/*

planner.c - buffers movement commands and manages the acceleration profile plan

Part of Grbl

Copyright (c) 2009-2011 Simen Svale Skogsrud

Copyright (c) 2011-2012 Sungeun K. Jeon

Copyright (c) 2011 Jens Geisler

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 <http://www.gnu.org/licenses/>.

*/

/* The ring buffer implementation gleaned from the wiring_serial library by David A. Mellis. */

#include <inttypes.h>

#include <math.h>

#include <stdlib.h>

#include "planner.h"

#include "nuts_bolts.h"

#include "stepper.h"

#include "settings.h"

#include "config.h"

#include "protocol.h"

// The number of linear motions that can be in the plan at any give time

#define BLOCK_BUFFER_SIZE 40

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 uint8_t next_buffer_head; // Index of the next buffer head

// Define planner variables

typedef struct {

int32_t position[4]; // The planner position of the tool in absolute steps. Kept separate

// from g-code position for movements requiring multiple line motions,

// i.e. arcs, canned cycles, and backlash compensation.

double previous_unit_vec[4]; // Unit vector of previous path line segment

double previous_nominal_speed; // Nominal speed of previous path line segment

} planner_t;

static planner_t pl;

// Returns the index of the next block in the ring buffer

// NOTE: Removed modulo (%) operator, which uses an expensive divide and multiplication.

static uint8_t next_block_index(uint8_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 uint8_t prev_block_index(uint8_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()

{

uint8_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()

{

uint8_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()

{

uint8_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_reset_buffer()

{

block_buffer_tail = block_buffer_head;

next_buffer_head = next_block_index(block_buffer_head);

}

void plan_init()

{

plan_reset_buffer();

memset(&pl, 0, sizeof(pl)); // Clear planner struct

}

inline void plan_discard_current_block()

{

if (block_buffer_head != block_buffer_tail) {

block_buffer_tail = next_block_index( block_buffer_tail );

}

}

inline block_t *plan_get_current_block()

{

if (block_buffer_head == block_buffer_tail) { return(NULL); }

return(&block_buffer[block_buffer_tail]);

}

// Returns the availability status of the block ring buffer. True, if full.

uint8_t plan_check_full_buffer()

{

if (block_buffer_tail == next_buffer_head) { return(true); }

return(false);

}

// Block until all buffered steps are executed.

void plan_synchronize()

{

while (plan_get_current_block() || sys.cycle_start) {

protocol_execute_runtime(); // Check and execute run-time commands

if (sys.abort) { return; } // Check for system abort

}

}

// Add a new linear movement to the buffer. x, y and z is the signed, absolute target position in

// millimeters. 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.

// All position data passed to the planner must be in terms of machine position to keep the planner

// independent of any coordinate system changes and offsets, which are handled by the g-code parser.

// NOTE: Assumes buffer is available. Buffer checks are handled at a higher level by motion_control.

void plan_buffer_line(double x, double y, double z, double c, double feed_rate, uint8_t invert_feed_rate)

{

// Prepare to set up new block

block_t *block = &block_buffer[block_buffer_head];

// Calculate target position in absolute steps

int32_t target[4];

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]);

target[C_AXIS] = lround(c*settings.steps_per_mm[C_AXIS]);

// Compute direction bits for this block

block->direction_bits = 0;

if (target[X_AXIS] < pl.position[X_AXIS]) { block->direction_bits |= (1<<X_DIRECTION_BIT); }

if (target[Y_AXIS] < pl.position[Y_AXIS]) { block->direction_bits |= (1<<Y_DIRECTION_BIT); }

if (target[Z_AXIS] < pl.position[Z_AXIS]) { block->direction_bits |= (1<<Z_DIRECTION_BIT); }

if (target[C_AXIS] < pl.position[C_AXIS]) { block->direction_bits |= (1<<C_DIRECTION_BIT); }

// Number of steps for each axis

block->steps_x = labs(target[X_AXIS]-pl.position[X_AXIS]);

block->steps_y = labs(target[Y_AXIS]-pl.position[Y_AXIS]);

block->steps_z = labs(target[Z_AXIS]-pl.position[Z_AXIS]);

block->steps_c = labs(target[C_AXIS]-pl.position[C_AXIS]);

block->step_event_count = max(block->steps_x, max(block->steps_y, max(block->steps_z, block->steps_c)));

// 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[4];

delta_mm[X_AXIS] = (target[X_AXIS]-pl.position[X_AXIS])/settings.steps_per_mm[X_AXIS];

delta_mm[Y_AXIS] = (target[Y_AXIS]-pl.position[Y_AXIS])/settings.steps_per_mm[Y_AXIS];

delta_mm[Z_AXIS] = (target[Z_AXIS]-pl.position[Z_AXIS])/settings.steps_per_mm[Z_AXIS];

delta_mm[C_AXIS] = (target[C_AXIS]-pl.position[C_AXIS])/settings.steps_per_mm[C_AXIS];

block->millimeters = sqrt(delta_mm[X_AXIS]*delta_mm[X_AXIS] + delta_mm[Y_AXIS]*delta_mm[Y_AXIS] +

delta_mm[Z_AXIS]*delta_mm[Z_AXIS] + delta_mm[C_AXIS]*delta_mm[C_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)

// Compute path unit vector

double unit_vec[4];

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;

unit_vec[C_AXIS] = delta_mm[C_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) && (pl.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 = - pl.previous_unit_vec[X_AXIS] * unit_vec[X_AXIS]

- pl.previous_unit_vec[Y_AXIS] * unit_vec[Y_AXIS]

- pl.previous_unit_vec[Z_AXIS] * unit_vec[Z_AXIS]

- pl.previous_unit_vec[C_AXIS] * unit_vec[C_AXIS] ;

// Skip and use default max junction speed for 0 degree acute junction.

if (cos_theta < 0.95) {

vmax_junction = min(pl.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(pl.previous_unit_vec, unit_vec, sizeof(unit_vec)); // pl.previous_unit_vec[] = unit_vec[]

pl.previous_nominal_speed = block->nominal_speed;

// Update buffer head and next buffer head indices

block_buffer_head = next_buffer_head;

next_buffer_head = next_block_index(block_buffer_head);

// Update planner position

memcpy(pl.position, target, sizeof(target)); // pl.position[] = target[]

planner_recalculate();

}

// Reset the planner position vector (in steps). Called by the system abort routine.

void plan_set_current_position(int32_t x, int32_t y, int32_t z, int32_t c)

{

pl.position[X_AXIS] = x;

pl.position[Y_AXIS] = y;

pl.position[Z_AXIS] = z;

pl.position[C_AXIS] = c;

}

// Clear planner position vector. Called by homing routine.

void plan_clear_position()

{

clear_vector(pl.position);

}

// Re-initialize buffer plan with a partially completed block, assumed to exist at the buffer tail.

// Called after a steppers have come to a complete stop for a feed hold and the cycle is stopped.

void plan_cycle_reinitialize(int32_t step_events_remaining)

{

block_t *block = &block_buffer[block_buffer_tail]; // Point to partially completed block

// Only remaining millimeters and step_event_count need to be updated for planner recalculate.

// Other variables (step_x, step_y, step_z, rate_delta, etc.) all need to remain the same to

// ensure the original planned motion is resumed exactly.

block->millimeters = (block->millimeters*step_events_remaining)/block->step_event_count;

block->step_event_count = step_events_remaining;

// Re-plan from a complete stop. Reset planner entry speeds and flags.

block->entry_speed = 0.0;

block->max_entry_speed = 0.0;

block->nominal_length_flag = false;

block->recalculate_flag = true;

planner_recalculate();

}