.vscode | ||
config | ||
lib | ||
test | ||
.credo.exs | ||
.gitignore | ||
.gitlab-ci.yml | ||
LICENSE | ||
mix.exs | ||
mix.lock | ||
README.md |
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 yet. Maybe when it looks more complete.
For now, you can install it as a Git dependency:
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 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 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 and published on HexDocs. Once published, the docs can be found at https://hexdocs.pm/kinemat.