Trajectories

All trajectories inherit the methods and attributes from this base class. Note that the base class is not exported and can thus not be used.

class kontiki.trajectories.Trajectory

position(t : float) → ndarray

Position (3D vector) at time t

velocity(t : float) → ndarray

Velocity (3D vector) at time t

acceleration(t : float) → ndarray

Acceleration (3D vector) at time t

orientation(t : float) → ndarray

Orientation (unit quaternion) at time t

angular_velocity(t : float) → ndarray

The angular velocity at time t

from_world(X : ndarray) → ndarray

Transform a 3D point from the world coordinate frame to the trajectory coordinate frame.

to_world(X : ndarray) → ndarray

Transform a 3D point from the trajectory to the world coordinate frame.

clone() → Trajectory

Clone the trajectory

min_time

Minimum time (including) that the trajectory is valid

max_time

Maximum time (excluding) that the trajectory is valid

valid_time

Tuple of (min_time, max_time)

locked

If True then the trajectory is unchanged during estimation

Splined trajectories

The splined trajectories are cubic B-splines, defined as in [Qin2000].

class kontiki.trajectories.SplinedTrajectory(dt=1, t0=0)

A splined trajectory with knot spacing dt and time offset t0. The time offset t0 is the first valid time of the spline.

dt

Spline knot spacing

t0

Spline time offset (always same as Trajectory.min_time)

__len__() → int

Number of spline knots and control points

__getitem__(k : int) → ndarray

Return control point k

__setitem__(k : int, cp : ndarray)

Set control point k

append_knot(cp : ndarray)

Append a new control point (and knot)

extend_to(t : float, cp : ndarray)

Extend the spline to be valid at least up to t by appending control points cp

Splined trajectory classes

class kontiki.trajectories.UniformSE3SplineTrajectory

A spline with control points in SE(3)

Control points are 4x4 matrices T = [R, p; 0, 1].

class kontiki.trajectories.UniformR3SplineTrajectory

A spline with control points in R3

Control points are vectors in R3.

class kontiki.trajectories.UniformSO3SplineTrajectory

A spline with control points in SO(3)

Control points are unit quaternions q=(w, x, y, z).

Other trajectories

class kontiki.trajectories.SplitTrajectory

Split interpolation trajectory

This trajectory is implemented using two splines: one in R3 and one in SO3.

SplitTrajectory(r3_dt=1, so3_dt=1, r3_t0=0, so3_t0=0)

Construct new split trajectory from specified knot spacings and time offsets.

SplitTrajectory(r3_trajectory, so3_trajectory)

Construct split trajectory by wrapping two previously created UniformR3SplineTrajectory and UniformSO3SplineTrajectory instances.

R3_spline

The UniformR3SplineTrajectory instance

SO3_spline

The UniformSO3SplineTrajectory instance

References

[Qin2000]

Qin, K. General matrix representations for b-splines The Visual Computer, 16(3–4)