comparison: motion_control.cpp
motion_control.cpp
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| 1 /* | |
| 2 motion_control.c - high level interface for issuing motion commands | |
| 3 Part of Grbl | |
| 4 | |
| 5 Copyright (c) 2009-2011 Simen Svale Skogsrud | |
| 6 Copyright (c) 2011 Sungeun K. Jeon | |
| 7 | |
| 8 Grbl is free software: you can redistribute it and/or modify | |
| 9 it under the terms of the GNU General Public License as published by | |
| 10 the Free Software Foundation, either version 3 of the License, or | |
| 11 (at your option) any later version. | |
| 12 | |
| 13 Grbl is distributed in the hope that it will be useful, | |
| 14 but WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 15 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
| 16 GNU General Public License for more details. | |
| 17 | |
| 18 You should have received a copy of the GNU General Public License | |
| 19 along with Grbl. If not, see <http://www.gnu.org/licenses/>. | |
| 20 */ | |
| 21 | |
| 22 #include "Marlin.h" | |
| 23 #include "stepper.h" | |
| 24 #include "planner.h" | |
| 25 | |
| 26 // The arc is approximated by generating a huge number of tiny, linear segments. The length of each | |
| 27 // segment is configured in settings.mm_per_arc_segment. | |
| 28 void mc_arc(float *position, float *target, float *offset, uint8_t axis_0, uint8_t axis_1, | |
| 29 uint8_t axis_linear, float feed_rate, float radius, uint8_t isclockwise, uint8_t extruder) | |
| 30 { | |
| 31 // int acceleration_manager_was_enabled = plan_is_acceleration_manager_enabled(); | |
| 32 // plan_set_acceleration_manager_enabled(false); // disable acceleration management for the duration of the arc | |
| 33 float center_axis0 = position[axis_0] + offset[axis_0]; | |
| 34 float center_axis1 = position[axis_1] + offset[axis_1]; | |
| 35 float linear_travel = target[axis_linear] - position[axis_linear]; | |
| 36 float extruder_travel = target[E_AXIS] - position[E_AXIS]; | |
| 37 float r_axis0 = -offset[axis_0]; // Radius vector from center to current location | |
| 38 float r_axis1 = -offset[axis_1]; | |
| 39 float rt_axis0 = target[axis_0] - center_axis0; | |
| 40 float rt_axis1 = target[axis_1] - center_axis1; | |
| 41 | |
| 42 // CCW angle between position and target from circle center. Only one atan2() trig computation required. | |
| 43 float angular_travel = atan2(r_axis0*rt_axis1-r_axis1*rt_axis0, r_axis0*rt_axis0+r_axis1*rt_axis1); | |
| 44 if (angular_travel < 0) { angular_travel += 2*M_PI; } | |
| 45 if (isclockwise) { angular_travel -= 2*M_PI; } | |
| 46 | |
| 47 float millimeters_of_travel = hypot(angular_travel*radius, fabs(linear_travel)); | |
| 48 if (millimeters_of_travel < 0.001) { return; } | |
| 49 uint16_t segments = floor(millimeters_of_travel/MM_PER_ARC_SEGMENT); | |
| 50 if(segments == 0) segments = 1; | |
| 51 | |
| 52 /* | |
| 53 // Multiply inverse feed_rate to compensate for the fact that this movement is approximated | |
| 54 // by a number of discrete segments. The inverse feed_rate should be correct for the sum of | |
| 55 // all segments. | |
| 56 if (invert_feed_rate) { feed_rate *= segments; } | |
| 57 */ | |
| 58 float theta_per_segment = angular_travel/segments; | |
| 59 float linear_per_segment = linear_travel/segments; | |
| 60 float extruder_per_segment = extruder_travel/segments; | |
| 61 | |
| 62 /* Vector rotation by transformation matrix: r is the original vector, r_T is the rotated vector, | |
| 63 and phi is the angle of rotation. Based on the solution approach by Jens Geisler. | |
| 64 r_T = [cos(phi) -sin(phi); | |
| 65 sin(phi) cos(phi] * r ; | |
| 66 | |
| 67 For arc generation, the center of the circle is the axis of rotation and the radius vector is | |
| 68 defined from the circle center to the initial position. Each line segment is formed by successive | |
| 69 vector rotations. This requires only two cos() and sin() computations to form the rotation | |
| 70 matrix for the duration of the entire arc. Error may accumulate from numerical round-off, since | |
| 71 all double numbers are single precision on the Arduino. (True double precision will not have | |
| 72 round off issues for CNC applications.) Single precision error can accumulate to be greater than | |
| 73 tool precision in some cases. Therefore, arc path correction is implemented. | |
| 74 | |
| 75 Small angle approximation may be used to reduce computation overhead further. This approximation | |
| 76 holds for everything, but very small circles and large mm_per_arc_segment values. In other words, | |
| 77 theta_per_segment would need to be greater than 0.1 rad and N_ARC_CORRECTION would need to be large | |
| 78 to cause an appreciable drift error. N_ARC_CORRECTION~=25 is more than small enough to correct for | |
| 79 numerical drift error. N_ARC_CORRECTION may be on the order a hundred(s) before error becomes an | |
| 80 issue for CNC machines with the single precision Arduino calculations. | |
| 81 | |
| 82 This approximation also allows mc_arc to immediately insert a line segment into the planner | |
| 83 without the initial overhead of computing cos() or sin(). By the time the arc needs to be applied | |
| 84 a correction, the planner should have caught up to the lag caused by the initial mc_arc overhead. | |
| 85 This is important when there are successive arc motions. | |
| 86 */ | |
| 87 // Vector rotation matrix values | |
| 88 float cos_T = 1-0.5*theta_per_segment*theta_per_segment; // Small angle approximation | |
| 89 float sin_T = theta_per_segment; | |
| 90 | |
| 91 float arc_target[4]; | |
| 92 float sin_Ti; | |
| 93 float cos_Ti; | |
| 94 float r_axisi; | |
| 95 uint16_t i; | |
| 96 int8_t count = 0; | |
| 97 | |
| 98 // Initialize the linear axis | |
| 99 arc_target[axis_linear] = position[axis_linear]; | |
| 100 | |
| 101 // Initialize the extruder axis | |
| 102 arc_target[E_AXIS] = position[E_AXIS]; | |
| 103 | |
| 104 for (i = 1; i<segments; i++) { // Increment (segments-1) | |
| 105 | |
| 106 if (count < N_ARC_CORRECTION) { | |
| 107 // Apply vector rotation matrix | |
| 108 r_axisi = r_axis0*sin_T + r_axis1*cos_T; | |
| 109 r_axis0 = r_axis0*cos_T - r_axis1*sin_T; | |
| 110 r_axis1 = r_axisi; | |
| 111 count++; | |
| 112 } else { | |
| 113 // Arc correction to radius vector. Computed only every N_ARC_CORRECTION increments. | |
| 114 // Compute exact location by applying transformation matrix from initial radius vector(=-offset). | |
| 115 cos_Ti = cos(i*theta_per_segment); | |
| 116 sin_Ti = sin(i*theta_per_segment); | |
| 117 r_axis0 = -offset[axis_0]*cos_Ti + offset[axis_1]*sin_Ti; | |
| 118 r_axis1 = -offset[axis_0]*sin_Ti - offset[axis_1]*cos_Ti; | |
| 119 count = 0; | |
| 120 } | |
| 121 | |
| 122 // Update arc_target location | |
| 123 arc_target[axis_0] = center_axis0 + r_axis0; | |
| 124 arc_target[axis_1] = center_axis1 + r_axis1; | |
| 125 arc_target[axis_linear] += linear_per_segment; | |
| 126 arc_target[E_AXIS] += extruder_per_segment; | |
| 127 | |
| 128 if (min_software_endstops) { | |
| 129 if (arc_target[X_AXIS] < X_HOME_POS) arc_target[X_AXIS] = X_HOME_POS; | |
| 130 if (arc_target[Y_AXIS] < Y_HOME_POS) arc_target[Y_AXIS] = Y_HOME_POS; | |
| 131 if (arc_target[Z_AXIS] < Z_HOME_POS) arc_target[Z_AXIS] = Z_HOME_POS; | |
| 132 } | |
| 133 | |
| 134 if (max_software_endstops) { | |
| 135 if (arc_target[X_AXIS] > max_length[X_AXIS]) arc_target[X_AXIS] = max_length[X_AXIS]; | |
| 136 if (arc_target[Y_AXIS] > max_length[Y_AXIS]) arc_target[Y_AXIS] = max_length[Y_AXIS]; | |
| 137 if (arc_target[Z_AXIS] > max_length[Z_AXIS]) arc_target[Z_AXIS] = max_length[Z_AXIS]; | |
| 138 } | |
| 139 plan_buffer_line(arc_target[X_AXIS], arc_target[Y_AXIS], arc_target[Z_AXIS], arc_target[E_AXIS], feed_rate, extruder); | |
| 140 | |
| 141 } | |
| 142 // Ensure last segment arrives at target location. | |
| 143 plan_buffer_line(target[X_AXIS], target[Y_AXIS], target[Z_AXIS], target[E_AXIS], feed_rate, extruder); | |
| 144 | |
| 145 // plan_set_acceleration_manager_enabled(acceleration_manager_was_enabled); | |
| 146 } | |
| 147 |
