robometric_frame.trajectory_quality.path_smoothness

Path Smoothness metric for robotics policy trajectory evaluation.

Path Smoothness evaluates the rate of change in trajectory direction, detecting oscillations that may arise from velocity changes or directional adjustments.

Reference:

M. Dobiš, M. Dekan, P. Beňo, F. Duchoň, and A. Babinec, “Evaluation criteria for trajectories of robotic arms,” Robotics, vol. 11, p. 29, Feb. 2022.

S. Guillén Ruiz, L. V. Calderita, A. Hidalgo-Paniagua, and J. P. Bandera Rubio, “Measuring smoothness as a factor for efficient and socially accepted robot motion,” Sensors (Basel), vol. 20, p. 6822, Nov. 2020.

Classes

PathSmoothness(**kwargs)

Compute Path Smoothness for robotics policy trajectory evaluation.

class robometric_frame.trajectory_quality.path_smoothness.PathSmoothness(**kwargs)

Compute Path Smoothness for robotics policy trajectory evaluation.

Path Smoothness is calculated as:

PS = (1/PL) * Σ(i=1 to L-2) |(p_{i+2} - p_{i+1}) - (p_{i+1} - p_i)|_2

where p_i are trajectory points in D-dimensional space, L is the length of the trajectory, and PL is the path length. This metric measures the rate of change in trajectory direction, with lower values indicating smoother paths.

The metric calculates the difference between consecutive displacement vectors, effectively measuring the second derivative (acceleration) of the path. It is normalized by the total path length to make it scale-invariant.

This metric accumulates smoothness values across multiple trajectories and returns the average path smoothness when compute() is called.

Parameters:

**kwargs (Any) – Additional keyword arguments passed to the base Metric class.

Example

>>> from robometric_frame.trajectory_quality import PathSmoothness
>>> import torch
>>> metric = PathSmoothness()
>>> # Smooth straight line (perfect smoothness = 0)
>>> trajectory = torch.tensor([
...     [0.0, 0.0],
...     [1.0, 0.0],
...     [2.0, 0.0],
...     [3.0, 0.0]
... ])
>>> metric.update(trajectory)
>>> metric.compute()
tensor(0.0000)

Example (with direction change):

>>> # Path with a turn (higher smoothness value)
>>> metric = PathSmoothness()
>>> trajectory = torch.tensor([
...     [0.0, 0.0],
...     [1.0, 0.0],
...     [2.0, 0.0],
...     [2.0, 1.0]
... ])
>>> metric.update(trajectory)
>>> result = metric.compute()
>>> result > 0  # Non-zero smoothness due to direction change
tensor(True)

Example (batched):

>>> # Batch of trajectories - shape (B, L, D)
>>> metric = PathSmoothness()
>>> batch = torch.tensor([
...     [[0.0, 0.0], [1.0, 0.0], [2.0, 0.0], [3.0, 0.0]],  # smooth
...     [[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [2.0, 1.0]]   # has turn
... ])
>>> metric.update(batch)
>>> result = metric.compute()  # Average smoothness

Example (3D trajectories):

>>> # 3D trajectory
>>> metric = PathSmoothness()
>>> trajectory_3d = torch.tensor([
...     [0.0, 0.0, 0.0],
...     [1.0, 0.0, 0.0],
...     [2.0, 0.0, 0.0],
...     [3.0, 0.0, 0.0]
... ])
>>> metric.update(trajectory_3d)
>>> metric.compute()  # Perfect smoothness for straight line
tensor(0.0000)

Example (distributed):

>>> # In distributed training, metrics are automatically synced
>>> metric = PathSmoothness()
>>> # On GPU 0
>>> traj_gpu0 = torch.tensor([[0.0, 0.0], [1.0, 0.0], [2.0, 0.0]])
>>> metric.update(traj_gpu0)
>>> # On GPU 1
>>> traj_gpu1 = torch.tensor([[0.0, 0.0], [0.0, 1.0], [0.0, 2.0]])
>>> metric.update(traj_gpu1)
>>> # Final result aggregates across all GPUs
>>> result = metric.compute()  # Returns aggregated average smoothness

full_state_update: bool = False

total_smoothness: Tensor

num_trajectories: Tensor

__init__(**kwargs)

Initialize the PathSmoothness metric.

update(trajectory)

Update metric state with new trajectory or batch of trajectories.

Parameters:

trajectory (Tensor) –

Tensor of shape (…, L, D) where: - … represents any number of batch dimensions (can be empty) - L is the number of points (must be >= 3) - D is the spatial dimensionality (e.g., 2 for 2D, 3 for 3D)

Examples of valid shapes: - (L, D): Single trajectory - (B, L, D): Batch of B trajectories - (B, T, L, D): Batch of B sequences with T slices each

Points should be ordered chronologically along the L dimension.

Raises:

ValueError – If trajectory has invalid shape or insufficient points.

Return type:

None

compute()

Compute the average Path Smoothness across all trajectories.

Return type:

Tensor

Returns:

Average path smoothness as a scalar tensor. Lower values indicate smoother trajectories with less direction changes.

Raises:

RuntimeError – If no trajectories have been recorded.

training: bool