bolero.datasets.make_minimum_jerk¶

bolero.datasets.make_minimum_jerk(start, goal, execution_time=1.0, dt=0.01)[source]¶

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:	start : array-like, shape (n_task_dims,) Initial state goal : array-like, shape (n_task_dims,) Goal execution_time : float, optional (default: 1) Execution time in seconds dt : float, optional (default: 0.01) Time between successive steps in seconds
Returns:	X : array, shape (n_task_dims, n_steps, 1) The positions of the trajectory Xd : array, shape (n_task_dims, n_steps, 1) The velocities of the trajectory Xdd : array, shape (n_task_dims, n_steps, 1) The accelerations of the trajectory