https://github.com/devel0/scurve-speed-eval
Acceleration for an s-curve shaped speed
https://github.com/devel0/scurve-speed-eval
csharp multiplatform stepper-motor
Last synced: 9 months ago
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Acceleration for an s-curve shaped speed
- Host: GitHub
- URL: https://github.com/devel0/scurve-speed-eval
- Owner: devel0
- License: mit
- Created: 2020-11-29T19:05:21.000Z (over 5 years ago)
- Default Branch: main
- Last Pushed: 2024-06-19T20:09:46.000Z (about 2 years ago)
- Last Synced: 2025-04-01T20:08:51.207Z (about 1 year ago)
- Topics: csharp, multiplatform, stepper-motor
- Language: C#
- Homepage:
- Size: 1.07 MB
- Stars: 12
- Watchers: 2
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# scurve speed eval
Show how s-curve speed type can be obtained.
---
- [Description](#description)
- [Performance considerations](#performance-considerations)
- [Example](#example)
- [Prerequisites](#prerequisites)
- [Quickstart](#quickstart)
- [How this project was built](#how-this-project-was-built)
- [References](#references)
---
## Description
For symbolic calculus [AngouriMath](https://github.com/asc-community/AngouriMath) library was used.
For preliminary analysis [sympy](https://github.com/sympy/sympy) with [this](data/test.py) test was used.
- lets name
- **t** (time)
- **x** (distance)
- **d** (total duration accel/decel)
- **s** (final speed)
- suppose `[0,d/2]` the time for acceleration while `[d/2,d]` the time for deceleration to produce a target final speed `s` starting from speed=0 and pos=0
- from base acceleration function [1-cos(t)][1]
- expanding the period domain from `[0,2pi]` to `[0,d/2]` through [this][2] subst
- [stretching][3] the accel function so that its integral, the speed, achieve targetspeed
- acceleration results as [this][4]
:point_right: hit F5 if math not rendered
$$
\large
accel(t)=\frac{2\cdot s}{d}\cdot\left(1-\cos\left(\frac{4\cdot\pi\cdot t}{d}\right)\right)
$$
- positive max accel value is at midpoint ( t=1/4d because accel positive in `[0,d/2]` ) thus above can be simplified into
$$
\large
maxAccel=\frac{4\cdot s}{d}
$$
- [integration of accel][5] gives speed
$$
\large
speed(t) = \frac{2\cdot s}{d} \cdot \left( t - \frac{d\cdot \sin\left(\frac{4\cdot\pi\cdot t}{d}\right)}{4\cdot\pi} \right)
$$
- [integration of speed][6] gives pos ( normalized removing integration constant computed for t=0 )
$$
\large
pos(t) = \frac{s\cdot d \cdot \left( \cos\left(\frac{4\cdot\pi\cdot t}{d}\right)-1 \right)}{8\cdot\pi^2} + \frac{s\cdot t^2}{d}
$$
- [targetspeed][7] required from known final position `p` to reach in required time duration `d`
$$
\large
s = \frac{2\cdot p}{d}
$$
- from base deceleration function [cos(t)-1][8]
- sets `th` as
$$
\large
th=t-\frac{d}{2}
$$
- deceleration results as [this][9]
$$
\large
deAccel\left(th\right) = \frac{2\cdot s}{d}\cdot\left(\cos\left(\frac{4\cdot\pi\cdot th}{d}\right)-1\right)
$$
- despeed results as [this][10] ( given from deAccel integral subtracting integration constant and adding speed achieved by accel at `d/2` )
$$
\large
deSpeed\left(th\right) = \frac{2\cdot s\cdot\sin\left(\frac{4\cdot\pi\cdot th}{d} \right)}{4\cdot\pi}-\frac{2\cdot s\cdot th}{d}+s
$$
- depos results as [this][11] ( given from deSpeed integral subtracting integration constant and adding pos achieved by accel at `d/2` )
$$
\large
dePos\left(th\right) = \frac{s\cdot d\cdot\left( 1-\cos\left(\frac{4\cdot\pi\cdot th}{d}\right) \right)}{8\cdot\pi^2}-\frac{s\cdot th^2}{d}+s\cdot th+\frac{s\cdot d}{4}
$$
[1]: https://github.com/devel0/scurve-speed-eval/blob/435327c86769302a22fa54fb6b349a60a1b640d1/gui%2FProgram.cs#L48
[2]: https://github.com/devel0/scurve-speed-eval/blob/435327c86769302a22fa54fb6b349a60a1b640d1/gui%2FProgram.cs#L49
[3]: https://github.com/devel0/scurve-speed-eval/blob/435327c86769302a22fa54fb6b349a60a1b640d1/gui%2FProgram.cs#L50
[4]: https://github.com/devel0/scurve-speed-eval/blob/435327c86769302a22fa54fb6b349a60a1b640d1/gui%2FProgram.cs#L51
[5]: https://github.com/devel0/scurve-speed-eval/blob/435327c86769302a22fa54fb6b349a60a1b640d1/gui%2FProgram.cs#L53
[6]: https://github.com/devel0/scurve-speed-eval/blob/435327c86769302a22fa54fb6b349a60a1b640d1/gui%2FProgram.cs#L57
[7]: https://github.com/devel0/scurve-speed-eval/blob/435327c86769302a22fa54fb6b349a60a1b640d1/gui%2FProgram.cs#L60
[8]: https://github.com/devel0/scurve-speed-eval/blob/435327c86769302a22fa54fb6b349a60a1b640d1/gui%2FProgram.cs#L62
[9]: https://github.com/devel0/scurve-speed-eval/blob/435327c86769302a22fa54fb6b349a60a1b640d1/gui%2FProgram.cs#L65
[10]: https://github.com/devel0/scurve-speed-eval/blob/435327c86769302a22fa54fb6b349a60a1b640d1/gui%2FProgram.cs#L69
[11]: https://github.com/devel0/scurve-speed-eval/blob/435327c86769302a22fa54fb6b349a60a1b640d1/gui%2FProgram.cs#L72
## Performance considerations
For a realtime purpose a bezier approach should be used like the one implemented in the [Marlin](https://github.com/MarlinFirmware/Marlin/blob/d364babbc0cdb73337d86e2c4fd9170b46b7361a/Marlin/src/module/stepper.cpp#L651).
## Example
This [example](examples/scurve-xlsx/Program.cs) can be executed through
```
dotnet run --project examples/scurve-xlsx
```
and it will produce follow [output.xlsx](examples/scurve-xlsx/output.xlsx) by applying above formulas and doing some test calc about max allowable torque based on motion and supposed load.
## Prerequisites
- [vscode](https://code.visualstudio.com/)
- [dotnet 8.0](https://dotnet.microsoft.com/download)
## Quickstart
```sh
git clone https://github.com/devel0/netcore-util
cd netcore-util
git checkout bd8626104f4b5a9cb9de5db624cebbcd77a8b384
cd ..
git clone https://github.com/devel0/netcore-sci
cd netcore-sci
git checkout 151451d5cd40e8ccebf93718379e8d72dbadce86
cd ..
git clone https://github.com/devel0/scurve-speed-eval
cd scurve-speed-eval
dotnet build
dotnet run --project gui
```
## How this project was built
```sh
dotnet new console -n scurve-speed-eval
cd scurve-speed-eval
dotnet sln add scurve-speed-eval.csproj
dotnet sln add .
dotnet add reference ../netcore-util/netcore-util
dotnet add reference ../netcore-sci/netcore-sci
dotnet add package AngouriMath --version 1.3.0
dotnet add package Avalonia.Desktop --version 0.10.0-preview6
dotnet add package OxyPlot.Avalonia --version 2.1.0-20200725.1
dotnet add package UnitsNet --version 4.76.0
dotnet run
```
## References
- [How to get sinusoidal s-curve for a stepper motor](http://fightpc.blogspot.com/2018/04/how-to-get-sinusoidal-s-curve-for.html)