ManuelW/grbl-LPC-CoreXY
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added code to estimate steps in arc in order to support helical motion

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Simen Svale Skogsrud
2009-02-09 15:47:51 +01:00
parent 2992683c8d
commit c2981be94a
5 changed files with 178 additions and 30 deletions
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88
motion_control.c
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@ -34,6 +34,9 @@
#include <stdlib.h>
#include "nuts_bolts.h"
#include "stepper.h"
#include "geometry.h"
#include "wiring_serial.h"
#define ONE_MINUTE_OF_MICROSECONDS 60000000.0
@ -74,7 +77,7 @@ void mc_line(double x, double y, double z, float feed_rate, int invert_feed_rate
maximum_steps; // The larges absolute step-count of any axis
// Setup
// Setup ---------------------------------------------------------------------------------------------------
target[X_AXIS] = x*X_STEPS_PER_MM;
target[Y_AXIS] = y*Y_STEPS_PER_MM;
@ -109,7 +112,7 @@ void mc_line(double x, double y, double z, float feed_rate, int invert_feed_rate
st_buffer_pace(((millimeters_to_travel * ONE_MINUTE_OF_MICROSECONDS) / feed_rate) / maximum_steps);
}
// Execution
// Execution -----------------------------------------------------------------------------------------------
mode = MC_MODE_LINEAR;
@ -152,8 +155,7 @@ void mc_arc(double theta, double angular_travel, double radius, int axis_1, int
// local coordinate system of the arc-generator where [0,0] is the
// center of the arc.
int target_direction_x, target_direction_y; // signof(target_x)*angular_direction precalculated for speed
int32_t error, x2, y2; // error is always == (x**2 + y**2 - radius**2),
// x2 is always 2*x, y2 is always 2*y
int32_t error; // error is always == (x**2 + y**2 - radius**2),
uint8_t axis_x, axis_y; // maps the arc axes to stepper axes
int8_t diagonal_bits; // A bitmask with the stepper bits for both selected axes set
int incomplete; // True if the arc has not reached its target yet
@ -164,6 +166,9 @@ void mc_arc(double theta, double angular_travel, double radius, int axis_1, int
uint32_t radius_steps = round(radius*X_STEPS_PER_MM);
if(radius_steps == 0) { return; }
// Setup arc interpolation --------------------------------------------------------------------------------
// Determine angular direction (+1 = clockwise, -1 = counterclockwise)
angular_direction = signof(angular_travel);
// Calculate the initial position and target position in the local coordinate system of the arc
@ -178,26 +183,71 @@ void mc_arc(double theta, double angular_travel, double radius, int axis_1, int
// <0 we are inside the arc, when it is >0 we are outside of the arc, and when it is 0 we
// are exactly on top of the arc.
error = x*x + y*y - radius_steps*radius_steps;
// Because the error-value moves in steps of (+/-)2x+1 and (+/-)2y+1 we save a couple of multiplications
// by keeping track of the doubles of the arc coordinates at all times.
x2 = 2*x;
y2 = 2*y;
// Set up a vector with the steppers we are going to use tracing the plane of this arc
diagonal_bits = st_bit_for_stepper(axis_1);
diagonal_bits |= st_bit_for_stepper(axis_2);
// And map the local coordinate system of the arc onto the tool axes of the selected plane
axis_x = axis_1;
axis_y = axis_2;
// Estimate length of arc in steps -------------------------------------------------------------------------
/*
To support helical motion we need to know in advance how many steppings the arc will need.
The calculations are based on the fact that we trace the circle by offsetting a square. The circle has
four "sides" or quadrants. For each quadrant we step mainly in one axis. The amount steps for one quarter of the
circle (e.g. along the x axis with positive y) is equal to one side of a square inscribed in the circle we
are tracing.
Quadrants of the circle
+---- 0 ----+ 0 - y is always positive and |x| < |y|
| | 1 - x is always positive and |x| > |y|
| | 2 - y is always negative and |x| < |y|
3 + 1 3 - x is always negative and |x| > |y|
| |
| | length of one side: 2*radius/sqrt(2)
+---- 2 ----+
*/
int start_quadrant = quadrant_of_the_circle(start_x, start_y);
int target_quadrant = quadrant_of_the_circle(target_x, target_y);
uint32_t steps_to_travel=0;
// Is the start and target point in the same quadrant?
if (start_quadrant == target_quadrant && (abs(angular_travel) <= (M_PI/2))) {
if(quadrant_horizontal(start_quadrant)) { // a horizontal quadrant where x will be the primary direction
steps_to_travel = abs(target_x-start_x);
} else { // a vertical quadrant where y will be the primary direction
steps_to_travel = abs(target_y-start_y);
}
} else { // the start and target points are in different quadrants
// Lets estimate the amount of steps along one full quadrant
uint32_t steps_in_half_quadrant = ceil(radius_steps/sqrt(2));
// Add the steps in the first partial quadrant
steps_to_travel += steps_in_partial_quadrant(start_x, start_y,
start_quadrant, angular_direction, steps_in_half_quadrant);
// Count the number of full quadrants between the start and end quadrants
uint8_t full_quadrants_traveled = full_quadrants_between(start_quadrant, target_quadrant, angular_direction);
// Add steps for the full quadrants plus some stray steps for "corners"
steps_to_travel += full_quadrants_traveled*(steps_in_half_quadrant*2+1);
// Add the steps in the final partial quadrant. By inverting the angular direction we get the correct number for
// the target quadrant which steps through the opposite part of the quadrant with respect to the start quadrant.
steps_to_travel += steps_in_partial_quadrant(target_x, target_y,
target_quadrant, -angular_direction, steps_in_half_quadrant);
}
// Calculate feed rate -------------------------------------------------------------------------------------
// The amount of steppings performed while tracing a half circle is equal to the sum of sides in a
// square inscribed in the circle. We use this to estimate the amount of steps as if this arc was a half circle:
uint32_t steps_in_half_circle = round(radius_steps * 4 * (1/sqrt(2)));
uint32_t steps_in_half_circle = round((4*radius_steps)/sqrt(2)));
// We then calculate the millimeters of travel along the circumference of that same half circle
double millimeters_half_circumference = radius*M_PI;
// Then we calculate the microseconds between each step as if we will trace the full circle.
// It doesn't matter what fraction of the circle we are actually going to trace. The pace is the same.
st_buffer_pace(((millimeters_half_circumference * ONE_MINUTE_OF_MICROSECONDS) / feed_rate) / steps_in_half_circle);
// Execution
// Execution -----------------------------------------------------------------------------------------------
mode = MC_MODE_ARC;
@ -214,11 +264,11 @@ void mc_arc(double theta, double angular_travel, double radius, int axis_1, int
// Check which axis will be "major" for this stepping
if (abs(x)<abs(y)) {
// Step arc horizontally
error += 1+x2*dx;
x+=dx; x2 += 2*dx;
diagonal_error = error + 1 + y2*dy;
error += 1 + 2*x * dx;
x+=dx;
diagonal_error = error + 1 + 2*y*dy;
if(abs(error) >= abs(diagonal_error)) {
y += dy; y2 += 2*dy;
y += dy;
error = diagonal_error;
step_steppers(diagonal_bits); // step diagonal
} else {
@ -226,11 +276,11 @@ void mc_arc(double theta, double angular_travel, double radius, int axis_1, int
}
} else {
// Step arc vertically
error += 1+y2*dy;
y+=dy; y2 += 2*dy;
diagonal_error = error + 1 + x2*dx;
error += 1 + 2*y * dy;
y+=dy;
diagonal_error = error + 1 + 2*x * dx;
if(abs(error) >= abs(diagonal_error)) {
x += dx; x2 += 2*dx;
x += dx;
error = diagonal_error;
step_steppers(diagonal_bits); // step diagonal
} else {
@ -267,7 +317,7 @@ int mc_status()
// Set the direction bits for the stepper motors according to the provided vector.
// direction is an array of three 8 bit integers representing the direction of
// each motor. The values should be -1 (reverse), 0 or 1 (forward).
// each motor. The values should be negative (reverse), 0 or positive (forward).
void set_stepper_directions(int8_t *direction)
{
/* Sorry about this convoluted code! It uses the fact that bit 7 of each direction