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Scott Lahteine
2018-05-27 00:10:05 -05:00
parent 1b200f3312
commit 2566342979
1 changed files with 20 additions and 21 deletions
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41
Marlin/src/module/stepper.cpp
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@@ -320,15 +320,15 @@ void Stepper::set_directions() {
#if ENABLED(S_CURVE_ACCELERATION)
/**
* 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:
* This uses a quintic (fifth-degree) Bézier polynomial for the velocity curve, giving
* a "linear pop" velocity curve; with pop being the sixth derivative of position:
* velocity - 1st, acceleration - 2nd, jerk - 3rd, snap - 4th, crackle - 5th, pop - 6th
*
* 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)
* 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 + 5t^4 - 10t^3 + 10t^2 - 5t + 1
@@ -341,12 +341,12 @@ void Stepper::set_directions() {
* | | | | | |
* A B C D E F
*
* Unfortunately, we cannot use forward-differencing to calculate each position through
* 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
* 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
@@ -356,7 +356,7 @@ void Stepper::set_directions() {
* 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,
* 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:
*
@@ -367,12 +367,12 @@ void Stepper::set_directions() {
* E = 0
* F = P_i
*
* As the t is evaluated in non uniform steps here, there is no other way rather than evaluating
* 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
* 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 2µS hi/2µS lo), and allocating 2 bits to avoid
* overflows on the evaluation of the Bézier curve, means we can use
@@ -383,7 +383,7 @@ void Stepper::set_directions() {
* 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 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)
@@ -395,7 +395,7 @@ void Stepper::set_directions() {
*
* For Any 32bit CPU:
*
* At the start of each trapezoid, we calculate the coefficients A,B,C,F and Advance [AV], as follows:
* At the start of each trapezoid, 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)
@@ -403,7 +403,7 @@ void Stepper::set_directions() {
* F = 128*VI = 128*VI
* AV = (1<<32)/TS ~= 0xFFFFFFFF / TS (To use ARM UDIV, that is 32 bits) (this is computed at the planner, to offload expensive calculations from the ISR)
*
* And for each point, we will evaluate the curve with the following sequence:
* And for each point, evaluate the curve with the following sequence:
*
* void lsrs(uint32_t& d, uint32_t s, int cnt) {
* d = s >> cnt;
@@ -456,10 +456,10 @@ void Stepper::set_directions() {
* return alo;
* }
*
* This will be rewritten in ARM assembly to get peak performance and will take 43 cycles to execute
* This is rewritten in ARM assembly for optimal performance (43 cycles to execute).
*
* For AVR, we scale precision of coefficients to make it possible to evaluate the Bézier curve in
* realtime: Let's reduce precision as much as possible. After some experimentation we found that:
* For AVR, the precision of coefficients is scaled so the Bézier curve can be evaluated in real-time:
* Let's reduce precision as much as possible. After some experimentation we found that:
*
* Assume t and AV with 24 bits is enough
* A = 6*(VF - VI)
@@ -468,9 +468,9 @@ void Stepper::set_directions() {
* F = VI
* AV = (1<<24)/TS (this is computed at the planner, to offload expensive calculations from the ISR)
*
* Instead of storing sign for each coefficient, we will store its absolute value,
* Instead of storing sign for each coefficient, we will store its absolute value,
* and flag the sign of the A coefficient, so we can save to store the sign bit.
* It always holds that sign(A) = - sign(B) = sign(C)
* It always holds that sign(A) = - sign(B) = sign(C)
*
* So, the resulting range of the coefficients are:
*
@@ -480,7 +480,7 @@ void Stepper::set_directions() {
* C: signed Q24 , range = 250000 *10 = 2500000 = 0x1312D0 | 21 bits
* F: signed Q24 , range = 250000 = 250000 = 0x0ED090 | 20 bits
*
* And for each curve, we estimate its coefficients with:
* And for each curve, estimate its coefficients with:
*
* void _calc_bezier_curve_coeffs(int32_t v0, int32_t v1, uint32_t av) {
* // Calculate the Bézier coefficients
@@ -499,7 +499,7 @@ void Stepper::set_directions() {
* bezier_F = v0;
* }
*
* And for each point, we will evaluate the curve with the following sequence:
* And for each point, evaluate the curve with the following sequence:
*
* // unsigned multiplication of 24 bits x 24bits, return upper 16 bits
* void umul24x24to16hi(uint16_t& r, uint24_t op1, uint24_t op2) {
@@ -549,9 +549,8 @@ void Stepper::set_directions() {
* }
* return acc;
* }
* Those functions will be translated into assembler to get peak performance. coefficient calculations takes 70 cycles,
* Bezier point evaluation takes 150 cycles
*
* These functions are translated to assembler for optimal performance.
* Coefficient calculation takes 70 cycles. Bezier point evaluation takes 150 cycles.
*/
#ifdef __AVR__