planner.c

/*
  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 18

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;
}

// 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();  
}