Reference

ConstantAffineMap

A struct describing a transformation of the form x_target = A*x_source + b, and time derivatives of x_source, where A and b are constant in time.

ConstantAffineMaps are typically constructed internally from other KinematicTransformations.

ConstantLinearMap(A)

Construct a reference frame transformation of the form x_target = A*x_source, where A is constant with time.

ConstantVelocityTransformation(t0, x0, v)

Construct a transformation of a reference frame moving with a constant velocity, i.e., x_target = x_source + x0 .+ (t - t0)*v.

Arguments

• t0: Time at which the position of the source coordinate system's origin in the target coordinate system is equal to x0.
• x0: Position of the source coordinate system's origin in the target coordinate system's frame of reference at time t0.
• v: (Constant) velocity of the source coordinate system relative to the target coordinate system.

KinematicTransformation

An abstract type representing a transformation of kinematic quantities.

(trans::KinematicTransformation)(t, x, [v, [a, [j]]], linear_only::Bool=false)

Transform vector x, and optionally v, a, and j from the source coordinate system to the target coordinate system at time t according to the transformation trans, returning x and optionally v, a, and j in the target coordinate system.

v, a, and j are the first through third time derivatives of x.

If linear_only is true, the constant part (if any) of the transformation will not be applied. For example, with a ConstantAffineMap, which represents a transformation of the form x_target = A*x_source + b, the b will not be used. This is useful for properly transforming vectors that don't represent the position of a point and time derivatives of the same (e.g. force).

SteadyRotXTransformation(t0, ω, θ)

Construct a transformation of a reference frame rotating about the x axis at a constant rate ω.

The rotation angle as a function of time will be angle = ω*(t - t0) + θ.

Arguments

• t0: Time at which the angle between the target and source coordinate systems' y and z axes is θ.
• ω: Rotation rate of the target coordinate system, in units of rad/<time>.
• θ: Angle between the target and source coordinate systems' y and z axes at time t0.

SteadyRotYTransformation(t0, ω, θ)

Construct a transformation of a reference frame rotating about the y axis at a constant rate ω.

The rotation angle as a function of time will be angle = ω*(t - t0) + θ.

Arguments

• t0: Time at which the angle between the target and source coordinate systems' x and z axes is θ.
• ω: Rotation rate of the target coordinate system, in units of rad/<time>.
• θ: Angle between the target and source coordinate systems' x and z axes at time t0.

SteadyRotZTransformation(t0, ω, θ)

Construct a transformation of a reference frame rotating about the z axis at a constant rate ω.

The rotation angle as a function of time will be angle = ω*(t - t0) + θ.

Arguments

• t0: Time at which the angle between the target and source coordinate systems' x and y axes is θ.
• ω: Rotation rate of the target coordinate system, in units of rad/<time>.
• θ: Angle between the target and source coordinate systems' x and y axes at time t0.

compose(t, trans1::KinematicTransformation, trans2::KinematicTransformation)

Return a transformation resulting from applying trans2 and then trans1 at time t.

This will likely return a ConstantAffineMap, but may return a more specific transformation. For example, combining two ConstantLinearMaps will result in a new ConstantLinearMap.

transform(trans::KinematicTransformation, t, x, [v, [a, [j]]], linear_only::Bool=false)

Transform vector x, and optionally v, a, and j from the source coordinate system to the target coordinate system at time t according to the transformation trans, returning x and optionally v, a, and j in the target coordinate system.

v, a, and j are the first through third time derivatives of x.

If linear_only is true, the constant part (if any) of the transformation will not be applied. For example, with a ConstantAffineMap, which represents a transformation of the form x_target = A*x_source + b, the b will not be used. This is useful for properly transforming vectors that don't represent the position of a point and time derivatives of the same (e.g. force).

transform!(x_new, [v_new, [a_new, [j_new]]], trans::KinematicTransformation, t, x, [v, [a, [j]]], linear_only::Bool=false)

Transform vector x, and optionally v, a, and j from the source coordinate system to the target coordinate system at time t according to the transformation trans, returning the results in x_new and optionally v_new, a_new, and j_new in the target coordinate system.

v, a, and j are the first through third time derivatives of x.

If linear_only is true, the constant part (if any) of the transformation will not be applied. For example, with a ConstantAffineMap, which represents a transformation of the form x_target = A*x_source + b, the b will not be used. This is useful for properly transforming vectors that don't represent the position of a point and time derivatives of the same (e.g. force).