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Simen Svale Skogsrud 2011-02-19 00:32:36 +01:00
parent 6be195ba38
commit 464dcd12e8
5 changed files with 45 additions and 49 deletions
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30
doc/planner-maths.txt Normal file
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@ -0,0 +1,30 @@
Reasoning behind the mathematics in 'planner' module (in the key of 'Mathematica')
==================================================================================
s == speed, a == acceleration, t == time, d == distance
Basic definitions:
Speed[s_, a_, t_] := s + (a*t)
Travel[s_, a_, t_] := Integrate[Speed[s, a, t], t]
Distance to reach a specific speed with a constant acceleration:
Solve[{Speed[s, a, t] == m, Travel[s, a, t] == d}, d, t]
d -> (m^2 - s^2)/(2 a) --> estimate_acceleration_distance()
Speed after a given distance of travel with constant acceleration:
Solve[{Speed[s, a, t] == m, Travel[s, a, t] == d}, m, t]
m -> Sqrt[2 a d + s^2]
DestinationSpeed[s_, a_, d_] := Sqrt[2 a d + s^2]
When to start braking (di) to reach a specified destionation speed (s2) after accelerating
from initial speed s1 without ever stopping at a plateau:
Solve[{DestinationSpeed[s1, a, di] == DestinationSpeed[s2, a, d - di]}, di]
di -> (2 a d - s1^2 + s2^2)/(4 a) --> intersection_distance()
IntersectionDistance[s1_, s2_, a_, d_] := (2 a d - s1^2 + s2^2)/(4 a)

4
motion_control.h
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@ -27,14 +27,16 @@
// Execute linear motion in absolute millimeter coordinates. Feed rate given in millimeters/second
// unless invert_feed_rate is true. Then the feed_rate means that the motion should be completed in
// (1 minute)/feed_rate time.
#define mc_line(x, y, z, feed_rate, invert_feed_rate) plan_buffer_line(x, y, z, feed_rate, invert_feed_rate)
// NOTE: Although this function structurally belongs in this module, there is nothing to do but
// to forward the request to the planner. For efficiency the function is implemented with a macro.
#define mc_line(x, y, z, feed_rate, invert_feed_rate) plan_buffer_line(x, y, z, feed_rate, invert_feed_rate)
// Execute an arc. theta == start angle, angular_travel == number of radians to go along the arc,
// positive angular_travel means clockwise, negative means counterclockwise. Radius == the radius of the
// circle in millimeters. axis_1 and axis_2 selects the circle plane in tool space. Stick the remaining
// axis in axis_l which will be the axis for linear travel if you are tracing a helical motion.
void mc_arc(double theta, double angular_travel, double radius, double linear_travel, int axis_1, int axis_2,
int axis_linear, double feed_rate, int invert_feed_rate, double *position);

51
planner.c
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@ -20,38 +20,6 @@
/* The ring buffer implementation gleaned from the wiring_serial library by David A. Mellis. */
/*
Reasoning behind the mathematics in this module (in the key of 'Mathematica'):
s == speed, a == acceleration, t == time, d == distance
Basic definitions:
Speed[s_, a_, t_] := s + (a*t)
Travel[s_, a_, t_] := Integrate[Speed[s, a, t], t]
Distance to reach a specific speed with a constant acceleration:
Solve[{Speed[s, a, t] == m, Travel[s, a, t] == d}, d, t]
d -> (m^2 - s^2)/(2 a) --> estimate_acceleration_distance()
Speed after a given distance of travel with constant acceleration:
Solve[{Speed[s, a, t] == m, Travel[s, a, t] == d}, m, t]
m -> Sqrt[2 a d + s^2]
DestinationSpeed[s_, a_, d_] := Sqrt[2 a d + s^2]
When to start braking (di) to reach a specified destionation speed (s2) after accelerating
from initial speed s1 without ever stopping at a plateau:
Solve[{DestinationSpeed[s1, a, di] == DestinationSpeed[s2, a, d - di]}, di]
di -> (2 a d - s1^2 + s2^2)/(4 a) --> intersection_distance()
IntersectionDistance[s1_, s2_, a_, d_] := (2 a d - s1^2 + s2^2)/(4 a)
*/
#include <inttypes.h>
#include <math.h>
#include <stdlib.h>
@ -86,11 +54,6 @@ double estimate_acceleration_distance(double initial_rate, double target_rate, d
);
}
// This function gives you the point at which you must start braking (at the rate of -acceleration) if
// you started at speed initial_rate and accelerated until this point and want to end at the final_rate after
// a total travel of distance. This can be used to compute the intersection point between acceleration and
// deceleration in the cases where the trapezoid has no plateau (i.e. never reaches maximum speed)
/* + <- some maximum rate we don't care about
/|\
/ | \
@ -101,6 +64,12 @@ double estimate_acceleration_distance(double initial_rate, double target_rate, d
| |
intersection_distance distance */
// This function gives you the point at which you must start braking (at the rate of -acceleration) if
// you started at speed initial_rate and accelerated until this point and want to end at the final_rate after
// a total travel of distance. This can be used to compute the intersection point between acceleration and
// deceleration in the cases where the trapezoid has no plateau (i.e. never reaches maximum speed)
double intersection_distance(double initial_rate, double final_rate, double acceleration, double distance) {
return(
(2*acceleration*distance-initial_rate*initial_rate+final_rate*final_rate)/
@ -108,10 +77,6 @@ double intersection_distance(double initial_rate, double final_rate, double acce
);
}
// Calculates trapezoid parameters so that the entry- and exit-speed is compensated by the provided factors.
// The factors represent a factor of braking and must be in the range 0.0-1.0.
/*
+--------+ <- nominal_rate
/ \
@ -121,6 +86,9 @@ double intersection_distance(double initial_rate, double final_rate, double acce
time -->
*/
// Calculates trapezoid parameters so that the entry- and exit-speed is compensated by the provided factors.
// The factors represent a factor of braking and must be in the range 0.0-1.0.
void calculate_trapezoid_for_block(block_t *block, double entry_factor, double exit_factor) {
block->initial_rate = ceil(block->nominal_rate*entry_factor);
block->final_rate = ceil(block->nominal_rate*exit_factor);
@ -418,4 +386,3 @@ void plan_buffer_line(double x, double y, double z, double feed_rate, int invert
if (acceleration_manager_enabled) { planner_recalculate(); }
st_wake_up();
}

3
planner.h
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@ -18,9 +18,6 @@
along with Grbl. If not, see <http://www.gnu.org/licenses/>.
*/
// This module is to be considered a sub-module of stepper.c. Please don't include
// this file from any other module.
#ifndef planner_h
#define planner_h