/* planner.c - buffers movement commands and manages the acceleration profile plan Part of Grbl Copyright (c) 2009-2011 Simen Svale Skogsrud Copyright (c) 2011 Sungeun K. Jeon Grbl is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. Grbl is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with Grbl. If not, see . */ /* The ring buffer implementation gleaned from the wiring_serial library by David A. Mellis. */ #include #include #include #include "planner.h" #include "nuts_bolts.h" #include "stepper.h" #include "settings.h" #include "config.h" // The number of linear motions that can be in the plan at any give time #ifdef __AVR_ATmega328P__ #define BLOCK_BUFFER_SIZE 18 #else #define BLOCK_BUFFER_SIZE 5 #endif static block_t block_buffer[BLOCK_BUFFER_SIZE]; // A ring buffer for motion instructions static volatile uint8_t block_buffer_head; // Index of the next block to be pushed static volatile uint8_t block_buffer_tail; // Index of the block to process now static int32_t position[3]; // The current position of the tool in absolute steps static double previous_unit_vec[3]; // Unit vector of previous path line segment static double previous_nominal_speed; // Nominal speed of previous path line segment static uint8_t acceleration_manager_enabled; // Acceleration management active? // Returns the index of the next block in the ring buffer // NOTE: Removed modulo (%) operator, which uses an expensive divide and multiplication. static int8_t next_block_index(int8_t block_index) { block_index++; if (block_index == BLOCK_BUFFER_SIZE) { block_index = 0; } return(block_index); } // Returns the index of the previous block in the ring buffer static int8_t prev_block_index(int8_t block_index) { if (block_index == 0) { block_index = BLOCK_BUFFER_SIZE; } block_index--; return(block_index); } // Calculates the distance (not time) it takes to accelerate from initial_rate to target_rate using the // given acceleration: static double estimate_acceleration_distance(double initial_rate, double target_rate, double acceleration) { return( (target_rate*target_rate-initial_rate*initial_rate)/(2*acceleration) ); } /* + <- some maximum rate we don't care about /|\ / | \ / | + <- final_rate / | | initial_rate -> +----+--+ ^ ^ | | 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) static 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)/(4*acceleration) ); } // Calculates the maximum allowable speed at this point when you must be able to reach target_velocity // using the acceleration within the allotted distance. // NOTE: sqrt() reimplimented here from prior version due to improved planner logic. Increases speed // in time critical computations, i.e. arcs or rapid short lines from curves. Guaranteed to not exceed // BLOCK_BUFFER_SIZE calls per planner cycle. static double max_allowable_speed(double acceleration, double target_velocity, double distance) { return( sqrt(target_velocity*target_velocity-2*acceleration*distance) ); } // The kernel called by planner_recalculate() when scanning the plan from last to first entry. static void planner_reverse_pass_kernel(block_t *previous, block_t *current, block_t *next) { if (!current) { return; } // Cannot operate on nothing. if (next) { // If entry speed is already at the maximum entry speed, no need to recheck. Block is cruising. // If not, block in state of acceleration or deceleration. Reset entry speed to maximum and // check for maximum allowable speed reductions to ensure maximum possible planned speed. if (current->entry_speed != current->max_entry_speed) { // If nominal length true, max junction speed is guaranteed to be reached. Only compute // for max allowable speed if block is decelerating and nominal length is false. if ((!current->nominal_length_flag) && (current->max_entry_speed > next->entry_speed)) { current->entry_speed = min( current->max_entry_speed, max_allowable_speed(-settings.acceleration,next->entry_speed,current->millimeters)); } else { current->entry_speed = current->max_entry_speed; } current->recalculate_flag = true; } } // Skip last block. Already initialized and set for recalculation. } // planner_recalculate() needs to go over the current plan twice. Once in reverse and once forward. This // implements the reverse pass. static void planner_reverse_pass() { auto int8_t block_index = block_buffer_head; block_t *block[3] = {NULL, NULL, NULL}; while(block_index != block_buffer_tail) { block_index = prev_block_index( block_index ); block[2]= block[1]; block[1]= block[0]; block[0] = &block_buffer[block_index]; planner_reverse_pass_kernel(block[0], block[1], block[2]); } // Skip buffer tail/first block to prevent over-writing the initial entry speed. } // The kernel called by planner_recalculate() when scanning the plan from first to last entry. static void planner_forward_pass_kernel(block_t *previous, block_t *current, block_t *next) { if(!previous) { return; } // Begin planning after buffer_tail // If the previous block is an acceleration block, but it is not long enough to complete the // full speed change within the block, we need to adjust the entry speed accordingly. Entry // speeds have already been reset, maximized, and reverse planned by reverse planner. // If nominal length is true, max junction speed is guaranteed to be reached. No need to recheck. if (!previous->nominal_length_flag) { if (previous->entry_speed < current->entry_speed) { double entry_speed = min( current->entry_speed, max_allowable_speed(-settings.acceleration,previous->entry_speed,previous->millimeters) ); // Check for junction speed change if (current->entry_speed != entry_speed) { current->entry_speed = entry_speed; current->recalculate_flag = true; } } } } // planner_recalculate() needs to go over the current plan twice. Once in reverse and once forward. This // implements the forward pass. static void planner_forward_pass() { int8_t block_index = block_buffer_tail; block_t *block[3] = {NULL, NULL, NULL}; while(block_index != block_buffer_head) { block[0] = block[1]; block[1] = block[2]; block[2] = &block_buffer[block_index]; planner_forward_pass_kernel(block[0],block[1],block[2]); block_index = next_block_index( block_index ); } planner_forward_pass_kernel(block[1], block[2], NULL); } /* STEPPER RATE DEFINITION +--------+ <- nominal_rate / \ nominal_rate*entry_factor -> + \ | + <- nominal_rate*exit_factor +-------------+ 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. // This converts the planner parameters to the data required by the stepper controller. // NOTE: Final rates must be computed in terms of their respective blocks. static void calculate_trapezoid_for_block(block_t *block, double entry_factor, double exit_factor) { block->initial_rate = ceil(block->nominal_rate*entry_factor); // (step/min) block->final_rate = ceil(block->nominal_rate*exit_factor); // (step/min) int32_t acceleration_per_minute = block->rate_delta*ACCELERATION_TICKS_PER_SECOND*60.0; // (step/min^2) int32_t accelerate_steps = ceil(estimate_acceleration_distance(block->initial_rate, block->nominal_rate, acceleration_per_minute)); int32_t decelerate_steps = floor(estimate_acceleration_distance(block->nominal_rate, block->final_rate, -acceleration_per_minute)); // Calculate the size of Plateau of Nominal Rate. int32_t plateau_steps = block->step_event_count-accelerate_steps-decelerate_steps; // Is the Plateau of Nominal Rate smaller than nothing? That means no cruising, and we will // have to use intersection_distance() to calculate when to abort acceleration and start braking // in order to reach the final_rate exactly at the end of this block. if (plateau_steps < 0) { accelerate_steps = ceil( intersection_distance(block->initial_rate, block->final_rate, acceleration_per_minute, block->step_event_count)); accelerate_steps = max(accelerate_steps,0); // Check limits due to numerical round-off accelerate_steps = min(accelerate_steps,block->step_event_count); plateau_steps = 0; } block->accelerate_until = accelerate_steps; block->decelerate_after = accelerate_steps+plateau_steps; } /* PLANNER SPEED DEFINITION +--------+ <- current->nominal_speed / \ current->entry_speed -> + \ | + <- next->entry_speed +-------------+ time --> */ // Recalculates the trapezoid speed profiles for flagged blocks in the plan according to the // entry_speed for each junction and the entry_speed of the next junction. Must be called by // planner_recalculate() after updating the blocks. Any recalulate flagged junction will // compute the two adjacent trapezoids to the junction, since the junction speed corresponds // to exit speed and entry speed of one another. static void planner_recalculate_trapezoids() { int8_t block_index = block_buffer_tail; block_t *current; block_t *next = NULL; while(block_index != block_buffer_head) { current = next; next = &block_buffer[block_index]; if (current) { // Recalculate if current block entry or exit junction speed has changed. if (current->recalculate_flag || next->recalculate_flag) { // NOTE: Entry and exit factors always > 0 by all previous logic operations. calculate_trapezoid_for_block(current, current->entry_speed/current->nominal_speed, next->entry_speed/current->nominal_speed); current->recalculate_flag = false; // Reset current only to ensure next trapezoid is computed } } block_index = next_block_index( block_index ); } // Last/newest block in buffer. Exit speed is set with MINIMUM_PLANNER_SPEED. Always recalculated. calculate_trapezoid_for_block(next, next->entry_speed/next->nominal_speed, MINIMUM_PLANNER_SPEED/next->nominal_speed); next->recalculate_flag = false; } // Recalculates the motion plan according to the following algorithm: // // 1. Go over every block in reverse order and calculate a junction speed reduction (i.e. block_t.entry_speed) // so that: // a. The junction speed is equal to or less than the maximum junction speed limit // b. No speed reduction within one block requires faster deceleration than the one, true constant // acceleration. // 2. Go over every block in chronological order and dial down junction speed values if // a. The speed increase within one block would require faster acceleration than the one, true // constant acceleration. // // When these stages are complete all blocks have an entry speed that will allow all speed changes to // be performed using only the one, true constant acceleration, and where no junction speed is greater // than the max limit. Finally it will: // // 3. Recalculate trapezoids for all blocks using the recently updated junction speeds. Block trapezoids // with no updated junction speeds will not be recalculated and assumed ok as is. // // All planner computations are performed with doubles (float on Arduinos) to minimize numerical round- // off errors. Only when planned values are converted to stepper rate parameters, these are integers. static void planner_recalculate() { planner_reverse_pass(); planner_forward_pass(); planner_recalculate_trapezoids(); } void plan_init() { block_buffer_head = 0; block_buffer_tail = 0; plan_set_acceleration_manager_enabled(true); clear_vector(position); clear_vector_double(previous_unit_vec); previous_nominal_speed = 0.0; } void plan_set_acceleration_manager_enabled(uint8_t enabled) { if ((!!acceleration_manager_enabled) != (!!enabled)) { st_synchronize(); acceleration_manager_enabled = !!enabled; } } int plan_is_acceleration_manager_enabled() { return(acceleration_manager_enabled); } void plan_discard_current_block() { if (block_buffer_head != block_buffer_tail) { block_buffer_tail = next_block_index( block_buffer_tail ); } } block_t *plan_get_current_block() { if (block_buffer_head == block_buffer_tail) { return(NULL); } return(&block_buffer[block_buffer_tail]); } // Add a new linear movement to the buffer. x, y and z is the signed, absolute target position in // millimaters. Feed rate specifies the speed of the motion. If feed rate is inverted, the feed // rate is taken to mean "frequency" and would complete the operation in 1/feed_rate minutes. void plan_buffer_line(double x, double y, double z, double feed_rate, uint8_t invert_feed_rate) { // Calculate target position in absolute steps int32_t target[3]; target[X_AXIS] = lround(x*settings.steps_per_mm[X_AXIS]); target[Y_AXIS] = lround(y*settings.steps_per_mm[Y_AXIS]); target[Z_AXIS] = lround(z*settings.steps_per_mm[Z_AXIS]); // Calculate the buffer head after we push this byte int next_buffer_head = next_block_index( block_buffer_head ); // If the buffer is full: good! That means we are well ahead of the robot. // Rest here until there is room in the buffer. while(block_buffer_tail == next_buffer_head) { sleep_mode(); } // Prepare to set up new block block_t *block = &block_buffer[block_buffer_head]; // Compute direction bits for this block block->direction_bits = 0; if (target[X_AXIS] < position[X_AXIS]) { block->direction_bits |= (1<direction_bits |= (1<direction_bits |= (1<steps_x = labs(target[X_AXIS]-position[X_AXIS]); block->steps_y = labs(target[Y_AXIS]-position[Y_AXIS]); block->steps_z = labs(target[Z_AXIS]-position[Z_AXIS]); block->step_event_count = max(block->steps_x, max(block->steps_y, block->steps_z)); // Bail if this is a zero-length block if (block->step_event_count == 0) { return; }; // Compute path vector in terms of absolute step target and current positions double delta_mm[3]; delta_mm[X_AXIS] = (target[X_AXIS]-position[X_AXIS])/settings.steps_per_mm[X_AXIS]; delta_mm[Y_AXIS] = (target[Y_AXIS]-position[Y_AXIS])/settings.steps_per_mm[Y_AXIS]; delta_mm[Z_AXIS] = (target[Z_AXIS]-position[Z_AXIS])/settings.steps_per_mm[Z_AXIS]; block->millimeters = sqrt(square(delta_mm[X_AXIS]) + square(delta_mm[Y_AXIS]) + square(delta_mm[Z_AXIS])); double inverse_millimeters = 1.0/block->millimeters; // Inverse millimeters to remove multiple divides // Calculate speed in mm/minute for each axis. No divide by zero due to previous checks. // NOTE: Minimum stepper speed is limited by MINIMUM_STEPS_PER_MINUTE in stepper.c double inverse_minute; if (!invert_feed_rate) { inverse_minute = feed_rate * inverse_millimeters; } else { inverse_minute = 1.0 / feed_rate; } block->nominal_speed = block->millimeters * inverse_minute; // (mm/min) Always > 0 block->nominal_rate = ceil(block->step_event_count * inverse_minute); // (step/min) Always > 0 // Compute the acceleration rate for the trapezoid generator. Depending on the slope of the line // average travel per step event changes. For a line along one axis the travel per step event // is equal to the travel/step in the particular axis. For a 45 degree line the steppers of both // axes might step for every step event. Travel per step event is then sqrt(travel_x^2+travel_y^2). // To generate trapezoids with contant acceleration between blocks the rate_delta must be computed // specifically for each line to compensate for this phenomenon: // Convert universal acceleration for direction-dependent stepper rate change parameter block->rate_delta = ceil( block->step_event_count*inverse_millimeters * settings.acceleration / (60 * ACCELERATION_TICKS_PER_SECOND )); // (step/min/acceleration_tick) // Perform planner-enabled calculations if (acceleration_manager_enabled) { // Compute path unit vector double unit_vec[3]; unit_vec[X_AXIS] = delta_mm[X_AXIS]*inverse_millimeters; unit_vec[Y_AXIS] = delta_mm[Y_AXIS]*inverse_millimeters; unit_vec[Z_AXIS] = delta_mm[Z_AXIS]*inverse_millimeters; // Compute maximum allowable entry speed at junction by centripetal acceleration approximation. // Let a circle be tangent to both previous and current path line segments, where the junction // deviation is defined as the distance from the junction to the closest edge of the circle, // colinear with the circle center. The circular segment joining the two paths represents the // path of centripetal acceleration. Solve for max velocity based on max acceleration about the // radius of the circle, defined indirectly by junction deviation. This may be also viewed as // path width or max_jerk in the previous grbl version. This approach does not actually deviate // from path, but used as a robust way to compute cornering speeds, as it takes into account the // nonlinearities of both the junction angle and junction velocity. double vmax_junction = MINIMUM_PLANNER_SPEED; // Set default max junction speed // Skip first block or when previous_nominal_speed is used as a flag for homing and offset cycles. if ((block_buffer_head != block_buffer_tail) && (previous_nominal_speed > 0.0)) { // Compute cosine of angle between previous and current path. (prev_unit_vec is negative) // NOTE: Max junction velocity is computed without sin() or acos() by trig half angle identity. double cos_theta = - previous_unit_vec[X_AXIS] * unit_vec[X_AXIS] - previous_unit_vec[Y_AXIS] * unit_vec[Y_AXIS] - previous_unit_vec[Z_AXIS] * unit_vec[Z_AXIS] ; // Skip and use default max junction speed for 0 degree acute junction. if (cos_theta < 0.95) { vmax_junction = min(previous_nominal_speed,block->nominal_speed); // Skip and avoid divide by zero for straight junctions at 180 degrees. Limit to min() of nominal speeds. if (cos_theta > -0.95) { // Compute maximum junction velocity based on maximum acceleration and junction deviation double sin_theta_d2 = sqrt(0.5*(1.0-cos_theta)); // Trig half angle identity. Always positive. vmax_junction = min(vmax_junction, sqrt(settings.acceleration * settings.junction_deviation * sin_theta_d2/(1.0-sin_theta_d2)) ); } } } block->max_entry_speed = vmax_junction; // Initialize block entry speed. Compute based on deceleration to user-defined MINIMUM_PLANNER_SPEED. double v_allowable = max_allowable_speed(-settings.acceleration,MINIMUM_PLANNER_SPEED,block->millimeters); block->entry_speed = min(vmax_junction, v_allowable); // Initialize planner efficiency flags // Set flag if block will always reach maximum junction speed regardless of entry/exit speeds. // If a block can de/ac-celerate from nominal speed to zero within the length of the block, then // the current block and next block junction speeds are guaranteed to always be at their maximum // junction speeds in deceleration and acceleration, respectively. This is due to how the current // block nominal speed limits both the current and next maximum junction speeds. Hence, in both // the reverse and forward planners, the corresponding block junction speed will always be at the // the maximum junction speed and may always be ignored for any speed reduction checks. if (block->nominal_speed <= v_allowable) { block->nominal_length_flag = true; } else { block->nominal_length_flag = false; } block->recalculate_flag = true; // Always calculate trapezoid for new block // Update previous path unit_vector and nominal speed memcpy(previous_unit_vec, unit_vec, sizeof(unit_vec)); // previous_unit_vec[] = unit_vec[] previous_nominal_speed = block->nominal_speed; } else { // Acceleration planner disabled. Set minimum that is required. block->initial_rate = block->nominal_rate; block->final_rate = block->nominal_rate; block->accelerate_until = 0; block->decelerate_after = block->step_event_count; block->rate_delta = 0; } // Move buffer head block_buffer_head = next_buffer_head; // Update position memcpy(position, target, sizeof(target)); // position[] = target[] if (acceleration_manager_enabled) { planner_recalculate(); } st_cycle_start(); } // Reset the planner position vector and planner speed void plan_set_current_position(double x, double y, double z) { position[X_AXIS] = lround(x*settings.steps_per_mm[X_AXIS]); position[Y_AXIS] = lround(y*settings.steps_per_mm[Y_AXIS]); position[Z_AXIS] = lround(z*settings.steps_per_mm[Z_AXIS]); previous_nominal_speed = 0.0; // Resets planner junction speeds. Assumes start from rest. clear_vector_double(previous_unit_vec); }