129 lines
4.3 KiB
Markdown
129 lines
4.3 KiB
Markdown
# Kinemat
|
|
|
|
Kinemat is the beginnings of a library for solving forward and reverse
|
|
kinematics of robotic systems and graphical simulations.
|
|
|
|
## Installation
|
|
|
|
As this package currently doesn't do what it says on the tin, I've not
|
|
published a version to [hex](https://hex.pm) yet. Maybe when it looks
|
|
more complete.
|
|
|
|
For now, you can install it as a Git dependency:
|
|
|
|
```elixir
|
|
def deps do
|
|
[{:kinemat, "~> 0.1.0"}]
|
|
end
|
|
```
|
|
|
|
## Usage
|
|
|
|
### Representing angles regardless of unit
|
|
|
|
Since Angles are probably something you want to use we use the
|
|
[angle](https://hex.pm/packages/angle) package to store and convert between
|
|
different types of angles.
|
|
|
|
Most usefully you can use the `~a` sigil to create angles in different units.
|
|
See the [angle docs](https://hexdocs.pm/angle/api-reference.html) for more
|
|
information.
|
|
|
|
### Representing spacial coordinates
|
|
|
|
Kinemat uses the `Point` protocol to handle manipulations of spacial
|
|
coordinates. The protocol is implemented by `Cartesian`, `Cylindrical` and
|
|
`Spherical`.
|
|
|
|
iex> use Kinemat
|
|
...> use Kinemat.Coordinates
|
|
...> Cartesian.init(3,4,5)
|
|
...> |> Point.to_cylindrical()
|
|
#Kinemat.Point<[azimuth: #Angle<0.9272952180016122㎭>,
|
|
radial: 5.0,
|
|
vertical: 5]>
|
|
|
|
### Representing spacial orientations
|
|
|
|
Kinemat uses the `Orientation` module to allow manipulations and conversions
|
|
between the three primary orientation modules; `Euler`, `RotationMatrix` and
|
|
`Quaternion`.
|
|
|
|
Note that not all `Euler` orders are supported, but only so-called "Tait-Bryan"
|
|
angles.
|
|
|
|
iex> use Kinemat
|
|
...> use Kinemat.Orientations
|
|
...> Euler.init(:xyz, ~a(10)d, ~a(20)d, ~a(30)d)
|
|
...> |> Orientation.to_quaternion()
|
|
#Kinemat.Orientation<[
|
|
type: :quaternion,
|
|
w: #Angle<0.943714364147489㎭>,
|
|
x: 0.12767944069578063,
|
|
y: 0.14487812541736914,
|
|
z: 0.2685358227515692
|
|
]>
|
|
|
|
### Representing frames of reference
|
|
|
|
Kinemat can build a `Frame` given the combination of an `Orientation` and a `Point`;
|
|
|
|
iex> use Kinemat
|
|
...> point = Kinemat.Coordinates.Cylindrical.init(10, ~a(20)d, 30)
|
|
...> orientation = Kinemat.Orientations.Euler.init(:xyz, ~a(10)d, ~a(20)d, ~a(30)d)
|
|
...> frame = Frame.init(point, orientation)
|
|
#Kinemat.Frame<[
|
|
orientation: #Kinemat.Orientation<[
|
|
euler: :xyz,
|
|
x: #Angle<10°>,
|
|
y: #Angle<20°>,
|
|
z: #Angle<30°>
|
|
]>,
|
|
point: #Kinemat.Point<[azimuth: #Angle<20°>, radial: 10, vertical: 30]>
|
|
]>
|
|
|
|
And frames can be converted to homogeneous transformations
|
|
|
|
...> Kinemat.HomogeneousTransformation.to_homogeneous_transformation(frame)
|
|
{ 0.8137976813493738, 0.5438381424823255, -0.20487412870286215, 9.396926207859085,
|
|
-0.46984631039295416, 0.823172944645501, 0.3187957775971678, 3.420201433256687,
|
|
0.3420201433256687, -0.16317591116653482, 0.9254165783983234, 30,
|
|
0.0, 0.0, 0.0, 1.0}
|
|
|
|
### Representing joints
|
|
|
|
Kinemat can build `Revolute`, `Cylindrical` and `Prismatic` joints starting
|
|
with a frame and extra information based on the kind of joint in use.
|
|
|
|
iex> use Kinemat
|
|
...> use Kinemat.Joints
|
|
...> Revolute.init(Frame.zero(), limits: {~a(-10)d, ~a(10)d})
|
|
%Kinemat.Joints.Revolute{
|
|
frame: #Kinemat.Frame<[
|
|
orientation: #Kinemat.Orientation<[
|
|
euler: :xyz,
|
|
x: #Angle<0>,
|
|
y: #Angle<0>,
|
|
z: #Angle<0>
|
|
]>,
|
|
point: #Kinemat.Point<[x: 0, y: 0, z: 0]>
|
|
]>,
|
|
limits: {#Angle<-10°>, #Angle<10°>},
|
|
position: #Angle<-10°>
|
|
}
|
|
|
|
Documentation can be generated with [ExDoc](https://github.com/elixir-lang/ex_doc)
|
|
and published on [HexDocs](https://hexdocs.pm). Once published, the docs can
|
|
be found at [https://hexdocs.pm/kinemat](https://hexdocs.pm/kinemat).
|
|
|
|
## License
|
|
|
|
This software is licensed under the terms of the
|
|
[HL3-FULL](https://firstdonoharm.dev), see the `LICENSE.md` file included with
|
|
this package for the terms.
|
|
|
|
This license actively proscribes this software being used by and for some
|
|
industries, countries and activities. If your usage of this software doesn't
|
|
comply with the terms of this license, then [contact me](mailto:james@harton.nz)
|
|
with the details of your use-case to organise the purchase of a license - the
|
|
cost of which may include a donation to a suitable charity or NGO.
|