalFileName);
}
#if HAS_MASS_STORAGE
// Some SCARA printers cannot have individual axes homed safely. So it the user doesn't provide the homing file for an axis, default to homeall.
if (!reprap.GetPlatform().SysFileExists(filename.c_str()))
{
filename.copy(HomeAllFileName);
}
#endif
}
return ret;
}
// This function is called from the step ISR when an endstop switch is triggered during homing.
// Return true if the entire homing move should be terminated, false if only the motor associated with the endstop switch should be stopped.
bool ScaraKinematics::QueryTerminateHomingMove(size_t axis) const noexcept
{
// If crosstalk causes the axis motor concerned to affect other axes then must terminate the entire move
return (axis == X_AXIS && (crosstalk[0] != 0.0 || crosstalk[1] != 0.0))
|| (axis == Y_AXIS && crosstalk[2] != 0.0);
}
// This function is called from the step ISR when an endstop switch is triggered during homing after stopping just one motor or all motors.
// Take the action needed to define the current position, normally by calling dda.SetDriveCoordinate().
void ScaraKinematics::OnHomingSwitchTriggered(size_t axis, bool highEnd, const float stepsPerMm[], DDA& dda) const noexcept
{
switch (axis)
{
case X_AXIS: // proximal joint homing switch
{
const float hitPoint = (highEnd) ? thetaLimits[1] : thetaLimits[0];
dda.SetDriveCoordinate(lrintf(hitPoint * stepsPerMm[axis]), axis);
}
break;
case Y_AXIS: // distal joint homing switch
{
const float hitPoint = ((highEnd) ? psiLimits[1] : psiLimits[0])
- ((dda.DriveCoordinates()[X_AXIS] * crosstalk[0])/stepsPerMm[X_AXIS]);
dda.SetDriveCoordinate(lrintf(hitPoint * stepsPerMm[axis]), axis);
}
break;
case Z_AXIS: // Z axis homing switch
{
const float hitPoint = ((highEnd) ? reprap.GetPlatform().AxisMaximum(axis) : reprap.GetPlatform().AxisMinimum(axis))
- ((dda.DriveCoordinates()[X_AXIS] * crosstalk[1])/stepsPerMm[X_AXIS])
- ((dda.DriveCoordinates()[Y_AXIS] * crosstalk[2])/stepsPerMm[Y_AXIS]);
dda.SetDriveCoordinate(lrintf(hitPoint * stepsPerMm[axis]), axis);
}
break;
default: // Additional axis
{
const float hitPoint = (highEnd) ? reprap.GetPlatform().AxisMaximum(axis) : reprap.GetPlatform().AxisMinimum(axis);
dda.SetDriveCoordinate(lrintf(hitPoint * stepsPerMm[axis]), axis);
}
break;
}
}
// Return true if the specified axis is a continuous rotation axis
bool ScaraKinematics::IsContinuousRotationAxis(size_t axis) const noexcept
{
return (axis < 2 && supportsContinuousRotation[axis]) || Kinematics::IsContinuousRotationAxis(axis);
}
// Return a bitmap of axes that move linearly in response to the correct combination of linear motor movements.
// This is called to determine whether we can babystep the specified axis independently of regular motion.
AxesBitmap ScaraKinematics::GetLinearAxes() const noexcept
{
return (crosstalk[1] == 0.0 && crosstalk[2] == 0.0) ? AxesBitmap::MakeFromBits(Z_AXIS) : AxesBitmap();
}
// Recalculate the derived parameters
void ScaraKinematics::Recalc() noexcept
{
proximalArmLengthSquared = fsquare(proximalArmLength);
distalArmLengthSquared = fsquare(distalArmLength);
twoPd = proximalArmLength * distalArmLength * 2;
minRadius = max<float>(fastSqrtf(proximalArmLengthSquared + distalArmLengthSquared
+ twoPd * min<float>(cosf(psiLimits[0] * DegreesToRadians), cosf(psiLimits[1] * DegreesToRadians))) * 1.005,
requestedMinRadius);
minRadiusSquared = fsquare(minRadius);
// If the total angle range is greater than 360 degrees, we assume that it supports continuous rotation
supportsContinuousRotation[0] = (thetaLimits[1] - thetaLimits[0] > 360.0);
supportsContinuousRotation[1] = (psiLimits[1] - psiLimits[0] > 360.0);
if (supportsContinuousRotation[1] || (psiLimits[0] <= 0.0 && psiLimits[1] >= 0.0))
{
// Zero distal arm angle is reachable
maxRadius = proximalArmLength + distalArmLength;
}
else
{
const float minAngle = min<float>(fabsf(psiLimits[0]), fabsf(psiLimits[1])) * DegreesToRadians;
maxRadius = fastSqrtf(proximalArmLengthSquared + distalArmLengthSquared + (twoPd * cosf(minAngle)));
}
maxRadius *= 0.995;
cachedX = cachedY = std::numeric_limits<float>::quiet_NaN(); // make sure that the cached values won't match any coordinates
}
#endif // SUPPORT_SCARA
// End
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