marlin/Marlin/planner.cpp

/*
  planner.c - buffers movement commands and manages the acceleration profile plan
  Part of Grbl

  Copyright (c) 2009-2011 Simen Svale Skogsrud

  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. */

/*  
  Reasoning behind the mathematics in this module (in the key of 'Mathematica'):
  
  s == speed, a == acceleration, t == time, d == distance

  Basic definitions:

    Speed[s_, a_, t_] := s + (a*t) 
    Travel[s_, a_, t_] := Integrate[Speed[s, a, t], t]

  Distance to reach a specific speed with a constant acceleration:

    Solve[{Speed[s, a, t] == m, Travel[s, a, t] == d}, d, t]
      d -> (m^2 - s^2)/(2 a) --> estimate_acceleration_distance()

  Speed after a given distance of travel with constant acceleration:

    Solve[{Speed[s, a, t] == m, Travel[s, a, t] == d}, m, t]
      m -> Sqrt[2 a d + s^2]    

    DestinationSpeed[s_, a_, d_] := Sqrt[2 a d + s^2]

  When to start braking (di) to reach a specified destionation speed (s2) after accelerating
  from initial speed s1 without ever stopping at a plateau:

    Solve[{DestinationSpeed[s1, a, di] == DestinationSpeed[s2, a, d - di]}, di]
      di -> (2 a d - s1^2 + s2^2)/(4 a) --> intersection_distance()

    IntersectionDistance[s1_, s2_, a_, d_] := (2 a d - s1^2 + s2^2)/(4 a)
*/
                                                                                                            

//#include <inttypes.h>
//#include <math.h>       
//#include <stdlib.h>

#include "Marlin.h"
#include "Configuration.h"
#include "pins.h"
#include "fastio.h"
#include "planner.h"
#include "stepper.h"
#include "temperature.h"
#include "ultralcd.h"

//===========================================================================
//=============================public variables ============================
//===========================================================================

unsigned long minsegmenttime;
float max_feedrate[4]; // set the max speeds
float axis_steps_per_unit[4];
long max_acceleration_units_per_sq_second[4]; // Use M201 to override by software
float minimumfeedrate;
float acceleration;         // Normal acceleration mm/s^2  THIS IS THE DEFAULT ACCELERATION for all moves. M204 SXXXX
float retract_acceleration; //  mm/s^2   filament pull-pack and push-forward  while standing still in the other axis M204 TXXXX
float max_xy_jerk; //speed than can be stopped at once, if i understand correctly.
float max_z_jerk;
float mintravelfeedrate;
unsigned long axis_steps_per_sqr_second[NUM_AXIS];

// The current position of the tool in absolute steps
long position[4];   //rescaled from extern when axis_steps_per_unit are changed by gcode
static float previous_speed[4]; // Speed of previous path line segment
static float previous_nominal_speed; // Nominal speed of previous path line segment


//===========================================================================
//=============================private variables ============================
//===========================================================================
static block_t block_buffer[BLOCK_BUFFER_SIZE];            // A ring buffer for motion instfructions
static volatile unsigned char block_buffer_head;           // Index of the next block to be pushed
static volatile unsigned char block_buffer_tail;           // Index of the block to process now

// Used for the frequency limit
static unsigned char old_direction_bits = 0;               // Old direction bits. Used for speed calculations
static long x_segment_time[3]={0,0,0};                     // Segment times (in us). Used for speed calculations
static long y_segment_time[3]={0,0,0};

// 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);
}

//===========================================================================
//=============================functions         ============================
//===========================================================================

// Calculates the distance (not time) it takes to accelerate from initial_rate to target_rate using the 
// given acceleration:
inline float estimate_acceleration_distance(float initial_rate, float target_rate, float acceleration) {
  if (acceleration!=0) {
  return((target_rate*target_rate-initial_rate*initial_rate)/
         (2.0*acceleration));
  }
  else {
    return 0.0;  // acceleration was 0, set acceleration distance to 0
  }
}

// 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)

inline float intersection_distance(float initial_rate, float final_rate, float acceleration, float distance) {
 if (acceleration!=0) {
  return((2.0*acceleration*distance-initial_rate*initial_rate+final_rate*final_rate)/
         (4.0*acceleration) );
  }
  else {
    return 0.0;  // acceleration was 0, set intersection distance to 0
  }
}

// Calculates trapezoid parameters so that the entry- and exit-speed is compensated by the provided factors.

void calculate_trapezoid_for_block(block_t *block, float entry_factor, float exit_factor) {
  long initial_rate = ceil(block->nominal_rate*entry_factor); // (step/min)
  long final_rate = ceil(block->nominal_rate*exit_factor); // (step/min)

  // Limit minimal step rate (Otherwise the timer will overflow.)
  if(initial_rate <120) {initial_rate=120; }
  if(final_rate < 120) {final_rate=120;  }
  
  long acceleration = block->acceleration_st;
  int32_t accelerate_steps =
    ceil(estimate_acceleration_distance(block->initial_rate, block->nominal_rate, acceleration));
  int32_t decelerate_steps =
    floor(estimate_acceleration_distance(block->nominal_rate, block->final_rate, -acceleration));
    
  // 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, 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;
  }

  #ifdef ADVANCE
    long initial_advance = block->advance*entry_factor*entry_factor;
    long final_advance = block->advance*exit_factor*exit_factor;
  #endif // ADVANCE
  
 // block->accelerate_until = accelerate_steps;
 // block->decelerate_after = accelerate_steps+plateau_steps;
  
  CRITICAL_SECTION_START;  // Fill variables used by the stepper in a critical section
  if(block->busy == false) { // Don't update variables if block is busy.
    block->accelerate_until = accelerate_steps;
    block->decelerate_after = accelerate_steps+plateau_steps;
    block->initial_rate = initial_rate;
    block->final_rate = final_rate;
  #ifdef ADVANCE
      block->initial_advance = initial_advance;
      block->final_advance = final_advance;
  #endif //ADVANCE
  }
  CRITICAL_SECTION_END;
}                    

// Calculates the maximum allowable speed at this point when you must be able to reach target_velocity using the 
// acceleration within the allotted distance.
inline float max_allowable_speed(float acceleration, float target_velocity, float distance) {
  return  sqrt(target_velocity*target_velocity-2*acceleration*distance);
}

// "Junction jerk" in this context is the immediate change in speed at the junction of two blocks.
// This method will calculate the junction jerk as the euclidean distance between the nominal 
// velocities of the respective blocks.
//inline float junction_jerk(block_t *before, block_t *after) {
//  return sqrt(
//    pow((before->speed_x-after->speed_x), 2)+pow((before->speed_y-after->speed_y), 2));
//}


// The kernel called by planner_recalculate() when scanning the plan from last to first entry.
void planner_reverse_pass_kernel(block_t *previous, block_t *current, block_t *next) {
  if(!current) { return; }
  
    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(-current->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.
void planner_reverse_pass() {
  char block_index = block_buffer_head;
  if(((block_buffer_head-block_buffer_tail + BLOCK_BUFFER_SIZE) & (BLOCK_BUFFER_SIZE - 1)) > 3) {
    block_index = (block_buffer_head - 3) & (BLOCK_BUFFER_SIZE - 1);
    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]);
    }
  }
}

// The kernel called by planner_recalculate() when scanning the plan from first to last entry.
void planner_forward_pass_kernel(block_t *previous, block_t *current, block_t *next) {
  if(!previous) { return; }
  
  // 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(-previous->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.
void planner_forward_pass() {
  char 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);
}

// Recalculates the trapezoid speed profiles for all blocks in the plan according to the 
// entry_factor for each junction. Must be called by planner_recalculate() after 
// updating the blocks.
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.
  if(next != NULL) {
    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_factor) 
//      so that:
//     a. The junction jerk is within the set 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 reduction values if 
//     a. The speed increase within one block would require faster accelleration than the one, true 
//        constant acceleration.
//
// When these stages are complete all blocks have an entry_factor that will allow all speed changes to 
// be performed using only the one, true constant acceleration, and where no junction jerk is jerkier than 
// the set limit. Finally it will:
//
//   3. Recalculate trapezoids for all blocks.

void planner_recalculate() {   
  planner_reverse_pass();
  planner_forward_pass();
  planner_recalculate_trapezoids();
}

void plan_init() {
  block_buffer_head = 0;
  block_buffer_tail = 0;
  memset(position, 0, sizeof(position)); // clear position
  previous_speed[0] = 0.0;
  previous_speed[1] = 0.0;
  previous_speed[2] = 0.0;
  previous_speed[3] = 0.0;
  previous_nominal_speed = 0.0;
}


void plan_discard_current_block() {
  if (block_buffer_head != block_buffer_tail) {
    block_buffer_tail = (block_buffer_tail + 1) & (BLOCK_BUFFER_SIZE - 1);  
  }
}

block_t *plan_get_current_block() {
  if (block_buffer_head == block_buffer_tail) { 
    return(NULL); 
  }
  block_t *block = &block_buffer[block_buffer_tail];
  block->busy = true;
  return(block);
}

void check_axes_activity() {
  unsigned char x_active = 0;
  unsigned char y_active = 0;  
  unsigned char z_active = 0;
  unsigned char e_active = 0;
  block_t *block;

  if(block_buffer_tail != block_buffer_head) {
    char block_index = block_buffer_tail;
    while(block_index != block_buffer_head) {
      block = &block_buffer[block_index];
      if(block->steps_x != 0) x_active++;
      if(block->steps_y != 0) y_active++;
      if(block->steps_z != 0) z_active++;
      if(block->steps_e != 0) e_active++;
      block_index = (block_index+1) & (BLOCK_BUFFER_SIZE - 1);
    }
  }
  if((DISABLE_X) && (x_active == 0)) disable_x();
  if((DISABLE_Y) && (y_active == 0)) disable_y();
  if((DISABLE_Z) && (z_active == 0)) disable_z();
  if((DISABLE_E) && (e_active == 0)) disable_e();
}


float junction_deviation = 0.1;
// Add a new linear movement to the buffer. steps_x, _y and _z is the absolute position in 
// mm. Microseconds specify how many microseconds the move should take to perform. To aid acceleration
// calculation the caller must also provide the physical length of the line in millimeters.
void plan_buffer_line(const float &x, const float &y, const float &z, const float &e,  float feed_rate)
{
  // 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) { 
    manage_heater(); 
    manage_inactivity(1); 
    LCD_STATUS;
  }

  // The target position of the tool in absolute steps
  // Calculate target position in absolute steps
  //this should be done after the wait, because otherwise a M92 code within the gcode disrupts this calculation somehow
  long target[4];
  target[X_AXIS] = lround(x*axis_steps_per_unit[X_AXIS]);
  target[Y_AXIS] = lround(y*axis_steps_per_unit[Y_AXIS]);
  target[Z_AXIS] = lround(z*axis_steps_per_unit[Z_AXIS]);     
  target[E_AXIS] = lround(e*axis_steps_per_unit[E_AXIS]); 
  
  // Prepare to set up new block
  block_t *block = &block_buffer[block_buffer_head];
  
  // Mark block as not busy (Not executed by the stepper interrupt)
  block->busy = false;

  // Number of steps for each axis
  block->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->steps_e = labs(target[E_AXIS]-position[E_AXIS]);
  block->step_event_count = max(block->steps_x, max(block->steps_y, max(block->steps_z, block->steps_e)));

  // Bail if this is a zero-length block
  if (block->step_event_count <=dropsegments) { return; };

  // Compute direction bits for this block
  block->direction_bits = 0;
  if (target[X_AXIS] < position[X_AXIS]) { block->direction_bits |= (1<<X_AXIS); }
  if (target[Y_AXIS] < position[Y_AXIS]) { block->direction_bits |= (1<<Y_AXIS); }
  if (target[Z_AXIS] < position[Z_AXIS]) { block->direction_bits |= (1<<Z_AXIS); }
  if (target[E_AXIS] < position[E_AXIS]) { block->direction_bits |= (1<<E_AXIS); }
  
  //enable active axes
  if(block->steps_x != 0) enable_x();
  if(block->steps_y != 0) enable_y();
  if(block->steps_z != 0) enable_z();
  if(block->steps_e != 0) enable_e();

  float delta_mm[4];
  delta_mm[X_AXIS] = (target[X_AXIS]-position[X_AXIS])/axis_steps_per_unit[X_AXIS];
  delta_mm[Y_AXIS] = (target[Y_AXIS]-position[Y_AXIS])/axis_steps_per_unit[Y_AXIS];
  delta_mm[Z_AXIS] = (target[Z_AXIS]-position[Z_AXIS])/axis_steps_per_unit[Z_AXIS];
  delta_mm[E_AXIS] = (target[E_AXIS]-position[E_AXIS])/axis_steps_per_unit[E_AXIS];
  block->millimeters = sqrt(square(delta_mm[X_AXIS]) + square(delta_mm[Y_AXIS]) +
                            square(delta_mm[Z_AXIS]));
  float inverse_millimeters = 1.0/block->millimeters;  // Inverse millimeters to remove multiple divides 
  
  // Calculate speed in mm/second for each axis. No divide by zero due to previous checks.
  float inverse_second = feed_rate * inverse_millimeters;
  
  block->nominal_speed = block->millimeters * inverse_second; // (mm/sec) Always > 0
  block->nominal_rate = ceil(block->step_event_count * inverse_second); // (step/sec) Always > 0

//  unsigned long microseconds;
#if 0
  if (block->steps_e == 0) {
        if(feed_rate<mintravelfeedrate) feed_rate=mintravelfeedrate;
  }
  else {
    	if(feed_rate<minimumfeedrate) feed_rate=minimumfeedrate;
  } 

  microseconds = lround((block->millimeters/feed_rate)*1000000);

  // slow down when de buffer starts to empty, rather than wait at the corner for a buffer refill
  // reduces/removes corner blobs as the machine won't come to a full stop.
  int blockcount=(block_buffer_head-block_buffer_tail + BLOCK_BUFFER_SIZE) & (BLOCK_BUFFER_SIZE - 1);
  
  if ((blockcount>0) && (blockcount < (BLOCK_BUFFER_SIZE - 4))) {
    if (microseconds<minsegmenttime)  { // buffer is draining, add extra time.  The amount of time added increases if the buffer is still emptied more.
        microseconds=microseconds+lround(2*(minsegmenttime-microseconds)/blockcount);
    }
  }
  else {
    if (microseconds<minsegmenttime) microseconds=minsegmenttime;
  }
  //  END OF SLOW DOWN SECTION  
#endif  

 // Calculate speed in mm/sec for each axis
  float current_speed[4];
  for(int i=0; i < 4; i++) {
    current_speed[i] = delta_mm[i] * inverse_second;
  }

  // Limit speed per axis
  float speed_factor = 1.0; //factor <=1 do decrease speed
  for(int i=0; i < 4; i++) {
    if(abs(current_speed[i]) > max_feedrate[i])
      speed_factor = min(speed_factor, max_feedrate[i] / abs(current_speed[i]));
  }

// Max segement time in us.

#ifdef XY_FREQUENCY_LIMIT
#define MAX_FREQ_TIME (1000000.0/XY_FREQUENCY_LIMIT)

  // Check and limit the xy direction change frequency
  unsigned char direction_change = block->direction_bits ^ old_direction_bits;
  old_direction_bits = block->direction_bits;
  long segment_time = lround(1000000.0/inverse_second);
  if((direction_change & (1<<X_AXIS)) == 0) {
     x_segment_time[0] += segment_time;
  }
  else {
    x_segment_time[2] = x_segment_time[1];
    x_segment_time[1] = x_segment_time[0];
    x_segment_time[0] = segment_time;
  }
  if((direction_change & (1<<Y_AXIS)) == 0) {
     y_segment_time[0] += segment_time;
  }
  else {
    y_segment_time[2] = y_segment_time[1];
    y_segment_time[1] = y_segment_time[0];
    y_segment_time[0] = segment_time;
  }
  long max_x_segment_time = max(x_segment_time[0], max(x_segment_time[1], x_segment_time[2]));
  long max_y_segment_time = max(y_segment_time[0], max(y_segment_time[1], y_segment_time[2]));
  long min_xy_segment_time =min(max_x_segment_time, max_y_segment_time);
  if(min_xy_segment_time < MAX_FREQ_TIME) speed_factor = min(speed_factor, (float)min_xy_segment_time / (float)MAX_FREQ_TIME);
#endif


  // Correct the speed  
  if( speed_factor < 1.0) {
//    Serial.print("speed factor : "); Serial.println(speed_factor);
    for(int i=0; i < 4; i++) {
    if(abs(current_speed[i]) > max_feedrate[i])
      speed_factor = min(speed_factor, max_feedrate[i] / abs(current_speed[i]));
//      Serial.print("current_speed"); Serial.print(i); Serial.print(" : "); Serial.println(current_speed[i]);
  }
    for(unsigned char i=0; i < 4; i++) {
      current_speed[i] *= speed_factor;
    }
    block->nominal_speed *= speed_factor;
    block->nominal_rate *= speed_factor;
  }

  // Compute and limit the acceleration rate for the trapezoid generator.  
  float steps_per_mm = block->step_event_count/block->millimeters;
  if(block->steps_x == 0 && block->steps_y == 0 && block->steps_z == 0) {
    block->acceleration_st = ceil(retract_acceleration * steps_per_mm); // convert to: acceleration steps/sec^2
  }
  else {
    block->acceleration_st = ceil(acceleration * steps_per_mm); // convert to: acceleration steps/sec^2
    // Limit acceleration per axis
    if(((float)block->acceleration_st * (float)block->steps_x / (float)block->step_event_count) > axis_steps_per_sqr_second[X_AXIS])
      block->acceleration_st = axis_steps_per_sqr_second[X_AXIS];
    if(((float)block->acceleration_st * (float)block->steps_y / (float)block->step_event_count) > axis_steps_per_sqr_second[Y_AXIS])
      block->acceleration_st = axis_steps_per_sqr_second[Y_AXIS];
    if(((float)block->acceleration_st * (float)block->steps_e / (float)block->step_event_count) > axis_steps_per_sqr_second[E_AXIS])
      block->acceleration_st = axis_steps_per_sqr_second[E_AXIS];
    if(((float)block->acceleration_st * (float)block->steps_z / (float)block->step_event_count ) > axis_steps_per_sqr_second[Z_AXIS])
      block->acceleration_st = axis_steps_per_sqr_second[Z_AXIS];
  }
  block->acceleration = block->acceleration_st / steps_per_mm;
  block->acceleration_rate = (long)((float)block->acceleration_st * 8.388608);
  
#if 0  // Use old jerk for now
  // 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(block->acceleration * junction_deviation * sin_theta_d2/(1.0-sin_theta_d2)) );
      }
    }
  }
#endif
  // Start with a safe speed
  float vmax_junction = max_xy_jerk/2;  
  if(abs(current_speed[Z_AXIS]) > max_z_jerk/2) 
    vmax_junction = max_z_jerk/2;
  vmax_junction = min(vmax_junction, block->nominal_speed);

  if ((block_buffer_head != block_buffer_tail) && (previous_nominal_speed > 0.0)) {
    float jerk = sqrt(pow((current_speed[X_AXIS]-previous_speed[X_AXIS]), 2)+pow((current_speed[Y_AXIS]-previous_speed[Y_AXIS]), 2));
    if((previous_speed[X_AXIS] != 0.0) || (previous_speed[Y_AXIS] != 0.0)) {
      vmax_junction = block->nominal_speed;
    }
    if (jerk > max_xy_jerk) {
      vmax_junction *= (max_xy_jerk/jerk);
    } 
    if(abs(current_speed[Z_AXIS] - previous_speed[Z_AXIS]) > max_z_jerk) {
      vmax_junction *= (max_z_jerk/abs(current_speed[Z_AXIS] - previous_speed[Z_AXIS]));
    } 
  }
  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(-block->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_speed, current_speed, sizeof(previous_speed)); // previous_speed[] = current_speed[]
  previous_nominal_speed = block->nominal_speed;
  
  #ifdef ADVANCE
    // Calculate advance rate
    if((block->steps_e == 0) || (block->steps_x == 0 && block->steps_y == 0 && block->steps_z == 0)) {
      block->advance_rate = 0;
      block->advance = 0;
    }
    else {
      long acc_dist = estimate_acceleration_distance(0, block->nominal_rate, block->acceleration_st);
      float advance = (STEPS_PER_CUBIC_MM_E * EXTRUDER_ADVANCE_K) * 
        (block->speed_e * block->speed_e * EXTRUTION_AREA * EXTRUTION_AREA / 3600.0)*65536;
      block->advance = advance;
      if(acc_dist == 0) {
        block->advance_rate = 0;
      } 
      else {
        block->advance_rate = advance / (float)acc_dist;
      }
    }
  #endif // ADVANCE




  calculate_trapezoid_for_block(block, block->entry_speed/block->nominal_speed,
    MINIMUM_PLANNER_SPEED/block->nominal_speed);
    
  // Move buffer head
  block_buffer_head = next_buffer_head;
  
  // Update position
  memcpy(position, target, sizeof(target)); // position[] = target[]

  planner_recalculate();
  
  st_wake_up();
}

void plan_set_position(const float &x, const float &y, const float &z, const float &e)
{
  position[X_AXIS] = lround(x*axis_steps_per_unit[X_AXIS]);
  position[Y_AXIS] = lround(y*axis_steps_per_unit[Y_AXIS]);
  position[Z_AXIS] = lround(z*axis_steps_per_unit[Z_AXIS]);     
  position[E_AXIS] = lround(e*axis_steps_per_unit[E_AXIS]);  
  previous_nominal_speed = 0.0; // Resets planner junction speeds. Assumes start from rest.
  previous_speed[0] = 0.0;
  previous_speed[1] = 0.0;
  previous_speed[2] = 0.0;
  previous_speed[3] = 0.0;
}