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This file is part of Smoothie ( The motion control part is heavily based on Grbl ( with additions from Sungeun K. Jeon (
Smoothie 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.
Smoothie 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 Smoothie. If not, see <>.
using namespace std;
#include <vector>
#include "mri.h"
#include "nuts_bolts.h"
#include "RingBuffer.h"
#include "Gcode.h"
#include "Module.h"
#include "Kernel.h"
#include "Block.h"
#include "Planner.h"
#include "Conveyor.h"
#include "StepperMotor.h"
#include "Config.h"
#include "checksumm.h"
#include "Robot.h"
#include "ConfigValue.h"
#include <math.h>
#include <algorithm>
#define junction_deviation_checksum CHECKSUM("junction_deviation")
#define z_junction_deviation_checksum CHECKSUM("z_junction_deviation")
#define minimum_planner_speed_checksum CHECKSUM("minimum_planner_speed")
// The Planner does the acceleration math for the queue of Blocks ( movements ).
// It makes sure the speed stays within the configured constraints ( acceleration, junction_deviation, etc )
// It goes over the list in both direction, every time a block is added, re-doing the math to make sure everything is optimal
memset(this->previous_unit_vec, 0, sizeof this->previous_unit_vec);
// Configure acceleration
void Planner::config_load()
this->junction_deviation = THEKERNEL->config->value(junction_deviation_checksum)->by_default(0.05F)->as_number();
this->z_junction_deviation = THEKERNEL->config->value(z_junction_deviation_checksum)->by_default(NAN)->as_number(); // disabled by default
this->minimum_planner_speed = THEKERNEL->config->value(minimum_planner_speed_checksum)->by_default(0.0f)->as_number();
// Append a block to the queue, compute it's speed factors
bool Planner::append_block( ActuatorCoordinates &actuator_pos, uint8_t n_motors, float rate_mm_s, float distance, float *unit_vec, float acceleration, float s_value, bool g123)
// Create ( recycle ) a new block
Block* block = THECONVEYOR->queue.head_ref();
// Direction bits
bool has_steps = false;
for (size_t i = 0; i < n_motors; i++) {
int32_t steps = THEROBOT->actuators[i]->steps_to_target(actuator_pos[i]);
// Update current position
if(steps != 0) {
THEROBOT->actuators[i]->update_last_milestones(actuator_pos[i], steps);
has_steps = true;
// find direction
block->direction_bits[i] = (steps < 0) ? 1 : 0;
// save actual steps in block
block->steps[i] = labs(steps);
// sometimes even though there is a detectable movement it turns out there are no steps to be had from such a small move
if(!has_steps) {
return false;
// info needed by laser
block->s_value = roundf(s_value*(1<<11)); // 1.11 fixed point
block->is_g123 = g123;
// use default JD
float junction_deviation = this->junction_deviation;
// use either regular junction deviation or z specific and see if a primary axis move
block->primary_axis = true;
if(block->steps[ALPHA_STEPPER] == 0 && block->steps[BETA_STEPPER] == 0) {
if(block->steps[GAMMA_STEPPER] != 0) {
// z only move
if(!isnan(this->z_junction_deviation)) junction_deviation = this->z_junction_deviation;
} else {
// is not a primary axis move
block->primary_axis = false;
block->acceleration = acceleration; // save in block
// Max number of steps, for all axes
auto mi = std::max_element(block->steps.begin(), block->steps.end());
block->steps_event_count = *mi;
block->millimeters = distance;
// Calculate speed in mm/sec for each axis. No divide by zero due to previous checks.
if( distance > 0.0F ) {
block->nominal_speed = rate_mm_s; // (mm/s) Always > 0
block->nominal_rate = block->steps_event_count * rate_mm_s / distance; // (step/s) Always > 0
} else {
block->nominal_speed = 0.0F;
block->nominal_rate = 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).
// 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.
// NOTE however it does not take into account independent axis, in most cartesian X and Y and Z are totally independent
// and this allows one to stop with little to no decleration in many cases. This is particualrly bad on leadscrew based systems that will skip steps.
float vmax_junction = minimum_planner_speed; // Set default max junction speed
// if unit_vec was null then it was not a primary axis move so we skip the junction deviation stuff
if (unit_vec != nullptr && !THECONVEYOR->is_queue_empty()) {
Block *prev_block = THECONVEYOR->queue.item_ref(THECONVEYOR->queue.prev(THECONVEYOR->queue.head_i));
float previous_nominal_speed = prev_block->primary_axis ? prev_block->nominal_speed : 0;
if (junction_deviation > 0.0F && previous_nominal_speed > 0.0F) {
// 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.
float cos_theta = - this->previous_unit_vec[X_AXIS] * unit_vec[X_AXIS]
- this->previous_unit_vec[Y_AXIS] * unit_vec[Y_AXIS]
- this->previous_unit_vec[Z_AXIS] * unit_vec[Z_AXIS] ;
// Skip and use default max junction speed for 0 degree acute junction.
if (cos_theta < 0.95F) {
vmax_junction = std::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 > -0.95F) {
// Compute maximum junction velocity based on maximum acceleration and junction deviation
float sin_theta_d2 = sqrtf(0.5F * (1.0F - cos_theta)); // Trig half angle identity. Always positive.
vmax_junction = std::min(vmax_junction, sqrtf(acceleration * junction_deviation * sin_theta_d2 / (1.0F - sin_theta_d2)));
block->max_entry_speed = vmax_junction;
// Initialize block entry speed. Compute based on deceleration to user-defined minimum_planner_speed.
float v_allowable = max_allowable_speed(-acceleration, minimum_planner_speed, block->millimeters);
block->entry_speed = std::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; }
// Always calculate trapezoid for new block
block->recalculate_flag = true;
// Update previous path unit_vector and nominal speed
if(unit_vec != nullptr) {
memcpy(previous_unit_vec, unit_vec, sizeof(previous_unit_vec)); // previous_unit_vec[] = unit_vec[]
} else {
memset(previous_unit_vec, 0, sizeof(previous_unit_vec));
// Math-heavy re-computing of the whole queue to take the new
// The block can now be used
return true;
void Planner::recalculate()
Conveyor::Queue_t &queue = THECONVEYOR->queue;
unsigned int block_index;
Block* previous;
Block* current;
* a newly added block is decel limited
* we find its max entry speed given its exit speed
* for each block, walking backwards in the queue:
* if max entry speed == current entry speed
* then we can set recalculate to false, since clearly adding another block didn't allow us to enter faster
* and thus we don't need to check entry speed for this block any more
* once we find an accel limited block, we must find the max exit speed and walk the queue forwards
* for each block, walking forwards in the queue:
* given the exit speed of the previous block and our own max entry speed
* we can tell if we're accel or decel limited (or coasting)
* if prev_exit > max_entry
* then we're still decel limited. update previous trapezoid with our max entry for prev exit
* if max_entry >= prev_exit
* then we're accel limited. set recalculate to false, work out max exit speed
* finally, work out trapezoid for the final (and newest) block.
* Step 1:
* For each block, given the exit speed and acceleration, find the maximum entry speed
float entry_speed = minimum_planner_speed;
block_index = queue.head_i;
current = queue.item_ref(block_index);
if (!queue.is_empty()) {
while ((block_index != queue.tail_i) && current->recalculate_flag) {
entry_speed = current->reverse_pass(entry_speed);
block_index = queue.prev(block_index);
current = queue.item_ref(block_index);
* Step 2:
* now current points to either tail or first non-recalculate block
* and has not had its reverse_pass called
* or its calculate_trapezoid
* entry_speed is set to the *exit* speed of current.
* each block from current to head has its entry speed set to its max entry speed- limited by decel or nominal_rate
float exit_speed = current->max_exit_speed();
while (block_index != queue.head_i) {
previous = current;
block_index =;
current = queue.item_ref(block_index);
// we pass the exit speed of the previous block
// so this block can decide if it's accel or decel limited and update its fields as appropriate
exit_speed = current->forward_pass(exit_speed);
previous->calculate_trapezoid(previous->entry_speed, current->entry_speed);
* Step 3:
* work out trapezoid for final (and newest) block
// now current points to the head item
// which has not had calculate_trapezoid run yet
current->calculate_trapezoid(current->entry_speed, minimum_planner_speed);
// Calculates the maximum allowable speed at this point when you must be able to reach target_velocity using the
// acceleration within the allotted distance.
float Planner::max_allowable_speed(float acceleration, float target_velocity, float distance)
// Was acceleration*60*60*distance, in case this breaks, but here we prefer to use seconds instead of minutes
return(sqrtf(target_velocity * target_velocity - 2.0F * acceleration * distance));