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docs: Update documentation with iterative solver changes

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Signed-off-by: Kevin O'Connor <kevin@koconnor.net>
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Kevin O'Connor
2018-06-19 00:50:59 -04:00
parent 926829e737
commit 3ac9fc6e63
8 changed files with 101 additions and 892 deletions
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134
docs/Code_Overview.md
View File

@@ -163,28 +163,37 @@ provides further information on the mechanics of moves.
kinematic class is given a chance to audit the move
(`ToolHead.move() -> kin.check_move()`) before it goes on the
look-ahead queue, but once the move arrives in *kin*.move() the
kinematic class is required to handle the move as specified. The
kinematic classes translate the three parts of each move
(acceleration, constant "cruising" velocity, and deceleration) to
the associated movement on each stepper. Note that the extruder is
handled in its own kinematic class. Since the Move() class specifies
the exact movement time and since step pulses are sent to the
micro-controller with specific timing, stepper movements produced by
the extruder class will be in sync with head movement even though
the code is kept separate.
kinematic class is required to handle the move as specified. Note
that the extruder is handled in its own kinematic class. Since the
Move() class specifies the exact movement time and since step pulses
are sent to the micro-controller with specific timing, stepper
movements produced by the extruder class will be in sync with head
movement even though the code is kept separate.
* For efficiency reasons, the stepper pulse times are generated in C
code. The code flow is: `kin.move() -> MCU_Stepper.step_const() ->
stepcompress_push_const()`, or for delta kinematics:
`DeltaKinematics.move() -> MCU_Stepper.step_delta() ->
stepcompress_push_delta()`. The MCU_Stepper code just performs unit
and axis transformation (millimeters to step distances), and calls
the C code. The C code calculates the stepper step times for each
movement and fills an array (struct stepcompress.queue) with the
corresponding micro-controller clock counter times for every
step. Here the "micro-controller clock counter" value directly
corresponds to the micro-controller's hardware counter - it is
relative to when the micro-controller was last powered up.
* Klipper uses an
[iterative solver](https://en.wikipedia.org/wiki/Root-finding_algorithm)
to generate the step times for each stepper. For efficiency reasons,
the stepper pulse times are generated in C code. The code flow is:
`kin.move() -> MCU_Stepper.step_itersolve() ->
itersolve_gen_steps()` (in klippy/chelper/itersolve.c). The goal of
the iterative solver is to find step times given a formula that
calculates a stepper position from a given time in a move. This is
done by repeatedly "guessing" various times until the stepper
position formula returns the desired position of the next step on
the stepper. The feedback produced from each guess is used to
improve future guesses so that the process rapidly converges to the
desired time. The kinematic stepper position formulas are located in
the klippy/chelper/ directory (eg, kin_cart.c, kin_corexy.c,
kin_delta.c, kin_extruder.c).
* After the iterative solver calculates the step times they are added
to an array: `itersolve_gen_steps() -> queue_append()` (in
klippy/chelper/stepcompress.c). The array (struct
stepcompress.queue) stores the corresponding micro-controller clock
counter times for every step. Here the "micro-controller clock
counter" value directly corresponds to the micro-controller's
hardware counter - it is relative to when the micro-controller was
last powered up.
* The next major step is to compress the steps: `stepcompress_flush()
-> compress_bisect_add()` (in klippy/chelper/stepcompress.c). This
@@ -293,8 +302,7 @@ This section provides some tips on adding support to Klipper for
additional types of printer kinematics. This type of activity requires
excellent understanding of the math formulas for the target
kinematics. It also requires software development skills - though one
should only need to update the host software (which is written in
Python).
should only need to update the host software.
Useful steps:
1. Start by studying the
@@ -304,74 +312,30 @@ Useful steps:
and delta.py. The kinematic classes are tasked with converting a
move in cartesian coordinates to the movement on each stepper. One
should be able to copy one of these files as a starting point.
3. Implement the `get_postion()` method in the new kinematics
class. This method converts the current stepper position of each
stepper axis (stored in millimeters) to a position in cartesian
space (also in millimeters).
4. Implement the `set_postion()` method. This is the inverse of
get_position() - it sets each axis position (in millimeters) given
a position in cartesian coordinates.
5. Implement the `move()` method. The goal of the move() method is to
convert a move defined in cartesian space to a series of stepper
step times that implement the requested movement.
* The `move()` method is passed a "print_time" parameter (which
stores a time in seconds) and a "move" class instance that fully
defines the movement. The goal is to repeatedly invoke the
`stepper.step()` method with the time (relative to print_time)
that each stepper should step at to obtain the desired motion.
* One "trick" to help with the movement calculations is to imagine
there is a physical rail between `move.start_pos` and
`move.end_pos` that confines the print head so that it can only
move along this straight line of motion. Then, if the head is
confined to that imaginary rail, the head is at `move.start_pos`,
only one stepper is enabled (all other steppers can move freely),
and the given stepper is stepped a single step, then one can
imagine that the head will move along the line of movement some
distance. Determine the formula converting this step distance to
distance along the line of movement. Once one has the distance
along the line of movement, one can figure out the time that the
head should be at that position (using the standard formulas for
velocity and acceleration). This time is the ideal step time for
the given stepper and it can be passed to the `stepper.step()`
method.
* The `stepper.step()` method must always be called with an
increasing time for a given stepper (steps must be scheduled in
the order they are to be executed). A common error during
kinematic development is to receive an "Internal error in
stepcompress" failure - this is generally due to the step()
method being invoked with a time earlier than the last scheduled
step. For example, if the last step in move1 is scheduled at a
time greater than the first step in move2 it will generally
result in the above error.
* Fractional steps. Be aware that a move request is given in
cartesian space and it is not confined to discreet
locations. Thus a move's start and end locations may translate to
a location on a stepper axis that is between two steps (a
fractional step). The code must handle this. The preferred
approach is to schedule the next step at the time a move would
position the stepper axis at least half way towards the next
possible step location. Incorrect handling of fractional steps is
a common cause of "Internal error in stepcompress" failures.
6. Other methods. The `home()`, `check_move()`, and other methods
3. Implement the C stepper kinematic position functions for each
stepper if they are not already available (see kin_cart.c,
kin_corexy.c, and kin_delta.c in klippy/chelper/). The function
should call `move_get_coord()` to convert a given move time (in
seconds) to a cartesian coordinate (in millimeters), and then
calculate the desired stepper position (in millimeters) from that
cartesian coordinate.
4. Implement the `set_position()` method in the python code. This also
calculates the desired stepper positions given a cartesian
coordinate.
5. Implement the `get_position()` method in the new kinematics
class. This method is the inverse of set_position(). It does not
need to be efficient as it is typically only called during homing
and probing operations.
6. Implement the `move()` method. This method generally invokes the
iterative solver for each stepper.
7. Other methods. The `home()`, `check_move()`, and other methods
should also be implemented. However, at the start of development
one can use empty code here.
7. Implement test cases. Create a g-code file with a series of moves
8. Implement test cases. Create a g-code file with a series of moves
that can test important cases for the given kinematics. Follow the
[debugging documentation](Debugging.md) to convert this g-code file
to micro-controller commands. This is useful to exercise corner
cases and to check for regressions.
8. Optimize if needed. One may notice that the existing kinematic
classes do not call `stepper.step()`. This is purely an
optimization - the inner loop of the kinematic calculations were
moved to C to reduce load on the host cpu. All of the existing
kinematic classes started development using `stepper.step()` and
then were later optimized. The g-code to mcu command translation
(described in the previous step) is a useful tool during
optimization - if a code change is purely an optimization then it
should not impact the resulting text representation of the mcu
commands (though minor changes in output due to floating point
rounding are possible). So, one can use this system to detect
regressions.
Time
====

104
docs/Kinematics.md
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@@ -139,15 +139,32 @@ tracked in millimeters, seconds, and in cartesian coordinate space.
It's the task of the kinematic classes to convert from this generic
coordinate system to the hardware specifics of the particular printer.
In general, the code determines each step time by first calculating
where along the line of movement the head would be if a step is
taken. It then calculates what time the head should be at that
position. Determining the time along the line of movement can be done
using the formulas for constant acceleration and constant velocity:
Klipper uses an
[iterative solver](https://en.wikipedia.org/wiki/Root-finding_algorithm)
to generate the step times for each stepper. The code contains the
formulas to calculate the ideal cartesian coordinates of the head at
each moment in time, and it has the kinematic formulas to calculate
the ideal stepper positions based on those cartesian coordinates. With
these formulas, Klipper can determine the ideal time that the stepper
should be at each step position. The given steps are then scheduled at
these calculated times.
The key formula to determine how far a move should travel under
constant acceleration is:
```
time = sqrt(2*distance/accel + (start_velocity/accel)^2) - start_velocity/accel
time = distance/cruise_velocity
move_distance = (start_velocity + .5 * accel * move_time) * move_time
```
and the key formula for movement with constant velocity is:
```
move_distance = cruise_velocity * move_time
```
The key formulas for determining the cartesian coordinate of a move
given a move distance is:
```
cartesian_x_position = start_x + move_distance * total_x_movement / total_movement
cartesian_y_position = start_y + move_distance * total_y_movement / total_movement
cartesian_z_position = start_z + move_distance * total_z_movement / total_movement
```
Cartesian Robots
@@ -157,54 +174,35 @@ Generating steps for cartesian printers is the simplest case. The
movement on each axis is directly related to the movement in cartesian
space.
Key formulas:
```
stepper_x_position = cartesian_x_position
stepper_y_position = cartesian_y_position
stepper_z_position = cartesian_z_position
```
CoreXY Robots
----------------
Generating steps on a CoreXY machine is only a little more complex
than basic cartesian robots. The key formulas are:
```
stepper_a_position = cartesian_x_position + cartesian_y_position
stepper_b_position = cartesian_x_position - cartesian_y_position
stepper_z_position = cartesian_z_position
```
Delta Robots
------------
To generate step times on Delta printers it is necessary to correlate
the movement in cartesian space with the movement on each stepper
tower.
To simplify the math, for each stepper tower, the code calculates the
location of a "virtual tower" that is along the line of movement.
This virtual tower is chosen at the point where the line of movement
(extended infinitely in both directions) would be closest to the
actual tower.
![delta-tower](img/delta-tower.svg.png)
It is then possible to calculate where the head will be along the line
of movement after each step is taken on the virtual tower.
![virtual-tower](img/virtual-tower.svg.png)
The key formula is Pythagoras's theorem:
Step generation on a delta robot is based on Pythagoras's theorem:
```
distance_to_tower^2 = arm_length^2 - tower_height^2
stepper_position = (sqrt(arm_length^2
- (cartesian_x_position - tower_x_position)^2
- (cartesian_y_position - tower_y_position)^2)
+ cartesian_z_position)
```
One complexity is that if the print head passes the virtual tower
location then the stepper direction must be reversed. In this case
forward steps will be taken at the start of the move and reverse steps
will be taken at the end of the move.
### Delta movements beyond simple XY plane ###
Movement calculation is more complicated if a single move contains
both XY movement and Z movement. These moves are rare, but they must
still be handled correctly. A virtual tower along the line of movement
is still calculated, but in this case the tower is not at a 90 degree
angle relative to the line of movement:
![xy+z-tower](img/xy+z-tower.svg.png)
The code continues to calculate step times using the same general
scheme as delta moves within an XY plane, but the slope of the tower
must also be used in the calculations.
Should the move contain only Z movement (ie, no XY movement at all)
then the same math is used - just in this case the tower is parallel
to the line of movement.
### Stepper motor acceleration limits ###
With delta kinematics it is possible for a move that is accelerating
@@ -236,8 +234,10 @@ independently from the step time calculations of the print head
movement.
Basic extruder movement is simple to calculate. The step time
generation uses the same constant acceleration and constant velocity
formulas that cartesian robots use.
generation uses the same formulas that cartesian robots use:
```
stepper_position = requested_e_position
```
### Pressure advance ###
@@ -264,7 +264,7 @@ through the nozzle orifice (as in
key idea is that the relationship between filament, pressure, and flow
rate can be modeled using a linear coefficient:
```
extra_filament = pressure_advance_coefficient * extruder_velocity
stepper_position = requested_e_position + pressure_advance_coefficient * nominal_extruder_velocity
```
See the [pressure advance](Pressure_Advance.md) document for

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