@ -44,6 +44,13 @@
/* The timer calculations of this module informed by the 'RepRap cartesian firmware' by Zack Smith
and Philipp Tiefenbacher . */
/* Jerk controlled movements planner added by Eduardo José Tagle in April
2018 , Equations based on Synthethos TinyG2 sources , but the fixed - point
implementation is a complete new one , as we are running the ISR with a
variable period .
Also implemented the Bézier velocity curve evaluation in ARM assembler ,
to avoid impacting ISR speed . */
# include "stepper.h"
# ifdef __AVR__
@ -109,6 +116,15 @@ long Stepper::counter_X = 0,
volatile uint32_t Stepper : : step_events_completed = 0 ; // The number of step events executed in the current block
# if ENABLED(BEZIER_JERK_CONTROL)
int32_t Stepper : : bezier_A , // A coefficient in Bézier speed curve
Stepper : : bezier_B , // B coefficient in Bézier speed curve
Stepper : : bezier_C , // C coefficient in Bézier speed curve
Stepper : : bezier_F ; // F coefficient in Bézier speed curve
uint32_t Stepper : : bezier_AV ; // AV coefficient in Bézier speed curve
bool Stepper : : bezier_2nd_half ; // =false If Bézier curve has been initialized or not
# endif
# if ENABLED(LIN_ADVANCE)
uint32_t Stepper : : LA_decelerate_after ;
@ -134,9 +150,9 @@ volatile uint32_t Stepper::step_events_completed = 0; // The number of step even
# endif // LIN_ADVANCE
long Stepper : : acceleration_time , Stepper : : deceleration_time ;
int32_t Stepper : : acceleration_time , Stepper : : deceleration_time ;
volatile long Stepper : : count_position [ NUM_AXIS ] = { 0 } ;
volatile int32_t Stepper : : count_position [ NUM_AXIS ] = { 0 } ;
volatile signed char Stepper : : count_direction [ NUM_AXIS ] = { 1 , 1 , 1 , 1 } ;
# if ENABLED(MIXING_EXTRUDER)
@ -145,8 +161,10 @@ volatile signed char Stepper::count_direction[NUM_AXIS] = { 1, 1, 1, 1 };
uint8_t Stepper : : step_loops , Stepper : : step_loops_nominal ;
hal_timer_t Stepper : : OCR1A_nominal ,
Stepper : : acc_step_rate ; // needed for deceleration start point
hal_timer_t Stepper : : OCR1A_nominal ;
# if DISABLED(BEZIER_JERK_CONTROL)
hal_timer_t Stepper : : acc_step_rate ; // needed for deceleration start point
# endif
volatile long Stepper : : endstops_trigsteps [ XYZ ] ;
@ -298,6 +316,207 @@ void Stepper::set_directions() {
extern volatile uint8_t e_hit ;
# endif
# if ENABLED(BEZIER_JERK_CONTROL)
/**
* We are using a quintic ( fifth - degree ) Bézier polynomial for the velocity curve .
* This gives us a " linear pop " velocity curve ; with pop being the sixth derivative of position :
* velocity - 1 st , acceleration - 2 nd , jerk - 3 rd , snap - 4 th , crackle - 5 th , pop - 6 th
*
* The Bézier curve takes the form :
*
* V ( t ) = P_0 * B_0 ( t ) + P_1 * B_1 ( t ) + P_2 * B_2 ( t ) + P_3 * B_3 ( t ) + P_4 * B_4 ( t ) + P_5 * B_5 ( t )
*
* Where 0 < = t < = 1 , and V ( t ) is the velocity . P_0 through P_5 are the control points , and B_0 ( t )
* through B_5 ( t ) are the Bernstein basis as follows :
*
* B_0 ( t ) = ( 1 - t ) ^ 5 = - t ^ 5 + 5 t ^ 4 - 10 t ^ 3 + 10 t ^ 2 - 5 t + 1
* B_1 ( t ) = 5 ( 1 - t ) ^ 4 * t = 5 t ^ 5 - 20 t ^ 4 + 30 t ^ 3 - 20 t ^ 2 + 5 t
* B_2 ( t ) = 10 ( 1 - t ) ^ 3 * t ^ 2 = - 10 t ^ 5 + 30 t ^ 4 - 30 t ^ 3 + 10 t ^ 2
* B_3 ( t ) = 10 ( 1 - t ) ^ 2 * t ^ 3 = 10 t ^ 5 - 20 t ^ 4 + 10 t ^ 3
* B_4 ( t ) = 5 ( 1 - t ) * t ^ 4 = - 5 t ^ 5 + 5 t ^ 4
* B_5 ( t ) = t ^ 5 = t ^ 5
* ^ ^ ^ ^ ^ ^
* | | | | | |
* A B C D E F
*
* Unfortunately , we cannot use forward - differencing to calculate each position through
* the curve , as Marlin uses variable timer periods . So , we require a formula of the form :
*
* V_f ( t ) = A * t ^ 5 + B * t ^ 4 + C * t ^ 3 + D * t ^ 2 + E * t + F
*
* Looking at the above B_0 ( t ) through B_5 ( t ) expanded forms , if we take the coefficients of t ^ 5
* through t of the Bézier form of V ( t ) , we can determine that :
*
* A = - P_0 + 5 * P_1 - 10 * P_2 + 10 * P_3 - 5 * P_4 + P_5
* B = 5 * P_0 - 20 * P_1 + 30 * P_2 - 20 * P_3 + 5 * P_4
* C = - 10 * P_0 + 30 * P_1 - 30 * P_2 + 10 * P_3
* D = 10 * P_0 - 20 * P_1 + 10 * P_2
* E = - 5 * P_0 + 5 * P_1
* F = P_0
*
* Now , since we will ( currently ) * always * want the initial acceleration and jerk values to be 0 ,
* We set P_i = P_0 = P_1 = P_2 ( initial velocity ) , and P_t = P_3 = P_4 = P_5 ( target velocity ) ,
* which , after simplification , resolves to :
*
* A = - 6 * P_i + 6 * P_t = 6 * ( P_t - P_i )
* B = 15 * P_i - 15 * P_t = 15 * ( P_i - P_t )
* C = - 10 * P_i + 10 * P_t = 10 * ( P_t - P_i )
* D = 0
* E = 0
* F = P_i
*
* As the t is evaluated in non uniform steps here , there is no other way rather than evaluating
* the Bézier curve at each point :
*
* V_f ( t ) = A * t ^ 5 + B * t ^ 4 + C * t ^ 3 + F [ 0 < = t < = 1 ]
*
* Floating point arithmetic execution time cost is prohibitive , so we will transform the math to
* use fixed point values to be able to evaluate it in realtime . Assuming a maximum of 250000 steps
* per second ( driver pulses should at least be 2u S hi / 2u S lo ) , and allocating 2 bits to avoid
* overflows on the evaluation of the Bézier curve , means we can use
*
* t : unsigned Q0 .32 ( 0 < = t < 1 ) | range 0 to 0xFFFFFFFF unsigned
* A : signed Q24 .7 , | range = + / - 250000 * 6 * 128 = + / - 192000000 = 0x0B71B000 | 28 bits + sign
* B : signed Q24 .7 , | range = + / - 250000 * 15 * 128 = + / - 480000000 = 0x1C9C3800 | 29 bits + sign
* C : signed Q24 .7 , | range = + / - 250000 * 10 * 128 = + / - 320000000 = 0x1312D000 | 29 bits + sign
* F : signed Q24 .7 , | range = + / - 250000 * 128 = 32000000 = 0x01E84800 | 25 bits + sign
*
* The trapezoid generator state contains the following information , that we will use to create and evaluate
* the Bézier curve :
*
* blk - > step_event_count [ TS ] = The total count of steps for this movement . ( = distance )
* blk - > initial_rate [ VI ] = The initial steps per second ( = velocity )
* blk - > final_rate [ VF ] = The ending steps per second ( = velocity )
* and the count of events completed ( step_events_completed ) [ CS ] ( = distance until now )
*
* Note the abbreviations we use in the following formulae are between [ ] s
*
* At the start of each trapezoid , we calculate the coefficients A , B , C , F and Advance [ AV ] , as follows :
*
* A = 6 * 128 * ( VF - VI ) = 768 * ( VF - VI )
* B = 15 * 128 * ( VI - VF ) = 1920 * ( VI - VF )
* C = 10 * 128 * ( VF - VI ) = 1280 * ( VF - VI )
* F = 128 * VI = 128 * VI
* AV = ( 1 < < 32 ) / TS ~ = 0xFFFFFFFF / TS ( To use ARM UDIV , that is 32 bits )
*
* And for each point , we will evaluate the curve with the following sequence :
*
* uint32_t t = bezier_AV * curr_step ; // t: Range 0 - 1^32 = 32 bits
* uint64_t f = t ;
* f * = t ; // Range 32*2 = 64 bits (unsigned)
* f > > = 32 ; // Range 32 bits (unsigned)
* f * = t ; // Range 32*2 = 64 bits (unsigned)
* f > > = 32 ; // Range 32 bits : f = t^3 (unsigned)
* int64_t acc = ( int64_t ) bezier_F < < 31 ; // Range 63 bits (signed)
* acc + = ( ( uint32_t ) f > > 1 ) * ( int64_t ) bezier_C ; // Range 29bits + 31 = 60bits (plus sign)
* f * = t ; // Range 32*2 = 64 bits
* f > > = 32 ; // Range 32 bits : f = t^3 (unsigned)
* acc + = ( ( uint32_t ) f > > 1 ) * ( int64_t ) bezier_B ; // Range 29bits + 31 = 60bits (plus sign)
* f * = t ; // Range 32*2 = 64 bits
* f > > = 32 ; // Range 32 bits : f = t^3 (unsigned)
* acc + = ( ( uint32_t ) f > > 1 ) * ( int64_t ) bezier_A ; // Range 28bits + 31 = 59bits (plus sign)
* acc > > = ( 31 + 7 ) ; // Range 24bits (plus sign)
*
* This can be translated to the following ARM assembly sequence :
*
* At start :
* fhi = AV , flo = CS , alo = F
*
* muls fhi , flo | f = AV * CS 1 cycles
* mov t , fhi | t = AV * CS 1 cycles
* lsrs ahi , alo , # 1 | a = F < < 31 1 cycles
* lsls alo , alo , # 31 | 1 cycles
* umull flo , fhi , fhi , t | f * = t 5 cycles [ fhi : flo = 64 bits
* umull flo , fhi , fhi , t | f > > = 32 ; f * = t 5 cycles [ fhi : flo = 64 bits
* lsrs flo , fhi , # 1 | 1 cycles [ 31 bits
* smlal alo , ahi , flo , C | a + = ( f > > 33 ) * C ; 5 cycles
* umull flo , fhi , fhi , t | f > > = 32 ; f * = t 5 cycles [ fhi : flo = 64 bits
* lsrs flo , fhi , # 1 | 1 cycles [ 31 bits
* smlal alo , ahi , flo , B | a + = ( f > > 33 ) * B ; 5 cycles
* umull flo , fhi , fhi , t | f > > = 32 ; f * = t 5 cycles [ fhi : flo = 64 bits
* lsrs flo , fhi , # 1 | f > > = 33 ; 1 cycles [ 31 bits
* smlal alo , ahi , flo , A | a + = ( f > > 33 ) * A ; 5 cycles
* lsrs alo , ahi , # 6 | a > > = 38 1 cycles
* 43 cycles total
*/
FORCE_INLINE void Stepper : : _calc_bezier_curve_coeffs ( const int32_t v0 , const int32_t v1 , const uint32_t interval ) {
// Calculate the Bézier coefficients
bezier_A = 768 * ( v1 - v0 ) ;
bezier_B = 1920 * ( v0 - v1 ) ;
bezier_C = 1280 * ( v1 - v0 ) ;
bezier_F = 128 * v0 ;
bezier_AV = 0xFFFFFFFF / interval ;
}
FORCE_INLINE int32_t Stepper : : _eval_bezier_curve ( const uint32_t curr_step ) {
# if defined(__ARM__) || defined(__thumb__)
// For ARM CORTEX M3/M4 CPUs, we have the optimized assembler version, that takes 43 cycles to execute
register uint32_t flo = 0 ;
register uint32_t fhi = bezier_AV * curr_step ;
register uint32_t t = fhi ;
register int32_t alo = bezier_F ;
register int32_t ahi = 0 ;
register int32_t A = bezier_A ;
register int32_t B = bezier_B ;
register int32_t C = bezier_C ;
__asm__ __volatile__ (
" .syntax unified " " \n \t " // is to prevent CM0,CM1 non-unified syntax
" lsrs %[ahi],%[alo],#1 " " \n \t " // a = F << 31 1 cycles
" lsls %[alo],%[alo],#31 " " \n \t " // 1 cycles
" umull %[flo],%[fhi],%[fhi],%[t] " " \n \t " // f *= t 5 cycles [fhi:flo=64bits]
" umull %[flo],%[fhi],%[fhi],%[t] " " \n \t " // f>>=32; f*=t 5 cycles [fhi:flo=64bits]
" lsrs %[flo],%[fhi],#1 " " \n \t " // 1 cycles [31bits]
" smlal %[alo],%[ahi],%[flo],%[C] " " \n \t " // a+=(f>>33)*C; 5 cycles
" umull %[flo],%[fhi],%[fhi],%[t] " " \n \t " // f>>=32; f*=t 5 cycles [fhi:flo=64bits]
" lsrs %[flo],%[fhi],#1 " " \n \t " // 1 cycles [31bits]
" smlal %[alo],%[ahi],%[flo],%[B] " " \n \t " // a+=(f>>33)*B; 5 cycles
" umull %[flo],%[fhi],%[fhi],%[t] " " \n \t " // f>>=32; f*=t 5 cycles [fhi:flo=64bits]
" lsrs %[flo],%[fhi],#1 " " \n \t " // f>>=33; 1 cycles [31bits]
" smlal %[alo],%[ahi],%[flo],%[A] " " \n \t " // a+=(f>>33)*A; 5 cycles
" lsrs %[alo],%[ahi],#6 " " \n \t " // a>>=38 1 cycles
: [ alo ] " +r " ( alo ) ,
[ flo ] " +r " ( flo ) ,
[ fhi ] " +r " ( fhi ) ,
[ ahi ] " +r " ( ahi ) ,
[ A ] " +r " ( A ) , // <== Note: Even if A, B, C, and t registers are INPUT ONLY
[ B ] " +r " ( B ) , // GCC does bad optimizations on the code if we list them as
[ C ] " +r " ( C ) , // such, breaking this function. So, to avoid that problem,
[ t ] " +r " ( t ) // we list all registers as input-outputs.
:
: " cc "
) ;
return alo ;
# else
// For non ARM targets, we provide a fallback implementation. Really doubt it
// will be useful, unless the processor is extremely fast.
uint32_t t = bezier_AV * curr_step ; // t: Range 0 - 1^32 = 32 bits
uint64_t f = t ;
f * = t ; // Range 32*2 = 64 bits (unsigned)
f > > = 32 ; // Range 32 bits (unsigned)
f * = t ; // Range 32*2 = 64 bits (unsigned)
f > > = 32 ; // Range 32 bits : f = t^3 (unsigned)
int64_t acc = ( int64_t ) bezier_F < < 31 ; // Range 63 bits (signed)
acc + = ( ( uint32_t ) f > > 1 ) * ( int64_t ) bezier_C ; // Range 29bits + 31 = 60bits (plus sign)
f * = t ; // Range 32*2 = 64 bits
f > > = 32 ; // Range 32 bits : f = t^3 (unsigned)
acc + = ( ( uint32_t ) f > > 1 ) * ( int64_t ) bezier_B ; // Range 29bits + 31 = 60bits (plus sign)
f * = t ; // Range 32*2 = 64 bits
f > > = 32 ; // Range 32 bits : f = t^3 (unsigned)
acc + = ( ( uint32_t ) f > > 1 ) * ( int64_t ) bezier_A ; // Range 28bits + 31 = 59bits (plus sign)
acc > > = ( 31 + 7 ) ; // Range 24bits (plus sign)
return ( int32_t ) acc ;
# endif
}
# endif // BEZIER_JERK_CONTROL
/**
* Stepper Driver Interrupt
*
@ -394,26 +613,73 @@ void Stepper::isr() {
// If there is no current block, attempt to pop one from the buffer
if ( ! current_block ) {
// Anything in the buffer?
if ( ( current_block = planner . get_current_block ( ) ) ) {
trapezoid_generator_reset ( ) ;
// Initialize the trapezoid generator from the current block.
static int8_t last_extruder = - 1 ;
# if ENABLED(LIN_ADVANCE)
# if E_STEPPERS > 1
if ( current_block - > active_extruder ! = last_extruder ) {
current_adv_steps = 0 ; // If the now active extruder wasn't in use during the last move, its pressure is most likely gone.
LA_active_extruder = current_block - > active_extruder ;
}
# endif
if ( ( use_advance_lead = current_block - > use_advance_lead ) ) {
LA_decelerate_after = current_block - > decelerate_after ;
final_adv_steps = current_block - > final_adv_steps ;
max_adv_steps = current_block - > max_adv_steps ;
}
# endif
if ( current_block - > direction_bits ! = last_direction_bits | | current_block - > active_extruder ! = last_extruder ) {
last_direction_bits = current_block - > direction_bits ;
last_extruder = current_block - > active_extruder ;
set_directions ( ) ;
}
// No acceleration / deceleration time elapsed so far
acceleration_time = deceleration_time = 0 ;
// No step events completed so far
step_events_completed = 0 ;
// step_rate to timer interval
OCR1A_nominal = calc_timer_interval ( current_block - > nominal_rate ) ;
// make a note of the number of step loops required at nominal speed
step_loops_nominal = step_loops ;
# if DISABLED(BEZIER_JERK_CONTROL)
// Set as deceleration point the initial rate of the block
acc_step_rate = current_block - > initial_rate ;
# endif
# if ENABLED(BEZIER_JERK_CONTROL)
// Initialize the Bézier speed curve
_calc_bezier_curve_coeffs ( current_block - > initial_rate , current_block - > cruise_rate , current_block - > acceleration_time ) ;
// We have not started the 2nd half of the trapezoid
bezier_2nd_half = false ;
# endif
// Initialize Bresenham counters to 1/2 the ceiling
counter_X = counter_Y = counter_Z = counter_E = - ( current_block - > step_event_count > > 1 ) ;
# if ENABLED(MIXING_EXTRUDER)
MIXING_STEPPERS_LOOP ( i )
counter_m [ i ] = - ( current_block - > mix_event_count [ i ] > > 1 ) ;
# endif
step_events_completed = 0 ;
# if ENABLED(ENDSTOP_INTERRUPTS_FEATURE)
e_hit = 2 ; // Needed for the case an endstop is already triggered before the new move begins.
// No 'change' can be detected.
# endif
# if ENABLED(Z_LATE_ENABLE)
// If delayed Z enable, postpone move for 1mS
if ( current_block - > steps [ Z_AXIS ] > 0 ) {
enable_Z ( ) ;
_NEXT_ISR ( HAL_STEPPER_TIMER_RATE / 1000 ) ; // Run at slow speed - 1 KHz
@ -423,6 +689,7 @@ void Stepper::isr() {
# endif
}
else {
// If no more queued moves, postpone next check for 1mS
_NEXT_ISR ( HAL_STEPPER_TIMER_RATE / 1000 ) ; // Run at slow speed - 1 KHz
HAL_ENABLE_ISRs ( ) ;
return ;
@ -542,7 +809,6 @@ void Stepper::isr() {
# endif
# if ENABLED(LIN_ADVANCE)
counter_E + = current_block - > steps [ E_AXIS ] ;
if ( counter_E > 0 ) {
# if DISABLED(MIXING_EXTRUDER)
@ -640,15 +906,23 @@ void Stepper::isr() {
// Calculate new timer value
if ( step_events_completed < = ( uint32_t ) current_block - > accelerate_until ) {
# ifdef CPU_32_BIT
MultiU32X24toH32 ( acc_step_rate , acceleration_time , current_block - > acceleration_rate ) ;
# if ENABLED(BEZIER_JERK_CONTROL)
// Get the next speed to use (Jerk limited!)
hal_timer_t acc_step_rate =
acceleration_time < current_block - > acceleration_time
? _eval_bezier_curve ( acceleration_time )
: current_block - > cruise_rate ;
# else
MultiU24X32toH16 ( acc_step_rate , acceleration_time , current_block - > acceleration_rate ) ;
# endif
acc_step_rate + = current_block - > initial_rate ;
# ifdef CPU_32_BIT
MultiU32X24toH32 ( acc_step_rate , acceleration_time , current_block - > acceleration_rate ) ;
# else
MultiU24X32toH16 ( acc_step_rate , acceleration_time , current_block - > acceleration_rate ) ;
# endif
acc_step_rate + = current_block - > initial_rate ;
// upper limit
NOMORE ( acc_step_rate , current_block - > nominal_rate ) ;
// upper limit
NOMORE ( acc_step_rate , current_block - > nominal_rate ) ;
# endif
// step_rate to timer interval
const hal_timer_t interval = calc_timer_interval ( acc_step_rate ) ;
@ -659,7 +933,6 @@ void Stepper::isr() {
acceleration_time + = interval ;
# if ENABLED(LIN_ADVANCE)
if ( current_block - > use_advance_lead ) {
if ( step_events_completed = = step_loops | | ( e_steps & & eISR_Rate ! = current_block - > advance_speed ) ) {
nextAdvanceISR = 0 ; // Wake up eISR on first acceleration loop and fire ISR if final adv_rate is reached
@ -670,23 +943,40 @@ void Stepper::isr() {
eISR_Rate = ADV_NEVER ;
if ( e_steps ) nextAdvanceISR = 0 ;
}
# endif // LIN_ADVANCE
}
else if ( step_events_completed > ( uint32_t ) current_block - > decelerate_after ) {
hal_timer_t step_rate ;
# ifdef CPU_32_BIT
MultiU32X24toH32 ( step_rate , deceleration_time , current_block - > acceleration_rate ) ;
# if ENABLED(BEZIER_JERK_CONTROL)
// If this is the 1st time we process the 2nd half of the trapezoid...
if ( ! bezier_2nd_half ) {
// Initialize the Bézier speed curve
_calc_bezier_curve_coeffs ( current_block - > cruise_rate , current_block - > final_rate , current_block - > deceleration_time ) ;
bezier_2nd_half = true ;
}
// Calculate the next speed to use
step_rate = deceleration_time < current_block - > deceleration_time
? _eval_bezier_curve ( deceleration_time )
: current_block - > final_rate ;
# else
MultiU24X32toH16 ( step_rate , deceleration_time , current_block - > acceleration_rate ) ;
# endif
if ( step_rate < acc_step_rate ) { // Still decelerating?
step_rate = acc_step_rate - step_rate ;
NOLESS ( step_rate , current_block - > final_rate ) ;
}
else
step_rate = current_block - > final_rate ;
// Using the old trapezoidal control
# ifdef CPU_32_BIT
MultiU32X24toH32 ( step_rate , deceleration_time , current_block - > acceleration_rate ) ;
# else
MultiU24X32toH16 ( step_rate , deceleration_time , current_block - > acceleration_rate ) ;
# endif
if ( step_rate < acc_step_rate ) { // Still decelerating?
step_rate = acc_step_rate - step_rate ;
NOLESS ( step_rate , current_block - > final_rate ) ;
}
else
step_rate = current_block - > final_rate ;
# endif
// step_rate to timer interval
const hal_timer_t interval = calc_timer_interval ( step_rate ) ;
@ -697,7 +987,6 @@ void Stepper::isr() {
deceleration_time + = interval ;
# if ENABLED(LIN_ADVANCE)
if ( current_block - > use_advance_lead ) {
if ( step_events_completed < = ( uint32_t ) current_block - > decelerate_after + step_loops | | ( e_steps & & eISR_Rate ! = current_block - > advance_speed ) ) {
nextAdvanceISR = 0 ; // Wake up eISR on first deceleration loop
@ -708,16 +997,13 @@ void Stepper::isr() {
eISR_Rate = ADV_NEVER ;
if ( e_steps ) nextAdvanceISR = 0 ;
}
# endif // LIN_ADVANCE
}
else {
# if ENABLED(LIN_ADVANCE)
// If we have esteps to execute, fire the next advance_isr "now"
if ( e_steps & & eISR_Rate ! = current_block - > advance_speed ) nextAdvanceISR = 0 ;
# endif
SPLIT ( OCR1A_nominal ) ; // split step into multiple ISRs if larger than ENDSTOP_NOMINAL_OCR_VAL
etagle
6 years ago
Scott Lahteine