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Implemented a least squares fit of the bed equation for auto bed leveling.

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The code for the LSQ solver (qr_solve) is copyrighted by John Burkardt and released under LGPL here:
http://people.sc.fsu.edu/~%20jburkardt/c_src/qr_solve/qr_solve.html
(see qr_solve.cpp for further copyright information)
This commit is contained in:
fsantini 2013-12-06 21:46:25 +01:00
parent b64661070e
commit cc2925b705
4 changed files with 2075 additions and 2 deletions
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9
Marlin/Configuration.h
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@ -366,6 +366,15 @@ const bool Z_MAX_ENDSTOP_INVERTING = true; // set to true to invert the logic of
#endif
// with accurate bed leveling, the bed is sampled in a ACCURATE_BED_LEVELING_POINTSxACCURATE_BED_LEVELING_POINTS grid and least squares solution is calculated
// Note: this feature occupies 10'206 byte
#define ACCURATE_BED_LEVELING
#ifdef ACCURATE_BED_LEVELING
// I wouldn't see a reason to go above 3 (=9 probing points on the bed)
#define ACCURATE_BED_LEVELING_POINTS 2
#endif
#endif

114
Marlin/Marlin_main.cpp
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@ -31,6 +31,9 @@
#ifdef ENABLE_AUTO_BED_LEVELING
#include "vector_3.h"
#ifdef ACCURATE_BED_LEVELING
#include "qr_solve.h"
#endif
#endif // ENABLE_AUTO_BED_LEVELING
#include "ultralcd.h"
@ -798,6 +801,35 @@ static void axis_is_at_home(int axis) {
}
#ifdef ENABLE_AUTO_BED_LEVELING
#ifdef ACCURATE_BED_LEVELING
static void set_bed_level_equation_lsq(double *plane_equation_coefficients)
{
vector_3 planeNormal = vector_3(-plane_equation_coefficients[0], -plane_equation_coefficients[1], 1);
planeNormal.debug("planeNormal");
plan_bed_level_matrix = matrix_3x3::create_look_at(planeNormal);
//bedLevel.debug("bedLevel");
plan_bed_level_matrix.debug("bed level before");
//vector_3 uncorrected_position = plan_get_position_mm();
//uncorrected_position.debug("position before");
// and set our bed level equation to do the right thing
// plan_bed_level_matrix = matrix_3x3::create_inverse(bedLevel);
// plan_bed_level_matrix.debug("bed level after");
vector_3 corrected_position = plan_get_position();
// corrected_position.debug("position after");
current_position[X_AXIS] = corrected_position.x;
current_position[Y_AXIS] = corrected_position.y;
current_position[Z_AXIS] = corrected_position.z;
// but the bed at 0 so we don't go below it.
current_position[Z_AXIS] = -Z_PROBE_OFFSET_FROM_EXTRUDER; // in the lsq we reach here after raising the extruder due to the loop structure
plan_set_position(current_position[X_AXIS], current_position[Y_AXIS], current_position[Z_AXIS], current_position[E_AXIS]);
}
#else
static void set_bed_level_equation(float z_at_xLeft_yFront, float z_at_xRight_yFront, float z_at_xLeft_yBack) {
plan_bed_level_matrix.set_to_identity();
@ -832,6 +864,7 @@ static void set_bed_level_equation(float z_at_xLeft_yFront, float z_at_xRight_yF
plan_set_position(current_position[X_AXIS], current_position[Y_AXIS], current_position[Z_AXIS], current_position[E_AXIS]);
}
#endif // ACCURATE_BED_LEVELING
static void run_z_probe() {
plan_bed_level_matrix.set_to_identity();
@ -1320,7 +1353,82 @@ void process_commands()
setup_for_endstop_move();
feedrate = homing_feedrate[Z_AXIS];
#ifdef ACCURATE_BED_LEVELING
int xGridSpacing = (RIGHT_PROBE_BED_POSITION - LEFT_PROBE_BED_POSITION) / (ACCURATE_BED_LEVELING_POINTS-1);
int yGridSpacing = (BACK_PROBE_BED_POSITION - FRONT_PROBE_BED_POSITION) / (ACCURATE_BED_LEVELING_POINTS-1);
// solve the plane equation ax + by + d = z
// A is the matrix with rows [x y 1] for all the probed points
// B is the vector of the Z positions
// the normal vector to the plane is formed by the coefficients of the plane equation in the standard form, which is Vx*x+Vy*y+Vz*z+d = 0
// so Vx = -a Vy = -b Vz = 1 (we want the vector facing towards positive Z
// "A" matrix of the linear system of equations
double eqnAMatrix[ACCURATE_BED_LEVELING_POINTS*ACCURATE_BED_LEVELING_POINTS*3];
// "B" vector of Z points
double eqnBVector[ACCURATE_BED_LEVELING_POINTS*ACCURATE_BED_LEVELING_POINTS];
int probePointCounter = 0;
for (int xProbe=LEFT_PROBE_BED_POSITION; xProbe <= RIGHT_PROBE_BED_POSITION; xProbe += xGridSpacing)
{
for (int yProbe=FRONT_PROBE_BED_POSITION; yProbe <= BACK_PROBE_BED_POSITION; yProbe += yGridSpacing)
{
if (probePointCounter == 0)
{
// raise before probing
do_blocking_move_to(current_position[X_AXIS], current_position[Y_AXIS], Z_RAISE_BEFORE_PROBING);
} else
{
// raise extruder
do_blocking_move_to(current_position[X_AXIS], current_position[Y_AXIS], current_position[Z_AXIS] + Z_RAISE_BETWEEN_PROBINGS);
}
do_blocking_move_to(xProbe - X_PROBE_OFFSET_FROM_EXTRUDER, yProbe - Y_PROBE_OFFSET_FROM_EXTRUDER, current_position[Z_AXIS]);
engage_z_probe(); // Engage Z Servo endstop if available
run_z_probe();
eqnBVector[probePointCounter] = current_position[Z_AXIS];
retract_z_probe();
SERIAL_PROTOCOLPGM("Bed x: ");
SERIAL_PROTOCOL(xProbe);
SERIAL_PROTOCOLPGM(" y: ");
SERIAL_PROTOCOL(yProbe);
SERIAL_PROTOCOLPGM(" z: ");
SERIAL_PROTOCOL(current_position[Z_AXIS]);
SERIAL_PROTOCOLPGM("\n");
eqnAMatrix[probePointCounter + 0*ACCURATE_BED_LEVELING_POINTS*ACCURATE_BED_LEVELING_POINTS] = xProbe;
eqnAMatrix[probePointCounter + 1*ACCURATE_BED_LEVELING_POINTS*ACCURATE_BED_LEVELING_POINTS] = yProbe;
eqnAMatrix[probePointCounter + 2*ACCURATE_BED_LEVELING_POINTS*ACCURATE_BED_LEVELING_POINTS] = 1;
probePointCounter++;
}
}
clean_up_after_endstop_move();
// solve lsq problem
double *plane_equation_coefficients = qr_solve(ACCURATE_BED_LEVELING_POINTS*ACCURATE_BED_LEVELING_POINTS, 3, eqnAMatrix, eqnBVector);
SERIAL_PROTOCOLPGM("Eqn coefficients: a: ");
SERIAL_PROTOCOL(plane_equation_coefficients[0]);
SERIAL_PROTOCOLPGM(" b: ");
SERIAL_PROTOCOL(plane_equation_coefficients[1]);
SERIAL_PROTOCOLPGM(" d: ");
SERIAL_PROTOCOLLN(plane_equation_coefficients[2]);
set_bed_level_equation_lsq(plane_equation_coefficients);
free(plane_equation_coefficients);
#else // ACCURATE_BED_LEVELING not defined
// prob 1
do_blocking_move_to(current_position[X_AXIS], current_position[Y_AXIS], Z_RAISE_BEFORE_PROBING);
do_blocking_move_to(LEFT_PROBE_BED_POSITION - X_PROBE_OFFSET_FROM_EXTRUDER, BACK_PROBE_BED_POSITION - Y_PROBE_OFFSET_FROM_EXTRUDER, current_position[Z_AXIS]);
@ -1376,7 +1484,9 @@ void process_commands()
clean_up_after_endstop_move();
set_bed_level_equation(z_at_xLeft_yFront, z_at_xRight_yFront, z_at_xLeft_yBack);
#endif // ACCURATE_BED_LEVELING
st_synchronize();
// The following code correct the Z height difference from z-probe position and hotend tip position.

1932
Marlin/qr_solve.cpp Normal file
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22
Marlin/qr_solve.h Normal file
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@ -0,0 +1,22 @@
#include "Configuration.h"
#ifdef ACCURATE_BED_LEVELING
void daxpy ( int n, double da, double dx[], int incx, double dy[], int incy );
double ddot ( int n, double dx[], int incx, double dy[], int incy );
double dnrm2 ( int n, double x[], int incx );
void dqrank ( double a[], int lda, int m, int n, double tol, int *kr,
int jpvt[], double qraux[] );
void dqrdc ( double a[], int lda, int n, int p, double qraux[], int jpvt[],
double work[], int job );
int dqrls ( double a[], int lda, int m, int n, double tol, int *kr, double b[],
double x[], double rsd[], int jpvt[], double qraux[], int itask );
void dqrlss ( double a[], int lda, int m, int n, int kr, double b[], double x[],
double rsd[], int jpvt[], double qraux[] );
int dqrsl ( double a[], int lda, int n, int k, double qraux[], double y[],
double qy[], double qty[], double b[], double rsd[], double ab[], int job );
void dscal ( int n, double sa, double x[], int incx );
void dswap ( int n, double x[], int incx, double y[], int incy );
double *qr_solve ( int m, int n, double a[], double b[] );
#endif