movement_primitives.data.generate_minimum_jerk

movement_primitives.data.generate_minimum_jerk(start, goal, execution_time=1.0, dt=0.01)

Create a minimum jerk trajectory.

A minimum jerk trajectory from \(x_0\) to \(g\) minimizes the third time derivative of the positions:

\[\arg \min_{x_0, \ldots, x_T} \int_{t=0}^T \dddot{x}(t)^2 dt\]

The trajectory will have

n_steps = 1 + execution_time / dt

steps because we start at 0 seconds and end at execution_time seconds.

Parameters:

startarray-like, shape (n_dims,)

Initial state

goalarray-like, shape (n_dims,)

Goal state

execution_timefloat, optional (default: 1)

Execution time in seconds

dtfloat, optional (default: 0.01)

Time between successive steps in seconds

Returns:

Xarray, shape (n_steps, n_dims)

The positions of the trajectory

Xdarray, shape (n_steps, n_dims)

The velocities of the trajectory

Xddarray, shape (n_steps, n_dims)

The accelerations of the trajectory

Raises:

ValueError

If the shapes of the initial and goal state do not match.