🥮 mooncakes.io

    moonbitstack/moonmcl/kinematics does not have a README file

    Ackermann

    source
    pub(all) struct Ackermann {
      wheelbase : Double
      track : Double
    } derive(
    Debug    )

    An Ackermann steering base: the inner and outer front wheels turn by different angles about a common centre.

    Ackermann::angles

    source
    fn Ackermann::angles(self : Ackermann, curvature~ : Double) -> (Double, Double)

    The inner and outer steering angles for a curvature: the wheel on the inside of the turn has to turn further, by the angle its shorter radius demands.

    Ackermann::forward

    source

    Ackermann::inverse

    source

    Ackermann::jacobian

    source

    Ackermann::new

    source
    fn Ackermann::new(wheelbase~ : Double, track~ : Double) -> Ackermann raise 
    Refused

    An Ackermann base with the given wheelbase and track.

    Ackermann::to_repr

    source

    Bicycle

    source
    pub(all) struct Bicycle {
      wheelbase : Double
    } derive(
    Debug    )

    A bicycle model: the joint space is (speed, steering angle) and the task space the body twist (vx, vy, omega).

    Bicycle::curvature

    source
    fn Bicycle::curvature(self : Bicycle, steering~ : Double) -> Double

    The curvature a steering angle gives.

    Bicycle::forward

    source

    Bicycle::inverse

    source

    Bicycle::jacobian

    source

    Bicycle::new

    source
    fn Bicycle::new(wheelbase~ : Double) -> Bicycle raise 
    Refused

    A bicycle with the given wheelbase.

    Bicycle::steering

    source
    fn Bicycle::steering(self : Bicycle, curvature~ : Double) -> Double

    The steering angle a curvature needs.

    Bicycle::to_repr

    source

    Delta

    source
    pub(all) struct Delta {
      base_radius : Double
      platform_radius : Double
      upper_arm : Double
      lower_arm : Double
    } derive(
    Debug    )

    A delta robot: three parallel arms from a fixed base to a moving platform.

    The joint space is the three upper-arm angles measured from horizontal and the task space the platform centre (x, y, z) under the base.
    impl Kinematics for Delta

    Delta::elbows

    source

    The three elbows, in the base frame, for the upper-arm angles q.

    A drawing of the cell needs the elbows as well as the platform, and the cell already computes them to solve its own forward map.

    Delta::forward

    source

    Delta::inverse

    source

    Delta::jacobian

    source

    Delta::new

    source
    fn Delta::new(base_radius~ : Double, platform_radius~ : Double, upper_arm~ : Double, lower_arm~ : Double) -> Delta raise 
    Refused

    A delta cell with the given geometry.

    Delta::to_repr

    source

    Differential

    source
    pub(all) struct Differential {
      wheel_radius : Double
      track : Double
    } derive(
    Debug    )

    A two-wheel differential drive.

    track is the distance between the wheels and wheel_radius the radius of each. The joint space is (omega_left, omega_right) in radians per second and the task space (v, omega) in metres and radians per second.

    Differential::advance

    source

    The pose after driving twist for dt seconds.

    The arc is integrated exactly: a straight chord would cut the corner of every turn, and the error grows with the square of the period.

    Differential::forward

    source

    Differential::inverse

    source

    Differential::jacobian

    source

    Differential::new

    source
    fn Differential::new(wheel_radius~ : Double, track~ : Double) -> Differential raise 
    Refused

    A differential drive with the given wheel radius and track width.

    Differential::to_repr

    source

    Gantry

    source
    pub(all) struct Gantry {
      track : Double
    } derive(
    Debug    )

    A gantry: two motors drive one gantry axis from either end, so the pair sets the position and the tilt of the beam.

    The joint space is (x, y_left, y_right, z) and the task space (x, y, z, tilt), where y is the middle of the beam and tilt the angle the difference between its ends makes.

    Gantry::forward

    source

    Gantry::inverse

    source

    Gantry::jacobian

    source

    Gantry::new

    source

    A gantry with the given beam length.

    Gantry::to_repr

    source

    Mecanum

    source
    pub(all) struct Mecanum {
      wheel_radius : Double
      half_length : Double
      half_width : Double
    } derive(
    Debug    )

    A four-wheel mecanum base. The joint space is the four wheel speeds in the order front left, front right, rear left, rear right, and the task space the body twist (vx, vy, omega).

    Mecanum::forward

    source

    Mecanum::inverse

    source

    Mecanum::jacobian

    source

    Mecanum::new

    source
    fn Mecanum::new(wheel_radius~ : Double, half_length~ : Double, half_width~ : Double) -> Mecanum raise 
    Refused

    A mecanum base with the given wheel radius and half extents.

    Mecanum::to_repr

    source

    Omnidirectional

    source
    pub(all) struct Omnidirectional {
      wheel_radius : Double
      radius : Double
      angles : Array[Double]
    } derive(
    Debug    )

    An omnidirectional base with three or more driven wheels on a circle.

    The wheels are mounted tangentially, so each one drives along theta and the map from twist to wheel speeds is one row per wheel. With three wheels it inverts exactly; with more the inverse is the least-squares one, which spreads the effort over the wheels that can help.

    Omnidirectional::forward

    source

    Omnidirectional::inverse

    source

    Omnidirectional::jacobian

    source

    Omnidirectional::new

    source
    fn Omnidirectional::new(wheel_radius~ : Double, radius~ : Double, angles~ : ArrayView[Double]) -> Omnidirectional raise 
    Refused

    An omnidirectional base whose wheel i sits at angles[i] radians on a circle of radius.

    Omnidirectional::to_repr

    source

    PlanarArm

    source
    pub(all) struct PlanarArm {
      lengths : Array[Double]
    } derive(
    Debug    )

    A planar chain of n links. The joint space is the joint angles and the task space the (x, y) of the tip.

    PlanarArm::forward

    source

    PlanarArm::inverse

    source

    PlanarArm::jacobian

    source

    PlanarArm::jacobian_analytic

    source

    The analytic Jacobian of the arm at the joint angles q: how far the tip moves for a small change in each joint.

    Link k and everything outboard of it turn with joint k, so column k is that joint's direction rotated by the total angle up to k, scaled by the reach still in front of it. Kinematics::jacobian defaults to a central difference; this is the same matrix in closed form.

    PlanarArm::new

    source

    A planar arm with the given link lengths.

    PlanarArm::solve

    source
    fn PlanarArm::solve(self : PlanarArm, target~ : 
    Vec    , seed~ : 
    Vec    , iterations? : Int, damping? : Double, tolerance? : Double) -> 
    Vec     raise 
    Refused

    The joint angles that put the tip on target, by damped least squares.

    The damping is what makes the solve usable near a singularity: without it the Jacobian's inverse blows up and the joint velocities with it, which on a real arm is a torque the drive cannot deliver. damping is the square of the smallest singular value the solve allows.

    PlanarArm::to_repr

    source

    Scara

    source
    pub(all) struct Scara {
      upper_arm : Double
      forearm : Double
      vertical : Double
    } derive(
    Debug    )

    A SCARA arm: two revolute joints about the vertical axis and one prismatic joint along it.
    impl Kinematics for Scara

    Scara::forward

    source

    Scara::inverse

    source

    Scara::jacobian

    source

    Scara::new

    source
    fn Scara::new(upper_arm~ : Double, forearm~ : Double, vertical~ : Double) -> Scara raise 
    Refused

    A SCARA with the two link lengths and the vertical stroke.

    Scara::to_repr

    source

    Source Files