Comfort Metrics¶

Use comfort metrics when evaluating passenger or payload smoothness, acceleration exposure, jerk exposure, and trajectory aggressiveness.

Reference¶

Standard finite-difference kinematics and RMS or peak acceleration summaries used in robotics motion evaluation.

Quick Example¶

import numpy as np
from robometrics import acceleration, jerk

traj = np.array([[0.0, 0.0], [1.0, 0.0], [2.5, 0.0], [4.5, 0.0]])
dt = 0.1
print(acceleration(traj, dt))
print(jerk(traj, dt))

Metrics¶

acceleration(traj, dt) -> NDArray[np.float64]¶

Formula: second finite difference of position divided by dt squared. Reference: Standard finite-difference kinematics Unit: m/s^2 Direction: lower magnitude is smoother

Acceleration returns vector samples for downstream peak, mean, or RMS summaries. Values with absolute magnitude below 1e-10 are returned as zero to suppress finite-difference roundoff noise.

jerk(traj, dt) -> NDArray[np.float64]¶

Formula: third finite difference of position divided by dt cubed. Reference: Standard finite-difference kinematics Unit: m/s^3 Direction: lower magnitude is smoother

Jerk exposes rapid acceleration changes that often correlate with discomfort. Values with absolute magnitude below 1e-10 are returned as zero to suppress finite-difference roundoff noise.

jerk_cost(traj, dt) -> float¶

Formula: mean squared jerk magnitude. Reference: RoboMetrics internal comfort cost Unit: m^2/s^6 Direction: lower is better

Jerk cost is a scalar penalty for abrupt motion.

acceleration_magnitude(traj, dt) -> NDArray[np.float64]¶

Formula: norm of each acceleration vector. Reference: Standard finite-difference kinematics Unit: m/s^2 Direction: lower is smoother

Acceleration magnitude converts vector acceleration into scalar samples.

jerk_magnitude(traj, dt) -> NDArray[np.float64]¶

Formula: norm of each jerk vector. Reference: Standard finite-difference kinematics Unit: m/s^3 Direction: lower is smoother

Jerk magnitude provides per-step scalar jerk exposure.

max_acceleration(traj, dt) -> float¶

Formula: max acceleration magnitude. Reference: Standard peak acceleration evaluation Unit: m/s^2 Direction: lower is better

Max acceleration flags extreme spikes.

mean_acceleration(traj, dt) -> float¶

Formula: mean acceleration magnitude. Reference: Standard mean acceleration evaluation Unit: m/s^2 Direction: lower is better

Mean acceleration summarizes sustained aggressiveness.

rms_acceleration(traj, dt) -> float¶

Formula: root mean square acceleration magnitude. Reference: Standard RMS acceleration evaluation Unit: m/s^2 Direction: lower is better

RMS acceleration weights sustained and peak exposure.

max_deceleration(traj, dt) -> float¶

Formula: maximum negative longitudinal acceleration magnitude. Reference: Standard peak deceleration evaluation Unit: m/s^2 Direction: lower is better

Max deceleration highlights harsh braking.

smoothness_score(traj) -> float¶

Formula: scale-normalized score derived from third differences. Reference: RoboMetrics internal heuristic Unit: score Direction: higher is better

Smoothness score maps trajectory regularity to a bounded score. Trajectories with fewer than four points return 1.0 with a RuntimeWarning because third finite differences are not measurable.