160 lines
8.4 KiB
C++
160 lines
8.4 KiB
C++
/*
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motion_control.c - high level interface for issuing motion commands
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Part of Grbl
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Copyright (c) 2009-2011 Simen Svale Skogsrud
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Copyright (c) 2011 Sungeun K. Jeon
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Copyright (c) 2020 Brad Hochgesang
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Grbl is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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Grbl is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with Grbl. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "Marlin.h"
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#include "stepper.h"
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#include "planner.h"
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// The arc is approximated by generating a huge number of tiny, linear segments. The length of each
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// segment is configured in settings.mm_per_arc_segment.
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void mc_arc(float* position, float* target, float* offset, float feed_rate, float radius, bool isclockwise, uint8_t extruder)
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{
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float r_axis_x = -offset[X_AXIS]; // Radius vector from center to current location
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float r_axis_y = -offset[Y_AXIS];
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float center_axis_x = position[X_AXIS] - r_axis_x;
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float center_axis_y = position[Y_AXIS] - r_axis_y;
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float travel_z = target[Z_AXIS] - position[Z_AXIS];
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float rt_x = target[X_AXIS] - center_axis_x;
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float rt_y = target[Y_AXIS] - center_axis_y;
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// 20200419 - Add a variable that will be used to hold the arc segment length
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float mm_per_arc_segment = cs.mm_per_arc_segment;
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// 20210109 - Add a variable to hold the n_arc_correction value
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unsigned char n_arc_correction = cs.n_arc_correction;
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// CCW angle between position and target from circle center. Only one atan2() trig computation required.
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float angular_travel_total = atan2(r_axis_x * rt_y - r_axis_y * rt_x, r_axis_x * rt_x + r_axis_y * rt_y);
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if (angular_travel_total < 0) { angular_travel_total += 2 * M_PI; }
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if (cs.min_arc_segments > 0)
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{
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// 20200417 - FormerLurker - Implement MIN_ARC_SEGMENTS if it is defined - from Marlin 2.0 implementation
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// Do this before converting the angular travel for clockwise rotation
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mm_per_arc_segment = radius * ((2.0f * M_PI) / cs.min_arc_segments);
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}
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if (cs.arc_segments_per_sec > 0)
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{
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// 20200417 - FormerLurker - Implement MIN_ARC_SEGMENTS if it is defined - from Marlin 2.0 implementation
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float mm_per_arc_segment_sec = (feed_rate / 60.0f) * (1.0f / cs.arc_segments_per_sec);
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if (mm_per_arc_segment_sec < mm_per_arc_segment)
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mm_per_arc_segment = mm_per_arc_segment_sec;
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}
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// Note: no need to check to see if min_mm_per_arc_segment is enabled or not (i.e. = 0), since mm_per_arc_segment can never be below 0.
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if (mm_per_arc_segment < cs.min_mm_per_arc_segment)
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{
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// 20200417 - FormerLurker - Implement MIN_MM_PER_ARC_SEGMENT if it is defined
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// This prevents a very high number of segments from being generated for curves of a short radius
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mm_per_arc_segment = cs.min_mm_per_arc_segment;
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}
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else if (mm_per_arc_segment > cs.mm_per_arc_segment) {
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// 20210113 - This can be implemented in an else if since we can't be below the min AND above the max at the same time.
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// 20200417 - FormerLurker - Implement MIN_MM_PER_ARC_SEGMENT if it is defined
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mm_per_arc_segment = cs.mm_per_arc_segment;
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}
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// Adjust the angular travel if the direction is clockwise
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if (isclockwise) { angular_travel_total -= 2 * M_PI; }
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//20141002:full circle for G03 did not work, e.g. G03 X80 Y80 I20 J0 F2000 is giving an Angle of zero so head is not moving
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//to compensate when start pos = target pos && angle is zero -> angle = 2Pi
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if (position[X_AXIS] == target[X_AXIS] && position[Y_AXIS] == target[Y_AXIS] && angular_travel_total == 0)
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{
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angular_travel_total += 2 * M_PI;
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}
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//end fix G03
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// 20200417 - FormerLurker - rename millimeters_of_travel to millimeters_of_travel_arc to better describe what we are
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// calculating here
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const float millimeters_of_travel_arc = hypot(angular_travel_total * radius, fabs(travel_z));
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if (millimeters_of_travel_arc < 0.001) { return; }
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// Calculate the number of arc segments
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unsigned short segments = static_cast<unsigned short>(ceil(millimeters_of_travel_arc / mm_per_arc_segment));
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/* Vector rotation by transformation matrix: r is the original vector, r_T is the rotated vector,
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and phi is the angle of rotation. Based on the solution approach by Jens Geisler.
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r_T = [cos(phi) -sin(phi);
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sin(phi) cos(phi] * r ;
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For arc generation, the center of the circle is the axis of rotation and the radius vector is
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defined from the circle center to the initial position. Each line segment is formed by successive
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vector rotations. This requires only two cos() and sin() computations to form the rotation
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matrix for the duration of the entire arc. Error may accumulate from numerical round-off, since
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all double numbers are single precision on the Arduino. (True double precision will not have
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round off issues for CNC applications.) Single precision error can accumulate to be greater than
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tool precision in some cases. Therefore, arc path correction is implemented.
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The small angle approximation was removed because of excessive errors for small circles (perhaps unique to
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3d printing applications, causing significant path deviation and extrusion issues).
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Now there will be no corrections applied, but an accurate initial sin and cos will be calculated.
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This seems to work with a very high degree of accuracy and results in much simpler code.
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Finding a faster way to approximate sin, knowing that there can be substantial deviations from the true
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arc when using the previous approximation, would be beneficial.
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*/
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// If there is only one segment, no need to do a bunch of work since this is a straight line!
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if (segments > 1)
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{
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// Calculate theta per segments, and linear (z) travel per segment, e travel per segment
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// as well as the small angle approximation for sin and cos.
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const float theta_per_segment = angular_travel_total / segments,
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linear_per_segment = travel_z / (segments),
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segment_extruder_travel = (target[E_AXIS] - position[E_AXIS]) / (segments),
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sq_theta_per_segment = theta_per_segment * theta_per_segment,
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sin_T = theta_per_segment - sq_theta_per_segment * theta_per_segment / 6,
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cos_T = 1 - 0.5f * sq_theta_per_segment;
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// Loop through all but one of the segments. The last one can be done simply
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// by moving to the target.
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for (uint16_t i = 1; i < segments; i++) {
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if (n_arc_correction-- == 0) {
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// Calculate the actual position for r_axis_x and r_axis_y
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const float cos_Ti = cos(i * theta_per_segment), sin_Ti = sin(i * theta_per_segment);
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r_axis_x = -offset[X_AXIS] * cos_Ti + offset[Y_AXIS] * sin_Ti;
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r_axis_y = -offset[X_AXIS] * sin_Ti - offset[Y_AXIS] * cos_Ti;
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// reset n_arc_correction
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n_arc_correction = cs.n_arc_correction;
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}
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else {
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// Calculate X and Y using the small angle approximation
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const float r_axisi = r_axis_x * sin_T + r_axis_y * cos_T;
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r_axis_x = r_axis_x * cos_T - r_axis_y * sin_T;
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r_axis_y = r_axisi;
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}
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// Update Position
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position[X_AXIS] = center_axis_x + r_axis_x;
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position[Y_AXIS] = center_axis_y + r_axis_y;
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position[Z_AXIS] += linear_per_segment;
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position[E_AXIS] += segment_extruder_travel;
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// Clamp to the calculated position.
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clamp_to_software_endstops(position);
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// Insert the segment into the buffer
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plan_buffer_line(position[X_AXIS], position[Y_AXIS], position[Z_AXIS], position[E_AXIS], feed_rate, extruder, position);
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}
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}
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// Clamp to the target position.
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clamp_to_software_endstops(target);
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// Ensure last segment arrives at target location.
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plan_buffer_line(target[X_AXIS], target[Y_AXIS], target[Z_AXIS], target[E_AXIS], feed_rate, extruder, target);
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}
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