algorithm proof of concept in perl, partial implementation in c
This commit is contained in:
Michael Moon
Markus Hitter
parent
b4bf8144fc
commit
a28526dddb
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#include <stdio.h>
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#include <stdint.h>
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#include <stdlib.h>
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#include <math.h>
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#define F_CPU 16000000UL
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#define X_STEPS_PER_MM 320.0
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#define Y_STEPS_PER_MM 320.0
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#define Z_STEPS_PER_MM 200.0
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#define E_STEPS_PER_MM 287.0
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#define X_UM_PER_STEP (1000.0 / X_STEPS_PER_MM)
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#define Y_UM_PER_STEP (1000.0 / Y_STEPS_PER_MM)
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#define Z_UM_PER_STEP (1000.0 / Z_STEPS_PER_MM)
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#define E_UM_PER_STEP (1000.0 / E_STEPS_PER_MM)
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#define X_ACCEL_MM_S_S 9.0
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#define Y_ACCEL_MM_S_S 5.0
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#define Z_ACCEL_MM_S_S 1.0
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#define E_ACCEL_MM_S_S 15.0
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#define X_DECEL_MM_S_S 3.0
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#define Y_DECEL_MM_S_S 8.0
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#define Z_DECEL_MM_S_S 1.0
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#define E_DECEL_MM_S_S 18.0
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// courtesy of http://www.flipcode.com/archives/Fast_Approximate_Distance_Functions.shtml
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/*! linear approximation 2d distance formula
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\param dx distance in X plane
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\param dy distance in Y plane
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\return 3-part linear approximation of \f$\sqrt{\Delta x^2 + \Delta y^2}\f$
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see http://www.flipcode.com/archives/Fast_Approximate_Distance_Functions.shtml
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*/
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uint32_t approx_distance( uint32_t dx, uint32_t dy )
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{
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uint32_t min, max, approx;
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if ( dx < dy )
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{
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min = dx;
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max = dy;
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} else {
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min = dy;
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max = dx;
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}
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approx = ( max * 1007 ) + ( min * 441 );
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if ( max < ( min << 4 ))
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approx -= ( max * 40 );
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// add 512 for proper rounding
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return (( approx + 512 ) >> 10 );
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}
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// courtesy of http://www.oroboro.com/rafael/docserv.php/index/programming/article/distance
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/*! linear approximation 3d distance formula
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\param dx distance in X plane
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\param dy distance in Y plane
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\param dz distance in Z plane
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\return 3-part linear approximation of \f$\sqrt{\Delta x^2 + \Delta y^2 + \Delta z^2}\f$
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see http://www.oroboro.com/rafael/docserv.php/index/programming/article/distance
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*/
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uint32_t approx_distance_3( uint32_t dx, uint32_t dy, uint32_t dz )
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{
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uint32_t min, med, max, approx;
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if ( dx < dy )
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{
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min = dy;
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med = dx;
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} else {
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min = dx;
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med = dy;
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}
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if ( dz < min )
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{
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max = med;
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med = min;
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min = dz;
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} else if ( dz < med ) {
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max = med;
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med = dz;
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} else {
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max = dz;
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}
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approx = ( max * 860 ) + ( med * 851 ) + ( min * 520 );
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if ( max < ( med << 1 )) approx -= ( max * 294 );
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if ( max < ( min << 2 )) approx -= ( max * 113 );
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if ( med < ( min << 2 )) approx -= ( med * 40 );
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// add 512 for proper rounding
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return (( approx + 512 ) >> 10 );
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}
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/*!
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integer square root algorithm
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\param a find square root of this number
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\return sqrt(a - 1) < returnvalue <= sqrt(a)
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see http://www.embedded-systems.com/98/9802fe2.htm
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*/
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// courtesy of http://www.embedded-systems.com/98/9802fe2.htm
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uint16_t int_sqrt(uint32_t a) {
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uint32_t rem = 0;
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uint32_t root = 0;
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uint16_t i;
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for (i = 0; i < 16; i++) {
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root <<= 1;
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rem = ((rem << 2) + (a >> 30));
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a <<= 2;
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root++;
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if (root <= rem) {
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rem -= root;
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root++;
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}
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else
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root--;
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}
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return (uint16_t) ((root >> 1) & 0xFFFFL);
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}
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// this is an ultra-crude pseudo-logarithm routine, such that:
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// 2 ^ msbloc(v) >= v
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/*! crude logarithm algorithm
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\param v value to find \f$log_2\f$ of
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\return floor(log(v) / log(2))
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*/
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const uint8_t msbloc (uint32_t v) {
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uint8_t i;
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uint32_t c;
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for (i = 31, c = 0x80000000; i; i--) {
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if (v & c)
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return i;
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c >>= 1;
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}
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return 0;
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}
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void move(int32_t dx, int32_t dy, int32_t dz, int32_t de, uint32_t f) {
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uint32_t distance = 0;
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uint32_t x_delta, y_delta, z_delta, e_delta;
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uint32_t x_speed, y_speed, z_speed, e_speed;
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uint32_t x_accel_distance, y_accel_distance, z_accel_distance, e_accel_distance;
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uint32_t x_c, y_c, z_c, e_c;
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int32_t x_n, y_n, z_n, e_n;
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uint32_t x_cr, y_cr, z_cr, e_cr;
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uint32_t x_minc, y_minc, z_minc, e_minc;
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uint32_t x_accel = X_ACCEL_MM_S_S * 1000.0, y_accel = Y_ACCEL_MM_S_S * 1000.0, z_accel = Z_ACCEL_MM_S_S * 1000.0, e_accel = E_ACCEL_MM_S_S * 1000.0;
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uint32_t duration;
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uint32_t accel_distance, decel_distance;
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uint32_t elapsed_ticks, total_ticks;
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// distance is micrometers
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if ((dx != 0 || dy != 0) && dz == 0)
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distance = approx_distance(dx * X_UM_PER_STEP, dy * Y_UM_PER_STEP);
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if (dx == 0 && dy == 0 && dz != 0)
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distance = dz * Z_UM_PER_STEP;
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if (distance < 2 && de != 0)
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distance = de * E_UM_PER_STEP;
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if (distance == 0)
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return;
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printf("distance: %dum\n", distance);
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// duration is microseconds
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duration = distance * 3UL * (F_CPU / 50UL / f);
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printf("duration: %d ticks (%ldms)\n", duration, duration / (F_CPU / 1000UL));
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// deltas are in steps
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x_delta = labs(dx);
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y_delta = labs(dy);
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z_delta = labs(dz);
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e_delta = labs(de);
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// speeds are in um per second
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if (x_delta)
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x_speed = x_delta * X_UM_PER_STEP * F_CPU / duration;
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if (y_delta)
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y_speed = y_delta * Y_UM_PER_STEP * F_CPU / duration;
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if (z_delta)
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z_speed = z_delta * Z_UM_PER_STEP * F_CPU / duration;
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if (e_delta)
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e_speed = e_delta * E_UM_PER_STEP * F_CPU / duration;
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printf("X speed: %dum/s, Y speed: %dum/s\n", x_speed, y_speed);
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accel_distance = 0;
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// n = w^2 / 2aw'
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// my $x_steps_to_accel = $x_speed * $x_speed * $x_steps_per_mm / 2 / $x_accel_mm_s_s;
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// x_accel_steps = (x_speed * x_speed / 1000000) * X_STEPS_PER_MM / 2 / X_ACCEL_MM_S_S;
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// x_accel_steps = (x_delta * 1000 / X_STEPS_PER_MM * F_CPU / duration * x_delta * 1000 / X_STEPS_PER_MM * F_CPU / duration / 1000000) * X_STEPS_PER_MM / 2 / X_ACCEL_MM_S_S;
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// x_accel_steps = (x_delta / X_STEPS_PER_MM * F_CPU / (distance * F_CPU * 3 / 50 / f) * x_delta / X_STEPS_PER_MM * F_CPU / (distance * F_CPU * 3 / 50 / f)) * X_STEPS_PER_MM / 2 / X_ACCEL_MM_S_S;
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// x_accel_steps = (x_delta * x_delta / X_STEPS_PER_MM * F_CPU / distance / F_CPU / 3 * 50 * f / X_STEPS_PER_MM * F_CPU / distance / F_CPU / 3 * 50 * f) * X_STEPS_PER_MM / 2 / X_ACCEL_MM_S_S;
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// x_accel_steps = (x_delta * x_delta / X_STEPS_PER_MM / distance / 3 * 50 * f / X_STEPS_PER_MM / distance / 3 * 50 * f) * X_STEPS_PER_MM / 2 / X_ACCEL_MM_S_S;
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// x_accel_steps = (x_delta * x_delta * 1250 * f * f / X_STEPS_PER_MM / distance / distance / 3 / 3) / X_ACCEL_MM_S_S;
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// x_accel_steps = (x_delta * f / distance / 3) * (x_delta * f / distance / 3) * 1250 / X_STEPS_PER_MM / X_ACCEL_MM_S_S;
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// x_accel_distance = x_accel_steps * X_UM_PER_STEP;
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#warning This calculation is susceptible to overflow!
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if (x_delta) {
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x_accel_distance = (x_delta * f / distance / 3UL) * (x_delta * f / distance / 3UL) * 1250UL / X_STEPS_PER_MM / X_ACCEL_MM_S_S * 1000UL / X_STEPS_PER_MM;
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if (x_accel_distance > accel_distance)
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accel_distance = x_accel_distance;
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}
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if (y_delta) {
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y_accel_distance = (y_delta * f / distance / 3UL) * (y_delta * f / distance / 3UL) * 1250UL / Y_STEPS_PER_MM / Y_ACCEL_MM_S_S * 1000UL / Y_STEPS_PER_MM;
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if (y_accel_distance > accel_distance)
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accel_distance = y_accel_distance;
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}
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if (z_delta) {
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z_accel_distance = (z_delta * f / distance / 3UL) * (z_delta * f / distance / 3UL) * 1250UL / Z_STEPS_PER_MM / Z_ACCEL_MM_S_S * 1000UL / Z_STEPS_PER_MM;
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if (z_accel_distance > accel_distance)
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accel_distance = z_accel_distance;
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}
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if (e_delta) {
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e_accel_distance = (e_delta * f / distance / 3UL) * (e_delta * f / distance / 3UL) * 1250UL / E_STEPS_PER_MM / E_ACCEL_MM_S_S * 1000UL / E_STEPS_PER_MM;
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if (e_accel_distance > accel_distance)
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accel_distance = e_accel_distance;
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}
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printf("Accel Distance: %dum\n", accel_distance);
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// n = w^2 / 2aw'
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// w' = w^2 / 2an
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// w' = w^2 * steps_per_mm / 2n
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// x_accel = x_speed * x_speed * X_STEPS_PER_MM / 2 / (accel_distance * X_STEPS_PER_MM)
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// x_accel = x_speed * x_speed / 2 / accel_distance / 1000
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// let's store in um/s2 instead of mm/s2 for precision
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#warning This calculation is susceptible to overflow!
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if (x_accel_distance < accel_distance)
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x_accel = x_speed * x_speed / accel_distance / 2UL;
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if (y_accel_distance < accel_distance)
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y_accel = y_speed * y_speed / accel_distance / 2UL;
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if (z_accel_distance < accel_distance)
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z_accel = z_speed * z_speed / accel_distance / 2UL;
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if (e_accel_distance < accel_distance)
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e_accel = e_speed * e_speed / accel_distance / 2UL;
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printf("X accel: %dum/s2, Y accel: %dum/s2\n", x_accel, y_accel);
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// c0 = f . sqrt(2a / accel)
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// = F_CPU * sqrt(2 / accel * steps_per_mm)
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// = F_CPU * sqrt(2) / sqrt(accel / 1000) / sqrt(steps_per_mm)
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// = F_CPU * sqrt(2) / int_sqrt(accel * steps_per_mm / 1000)
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// = F_CPU * sqrt(2) * sqrt(1000) / int_sqrt(accel * steps_per_mm)
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// = F_CPU / int_sqrt(accel * steps_per_mm) * (20 * sqrt(5))
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// 20.sqrt(5) ~= 313/7 (0.12%)
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// = F_CPU / int_sqrt(accel * steps_per_mm) * 313 / 7
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// 2**32 / 313 is about 13MHz, so we can't start with F_CPU * 313 if F_CPU is above 13MHz
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if (x_delta) {
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// printf("x_accel(%u) * X_STEPS_PER_MM(%u) = %u, sqrt() = %u\n", x_accel, ((uint32_t) X_STEPS_PER_MM), x_accel * ((uint32_t) X_STEPS_PER_MM), int_sqrt(x_accel * ((uint32_t) X_STEPS_PER_MM)));
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x_c = ((F_CPU * 256UL) / int_sqrt(x_accel * X_STEPS_PER_MM)) * 313UL / 7UL;
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// x_c = F_CPU * sqrt(2.0 / x_accel * X_UM_PER_STEP);
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x_minc = (F_CPU * 256UL) / (x_speed * X_STEPS_PER_MM);
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}
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if (y_delta) {
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y_c = (F_CPU * 256UL / int_sqrt(y_accel * Y_STEPS_PER_MM)) * 313UL / 7UL;
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// y_c = F_CPU * sqrt(Y_UM_PER_STEP / y_accel) * 1.414;
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y_minc = (F_CPU * 256UL) / (y_speed * Y_STEPS_PER_MM);
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}
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if (z_delta) {
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z_c = (F_CPU * 256UL / int_sqrt(z_accel * Z_STEPS_PER_MM)) * 313UL / 7UL;
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z_minc = (F_CPU * 256UL) / (z_speed * Z_STEPS_PER_MM);
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}
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if (e_delta) {
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e_c = (F_CPU * 256UL / int_sqrt(e_accel * E_STEPS_PER_MM)) * 313UL / 7UL;
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e_minc = (F_CPU * 256UL) / (e_speed * E_STEPS_PER_MM);
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}
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printf("Xc: %d, Yc: %d\n", x_c >> 8, y_c >> 8);
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printf("Xminc: %d, Yminc: %d\n", x_minc >> 8, y_minc >> 8);
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x_n = y_n = z_n = e_n = 1;
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x_cr = x_c >> 8;
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y_cr = y_c >> 8;
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z_cr = z_c >> 8;
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e_cr = e_c >> 8;
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total_ticks = 0;
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while (x_delta > 0 || y_delta > 0 || z_delta > 0 || e_delta > 0) {
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if (x_cr <= 0 && x_delta > 0) {
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x_delta--;
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// printf("x_c(%d) = %u", x_n, x_c >> 8);
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if (x_n == 1)
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x_c = x_c * 0.4056;
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else
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x_c = x_c - ((2 * x_c) / ((4 * x_n) + 1));
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// printf(" -> %u\n", x_c >> 8);
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if (x_c < x_minc)
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x_c = x_minc;
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x_cr = x_c >> 8;
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x_n++;
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}
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if (y_cr <= 0 && y_delta > 0) {
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y_delta--;
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if (y_n == 1)
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y_c = y_c * 0.4056;
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else
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y_c = y_c - ((2 * y_c) / ((4 * y_n) + 1));
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if (y_c < y_minc)
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y_c = y_minc;
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y_cr = y_c >> 8;
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y_n++;
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}
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if (z_cr <= 0 && z_delta > 0) {
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z_delta--;
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if (z_n == 1)
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z_c = z_c * 0.4056;
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else
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z_c = z_c - ((2 * z_c) / ((4 * z_n) + 1));
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if (z_c < z_minc)
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z_c = z_minc;
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z_cr = z_c >> 8;
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z_n++;
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}
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if (e_cr <= 0 && e_delta > 0) {
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e_delta--;
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if (e_n == 1)
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e_c = e_c * 0.4056;
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else
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e_c = e_c - ((2 * e_c) / ((4 * e_n) + 1));
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if (e_c < e_minc)
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e_c = e_minc;
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e_cr = e_c >> 8;
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e_n++;
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}
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// printf("[xc: %d, xd: %d, yc: %d, yd: %d, ", x_cr, x_delta, y_cr, y_delta);
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fprintf(stderr, "%u %.3f %.3f %u(%u) %u %u(%u) %u ", total_ticks, x_delta * X_UM_PER_STEP, y_delta * Y_UM_PER_STEP, x_c, x_c >> 8, x_n, y_c, y_c >> 8, y_n);
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elapsed_ticks = 0x7FFFFFFF;
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if ((x_delta > 0) && (x_cr < elapsed_ticks))
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elapsed_ticks = x_cr;
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if ((y_delta > 0) && (y_cr < elapsed_ticks))
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elapsed_ticks = y_cr;
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if ((z_delta > 0) && (z_cr < elapsed_ticks))
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elapsed_ticks = z_cr;
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if ((e_delta > 0) && (e_cr < elapsed_ticks))
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elapsed_ticks = e_cr;
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fprintf(stderr, "+%u", elapsed_ticks);
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// printf("e: %u]\n", elapsed_ticks);
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x_cr -= elapsed_ticks;
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y_cr -= elapsed_ticks;
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z_cr -= elapsed_ticks;
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e_cr -= elapsed_ticks;
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total_ticks += elapsed_ticks;
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fprintf(stderr, "\n");
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}
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}
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int main(int argc, char **argv) {
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float x = 40,
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y = 34,
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z = 0,
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e = 0,
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f = 1500;
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move(x * X_STEPS_PER_MM, y * Y_STEPS_PER_MM, z * Z_STEPS_PER_MM, e * E_STEPS_PER_MM, f);
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return 0;
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}
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@ -0,0 +1,4 @@
|
|||
#!/bin/bash
|
||||
|
||||
perl alg.pl 2>alg.data && gnuplot alg.plot && display alg.png
|
||||
|
||||
|
|
@ -0,0 +1,218 @@
|
|||
#!/usr/bin/perl
|
||||
|
||||
use strict;
|
||||
|
||||
# from http://www.eetimes.com/design/embedded/4006438/Generate-stepper-motor-speed-profiles-in-real-time
|
||||
# f = F_CPU
|
||||
# a = 1 / steps_per_mm (ie mm per step)
|
||||
# w = speed (mm/sec)
|
||||
# w' = accel (mm/sec/sec)
|
||||
# c = timer ticks (integer)
|
||||
# n = acceleration value (integer)
|
||||
# C0 = f * sqrt(2 a / w' )
|
||||
# = F_CPU * sqrt(2 / accel / steps_per_mm)
|
||||
# Cn = C0 * (sqrt(n + 1) - sqrt(n))
|
||||
# approximation:
|
||||
# Cn = Cn-1 - ((2 * Cn-1) / (4n + 1))
|
||||
# detach n from step index:
|
||||
# Ci = Ci-1 - ((2 * Ci-1) / (4ni + 1))
|
||||
# ramp down to stop in m steps:
|
||||
# ni = i - m
|
||||
# inaccuracies: C1 is inaccurate
|
||||
# use c1 = 0.4056 * C0
|
||||
|
||||
# number of steps to reach speed w with acceleration w':
|
||||
# n = (w^2 / (2 * a * w'))
|
||||
# = w * w * steps_per_mm / 2 / w'
|
||||
|
||||
# changes of acceleration
|
||||
# (n1 + 0.5).w'1 = (n2 + 0.5).w'2
|
||||
# n2 = ((n1 + 0.5) * w'1 / w'2) - 0.5
|
||||
|
||||
# when to decelerate (short move of m steps)
|
||||
# n = m.w'2 / (w'1 + w'2)
|
||||
|
||||
|
||||
my $f_cpu = 16000000;
|
||||
my ($x_mm, $y_mm, $f_mm_min) = (40, 34, 1500);
|
||||
my ($x_steps_per_mm, $y_steps_per_mm) = (320, 320);
|
||||
|
||||
my ($x_accel_mm_s_s, $y_accel_mm_s_s) = (9, 5);
|
||||
my ($x_decel_mm_s_s, $y_decel_mm_s_s) = (3, 8);
|
||||
|
||||
# **************************************
|
||||
|
||||
my ($x_um_per_step, $y_um_per_step) = (1000 / $x_steps_per_mm, 1000 / $y_steps_per_mm);
|
||||
|
||||
my ($x_delta, $y_delta) = ($x_mm * $x_steps_per_mm, $y_mm * $y_steps_per_mm);
|
||||
|
||||
my $distance = sqrt(($x_delta * $x_delta * $x_um_per_step * $x_um_per_step) + ($y_delta * $y_delta * $y_um_per_step * $y_um_per_step));
|
||||
|
||||
my $duration = $distance * $f_cpu * 60 / 1000 / $f_mm_min;
|
||||
|
||||
printf "MOVE %dmmx%dmm@%dmm/min: %d um (%d mm), %d ticks (%dms), %gmm/min (%gmm/s)\n", $x_mm, $y_mm, $f_mm_min, $distance, $distance / 1000, $duration, $duration / $f_cpu * 1000, $distance / 1000 / $duration * $f_cpu * 60, $distance / 1000 / $duration * $f_cpu;
|
||||
|
||||
my ($x_speed, $y_speed) = ($x_delta * $x_um_per_step / $duration * $f_cpu / 1000, $y_delta * $y_um_per_step / $duration * $f_cpu / 1000);
|
||||
|
||||
printf "X: %gmm/s, Y: %gmm/s\n", $x_speed, $y_speed;
|
||||
|
||||
# **************************************
|
||||
# n steps to accelerate to w at w' = w * w * steps_per_mm / 2 / w'
|
||||
my $x_steps_to_accel = $x_speed * $x_speed * $x_steps_per_mm / 2 / $x_accel_mm_s_s;
|
||||
my $y_steps_to_accel = $y_speed * $y_speed * $y_steps_per_mm / 2 / $y_accel_mm_s_s;
|
||||
|
||||
printf "Xns: %d (%dum), Yns: %d (%dum)\n", $x_steps_to_accel, $x_steps_to_accel * $x_um_per_step, $y_steps_to_accel, $y_steps_to_accel * $y_um_per_step;
|
||||
|
||||
# now we work out which axis reaches plateau last
|
||||
if ($x_steps_to_accel / $x_steps_per_mm > $y_steps_to_accel / $y_steps_per_mm) {
|
||||
# x reaches last- slow down Y
|
||||
# when X reaches plateau, where is Y?
|
||||
# x_steps / x_distance = y_steps / y_distance
|
||||
# y_steps = x_steps / x_distance * y_distance
|
||||
my $y_plateau_steps = $x_steps_to_accel / $x_delta * $y_delta;
|
||||
$y_accel_mm_s_s = $y_speed * $y_speed * $y_steps_per_mm / 2 / $y_plateau_steps;
|
||||
}
|
||||
else {
|
||||
# y reaches last- slow down X
|
||||
# when Y reaches plateau, where is X?
|
||||
# y_steps / y_distance = x_steps / x_distance
|
||||
# x_steps = y_steps / y_distance * x_distance
|
||||
my $x_plateau_steps = $y_steps_to_accel / $y_delta * $x_delta;
|
||||
$x_accel_mm_s_s = $x_speed * $x_speed * $x_steps_per_mm / 2 / $x_plateau_steps;
|
||||
}
|
||||
|
||||
$x_steps_to_accel = $x_speed * $x_speed * $x_steps_per_mm / 2 / $x_accel_mm_s_s;
|
||||
$y_steps_to_accel = $y_speed * $y_speed * $y_steps_per_mm / 2 / $y_accel_mm_s_s;
|
||||
|
||||
printf "new Xns: %d, Yns: %d\n", $x_steps_to_accel, $y_steps_to_accel;
|
||||
printf "Xaccel: %g, Yaccel: %g\n", $x_accel_mm_s_s, $y_accel_mm_s_s;
|
||||
|
||||
# now we work out which axis has to decelerate first
|
||||
# n steps to decelerate from w at w' = w * w * steps_per_mm / 2 / w'
|
||||
my $x_steps_to_decel = $x_speed * $x_speed * $x_steps_per_mm / 2 / $x_decel_mm_s_s;
|
||||
my $y_steps_to_decel = $y_speed * $y_speed * $y_steps_per_mm / 2 / $y_decel_mm_s_s;
|
||||
|
||||
printf "Xds: %d, Yds: %d\n", $x_steps_to_decel, $y_steps_to_decel;
|
||||
|
||||
# now we work out which axis reaches plateau last
|
||||
if ($x_steps_to_decel / $x_steps_per_mm > $y_steps_to_decel / $y_steps_per_mm) {
|
||||
# x reaches last- slow down Y
|
||||
# when X reaches plateau, where is Y?
|
||||
# x_steps / x_distance = y_steps / y_distance
|
||||
# y_steps = x_steps / x_distance * y_distance
|
||||
my $y_plateau_steps = $x_steps_to_decel / $x_delta * $y_delta;
|
||||
$y_decel_mm_s_s = $y_speed * $y_speed * $y_steps_per_mm / 2 / $y_plateau_steps;
|
||||
}
|
||||
else {
|
||||
# y reaches last- slow down X
|
||||
# when Y reaches plateau, where is X?
|
||||
# y_steps / y_distance = x_steps / x_distance
|
||||
# x_steps = y_steps / y_distance * x_distance
|
||||
my $x_plateau_steps = $y_steps_to_decel / $y_delta * $x_delta;
|
||||
$x_decel_mm_s_s = $x_speed * $x_speed * $x_steps_per_mm / 2 / $x_plateau_steps;
|
||||
}
|
||||
|
||||
my $x_steps_to_decel = $x_speed * $x_speed * $x_steps_per_mm / 2 / $x_decel_mm_s_s;
|
||||
my $y_steps_to_decel = $y_speed * $y_speed * $y_steps_per_mm / 2 / $y_decel_mm_s_s;
|
||||
|
||||
printf "new Xds: %d, Yds: %d\n", $x_steps_to_decel, $y_steps_to_decel;
|
||||
|
||||
if (($x_steps_to_accel + $x_steps_to_decel) > $x_delta) {
|
||||
# we will never reach full speed, however this doesn't affect our accel trimming so we can do this last
|
||||
# n = (m.w'2) / (w'1 + w'2)
|
||||
$x_steps_to_decel = int($x_delta * $x_decel_mm_s_s / ($x_accel_mm_s_s + $x_decel_mm_s_s));
|
||||
}
|
||||
if (($y_steps_to_accel + $y_steps_to_decel) > $y_delta) {
|
||||
# we will never reach full speed, however this doesn't affect our accel trimming so we can do this last
|
||||
# n = (m.w'2) / (w'1 + w'2)
|
||||
$y_steps_to_decel = int($y_delta * $y_decel_mm_s_s / ($y_accel_mm_s_s + $y_decel_mm_s_s));
|
||||
}
|
||||
|
||||
printf "new Xds: %d, Yds: %d\n", $x_steps_to_decel, $y_steps_to_decel;
|
||||
|
||||
# now we work out initial delays (C0)
|
||||
|
||||
# = F_CPU * sqrt(2 / accel / steps_per_mm)
|
||||
my $x_c = int($f_cpu * sqrt(2 / $x_accel_mm_s_s / $x_steps_per_mm));
|
||||
my $y_c = int($f_cpu * sqrt(2 / $y_accel_mm_s_s / $y_steps_per_mm));
|
||||
|
||||
# now we work out speed limits so we know when to stop accelerating
|
||||
|
||||
# mm/sec -> ticks per step
|
||||
# mm/sec * steps/mm = steps/sec
|
||||
# 1 / (mm/sec * steps/sec) = secs/step
|
||||
# f_cpu / (mm/sec * steps/sec) = ticks/step
|
||||
my $x_min_c = int($f_cpu / ($x_speed * $x_steps_per_mm));
|
||||
my $y_min_c = int($f_cpu / ($y_speed * $y_steps_per_mm));
|
||||
|
||||
printf "XminC: %dt/s, YminC: %dt/s\n", $x_min_c, $y_min_c;
|
||||
|
||||
# now we set up counters
|
||||
|
||||
my $x_n = 1;
|
||||
my $y_n = 1;
|
||||
|
||||
printf "Xc0: %d (%gus), Yc0: %d (%gus)\n", $x_c, $x_c / $f_cpu * 1000000, $y_c, $y_c / $f_cpu * 1000000;
|
||||
|
||||
my $elapsed_ticks = ($x_c < $y_c)?$x_c:$y_c;
|
||||
my ($x_cd, $y_cd) = ($x_c, $y_c);
|
||||
|
||||
my $total_ticks = 0;
|
||||
|
||||
printf stderr "%d %.3f %.3f\n", $total_ticks, $x_delta / $x_steps_per_mm, $y_delta / $y_steps_per_mm;
|
||||
|
||||
while ($x_delta > 0 || $y_delta > 0) {
|
||||
$x_cd -= $elapsed_ticks;
|
||||
$y_cd -= $elapsed_ticks;
|
||||
if ($x_cd <= 0 && $x_delta > 0) {
|
||||
$x_delta--;
|
||||
if ($x_delta == int($x_steps_to_decel)) {
|
||||
# start decelerating
|
||||
$x_n = -$x_delta;
|
||||
printf "[X DECEL]";
|
||||
}
|
||||
printf "[X: %ds:%gmm, %dc, %dn] ", $x_delta, $x_delta / $x_steps_per_mm, $x_c, $x_n;
|
||||
if ($x_n == 1) {
|
||||
$x_c = int(0.4056 * $x_c * 256) / 256;
|
||||
}
|
||||
else {
|
||||
$x_c = int(($x_c - ((2 * $x_c) / ((4 * $x_n) + 1))) * 256) / 256;
|
||||
}
|
||||
$x_cd = $x_c;
|
||||
$x_n++;
|
||||
$x_c = $x_min_c if $x_c < $x_min_c;
|
||||
}
|
||||
if ($y_cd <= 0 && $y_delta > 0) {
|
||||
$y_delta--;
|
||||
if ($y_delta == int($y_steps_to_decel)) {
|
||||
$y_n = -$y_delta;
|
||||
printf "[Y DECEL]";
|
||||
}
|
||||
printf "[Y: %ds:%gmm, %dc, %dn] ", $y_delta, $y_delta / $y_steps_per_mm, $y_c, $y_n;
|
||||
if ($y_n == 1) {
|
||||
$y_c = int(0.4056 * $y_c * 256) / 256;
|
||||
}
|
||||
else {
|
||||
$y_c = int(($y_c - ((2 * $y_c) / ((4 * $y_n) + 1))) * 256) / 256;
|
||||
}
|
||||
$y_cd = $y_c;
|
||||
$y_n++;
|
||||
$y_c = $y_min_c if $y_c < $y_min_c;
|
||||
}
|
||||
|
||||
printf stderr "%d %.3f %.3f\n", $total_ticks, $x_delta / $x_steps_per_mm, $y_delta / $y_steps_per_mm;
|
||||
|
||||
$elapsed_ticks = 2**31;
|
||||
$elapsed_ticks = $x_cd
|
||||
if $x_delta > 0 && $elapsed_ticks > $x_cd;
|
||||
$elapsed_ticks = $y_cd
|
||||
if $y_delta > 0 && $elapsed_ticks > $y_cd;
|
||||
|
||||
if ($elapsed_ticks < 2**31) {
|
||||
$total_ticks += $elapsed_ticks;
|
||||
printf "wait %d ticks\n", $elapsed_ticks;
|
||||
}
|
||||
else {
|
||||
print "finished\n";
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
# set terminal x11 persist raise
|
||||
set terminal png size 1024,768
|
||||
set output "alg.png"
|
||||
|
||||
set title "Move from [40,34] to [0,0] with acceleration [9,5] and deceleration [3,8]\n\
|
||||
showing geometric correctness as a result of acceleration and deceleration trimming"
|
||||
|
||||
set xlabel "seconds"
|
||||
set x2label "millimeters"
|
||||
set ylabel "millimeters"
|
||||
|
||||
plot "alg.data" using ($1 / 16000000):($2 / 1000) with lines title "X vs time", \
|
||||
"alg.data" using ($1 / 16000000):($3 / 1000) with lines title "Y vs time", \
|
||||
"alg.data" using ($2 / 1000):($3 / 1000) with lines axes x2y1 title "X vs Y", \
|
||||
(x * 34 / 40) with points axes x2y1 title "Ideal"
|
||||
Loading…
Reference in New Issue