Smoothness Ranks Skill, Not Success: An Audit of Published Trajectory-Smoothness Curation Metrics Under Episode-Length Controls

Jaiveer Bassi

cs.ROOct 12, 2026

Smoothness Ranks Skill, Not Success: An Audit of Published Trajectory-Smoothness Curation Metrics Under Episode-Length Controls

Authors: Jaiveer Bassi

Organizations: Independent Researcher

Abstract

Trajectory smoothness has been proposed as a cheap, training-free signal for curating imitation-learning demonstrations, most recently by rinse, which introduces Spectral Arc Length (SAL) and a contact-aware Trajectory-Envelope Distance (TED). We test whether these published metrics survive episode-length controls on real robomimic data. On can/mh, SAL separates better from worse operators with AUROC 0.952, but episode length alone achieves 0.957, and inside a duration-matched band SAL falls to 0.628 while raw mean jerk, the baseline rinse argues against, rises to 0.896. The confound replicates on square/mh. On can/mg, where every episode is exactly 150 steps, SAL is at chance (0.454) and TED is inverted (0.376) against task success, while jerk reaches 0.706. Training GMM behavior-cloning policies on each metric's curated subset (10 seeds), curating by TED costs roughly a third of downstream success relative to random selection of the same size (0.240 vs. 0.360, p=0.0001, surviving Bonferroni correction), while SAL and jerk are indistinguishable from not curating. Under a diffusion policy TED still ranks worst, though its deficit is not resolvable at five seeds, and jerk becomes significantly better than both baselines, so the curation decision does not transfer unchanged across the two policy configurations we tested. Inspecting trajectories shows why TED inverts: successful manipulation requires sustained high-deviation motion through contact, while failure is low-amplitude hovering that a smoothed envelope follows closely.

Figures & tables

Figure 1: What the four metrics reward, on illustrative synthetic data. Left: end-effector speed profiles of three synthetic pick-and-place demonstrations built from minimum-jerk segments between identical waypoints, with the same small band-limited jitter added to each (shaded: gripper closed). (a) is short and smooth. (b) is the same motion executed twice as slowly, so the episode is twice as long and every segment is just as smooth. (c) is (a) with a committed correction inserted before the grasp: lift, shift sideways, descend again. Right: how each metric ranks the three, computed with the implementations used throughout the paper, with every score given relative to the best of the three under that metric. SAL rates the slow copy (b) worst, by a wider margin than it charges the correction in (c). TED rates the correction (c) worst and the slow copy (b) best. Jerk also rates (c) worst and barely separates (a) from (b). Path length cannot separate (a) from (b), which travel the same route. Every ordering shown is stable across 30 noise seeds except the (a)/(b) near-tie under jerk, which swaps in about a third of them, and the (a)/(c) order under SAL, which swapped once ( scripts/fig_metric_primer.py ). Synthetic and illustrative only: no number in this figure is measured on robomimic.

Figure 2: Smoothness metrics rank duration, not quality. (a) Better-vs-worse operator AUROC on can/mh across duration bands of increasing tightness (shaded: 95% bootstrap CI). SAL (red) tracks the episode-length baseline (gray, dashed) almost exactly and falls from 0.952 to 0.628 as the band tightens; raw jerk (blue) moves the opposite way, 0.584 to 0.896; TED (green) never clears chance and inverts in the tightest band. In that band episode length itself is at chance (0.485), confirming the control. (b) On can/mg every episode is exactly 150 steps, so length carries no information by construction; against the task-success label, jerk retains signal (0.706), SAL is at chance (0.454), and TED is inverted (0.376).

	full ( $n{=}200$ )	$T\in[120,220]$ ( $n{=}98$ )	$T\in[130,190]$ ( $n{=}74$ )	$T\in[140,175]$ ( $n{=}40$ )
SAL	0.952 [.922,.975]	0.793 [.690,.881]	0.759 [.628,.875]	0.628 [.378,.856]
SAL $/T$	0.582 [.497,.662]	0.600 [.479,.715]	0.603 [.446,.755]	0.658 [.342,.923]
TED	0.558 [.480,.636]	0.653 [.522,.776]	0.631 [.468,.779]	0.359 [.147,.583]
jerk	0.584 [.505,.665]	0.862 [.783,.928]	0.906 [.832,.965]	0.896 [.783,.980]
path len.	0.783 [.718,.842]	0.590 [.449,.730]	0.624 [.461,.781]	0.429 [.215,.645]
length $T$	0.957 [.929,.980]	0.801 [.689,.901]	0.753 [.594,.891]	0.485 [.227,.740]

Table 1: Better-vs-worse operator AUROC on can/mh across duration bands, with 95% bootstrap CIs. The bottom row is the control: a band is duration-matched only where

T

itself is near chance. Per-timestep normalizations of TED and path length are omitted: unlike SAL, whose raw value grows with the number of spectral bins, these quantities do not scale linearly with

T

, and dividing by

T

turns them into inverse-speed proxies rather than duration-free measures of smoothness.

	full ( $n{=}200$ )	$T\in[150,300]$ ( $n{=}111$ )	$T\in[180,260]$ ( $n{=}55$ )	$T\in[200,240]$ ( $n{=}30$ )
SAL	0.898 [.852,.936]	0.759 [.658,.849]	0.529 [.344,.702]	0.480 [.250,.701]
SAL $/T$	0.458 [.376,.536]	0.485 [.372,.602]	0.468 [.300,.653]	0.520 [.280,.738]
TED	0.663 [.584,.736]	0.685 [.577,.788]	0.599 [.427,.758]	0.557 [.335,.785]
jerk	0.431 [.349,.509]	0.570 [.455,.687]	0.782 [.618,.923]	0.896 [.724,1.000]
path len.	0.931 [.893,.963]	0.817 [.726,.895]	0.796 [.654,.913]	0.887 [.742,.991]
length $T$	0.936 [.902,.964]	0.824 [.738,.898]	0.613 [.456,.766]	0.407 [.197,.629]

Table 2: Better-vs-worse operator AUROC on square /mh across duration bands, with 95% bootstrap CIs, in the same format as Table 1 . The bottom row is the control. The SAL/jerk crossover observed on Can reproduces here: SAL tracks the length baseline down while jerk rises, and in the band where length is at chance jerk reaches the same 0.896 it reaches in Can’s tightest band.

condition	pool size	best success rate (mean $\pm$ std)	95% CI
oracle (successes only)	716	0.892 $\pm$ 0.048	[0.866, 0.922]
no curation	1950	0.380 $\pm$ 0.063	[0.344, 0.420]
random 50%	1950	0.360 $\pm$ 0.061	[0.326, 0.398]
SAL	1950	0.332 $\pm$ 0.061	[0.298, 0.370]
jerk	1950	0.332 $\pm$ 0.041	[0.306, 0.354]
path length	1950	0.310 $\pm$ 0.030	[0.292, 0.328]

Table 3: Downstream GMM-BC policy success on can/mg after filtering to a fixed 1950-demonstration pool by each metric, 10 seeds each. The oracle pool is smaller (716, the number of successes that exist) and is a ceiling reference, not a matched condition. Pairwise tests against the baselines are in Table 4 .

	vs. random 50%		vs. no curation
metric	$\Delta$ [95% CI]	$p$	$\Delta$ [95% CI]	$p$
TED	$-0.120$ [ $-0.166$ , $-0.076$ ]	$\mathbf{0.0001}$	$-0.140$ [ $-0.186$ , $-0.096$ ]	$\mathbf{<0.0001}$
path length	$-0.050$ [ $-0.090$ , $-0.012$ ]	0.037	$-0.070$ [ $-0.112$ , $-0.030$ ]	0.0071
jerk	$-0.028$ [ $-0.072$ , $+0.014$ ]	0.25	$-0.048$ [ $-0.092$ , $-0.006$ ]	0.060
SAL	$-0.028$ [ $-0.080$ , $+0.024$ ]	0.32	$-0.048$ [ $-0.098$ , $+0.002$ ]	0.098

Table 4: Difference in mean best success rate between each metric-curated condition and the two baselines, with 95% bootstrap CIs on the difference (20,000 resamples) and Welch two-sample

p

-values. Bold marks the comparisons surviving Bonferroni correction across all eight tests (

\alpha=0.05/8=0.006

). Only TED clears that bar. For reference, random and no-curation are themselves indistinguishable (

\Delta=-0.020

, CI

[-0.072,+0.032]

condition	GMM-BC (10 seeds)	diffusion (5 seeds)
oracle (successes only)	0.892 $\pm$ 0.048	0.544 $\pm$ 0.030
no curation	0.380 $\pm$ 0.063	0.120 $\pm$ 0.014
random 50%	0.360 $\pm$ 0.061	0.116 $\pm$ 0.017
jerk	0.332 $\pm$ 0.041	0.212 $\pm$ 0.030
TED	0.240 $\pm$ 0.045	0.092 $\pm$ 0.030

Table 5: Mean best success rate under both policy configurations, restricted to the five conditions run under both. TED is the worst condition under each. Jerk moves from indistinguishable-from-baseline under BC to above both baselines under diffusion. Absolute rates are lower under diffusion in every condition, by factors ranging from

1.6\times

(oracle) to

3.1\times

(the two baselines).

	vs. random 50%		vs. no curation
metric	$\Delta$ [95% CI]	$p$	$\Delta$ [95% CI]	$p$
jerk	$+0.096$ [ $+0.068$ , $+0.124$ ]	$\mathbf{0.0007}$	$+0.092$ [ $+0.064$ , $+0.116$ ]	$\mathbf{0.0011}$
TED	$-0.024$ [ $-0.048$ , $+0.004$ ]	0.17	$-0.028$ [ $-0.052$ , $+0.000$ ]	0.11

Table 6: Diffusion-policy grid, same procedure as Table 4 : 95% bootstrap CIs on the difference (20,000 resamples) and Welch two-sample

p

-values. Bold marks comparisons surviving Bonferroni correction across the four tests reported for this architecture (

\alpha=0.05/4=0.0125

). Random and no-curation are again indistinguishable (

\Delta=-0.004

, CI

[-0.020,+0.012]

Figure 3: Failure stays inside the envelope; success does not. A successful (left) and failed (right) can/mg demonstration, with end-effector position, TED’s gripper-contact segment boundaries (red), the per-segment Bézier envelope (dashed), and the per-timestep envelope residual (bottom, orange bars are per-segment means). Both trajectories contain one high-deviation segment, but in the success it spans timesteps 12–96 and coincides with the descend-and-grasp, while in the failure it is confined to the initial free-space approach (0–24) and the remaining 126 steps are a flat tail of repeated gripper cycles that never completes a placement. TED averages over the alignment path and so rates the failure as the cleaner trajectory. Illustrative of the mechanism only; the quantitative claim is Figure 2 b.

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Apr 24, 2026J/K move · Enter open · S save

Learning from the Best: Smoothness-Driven Metrics for Data Quality in Imitation Learning

Soham Kulkarni, Raayan Dhar, Yuchen Cui

Department of Computer Science, University of California, Los Angeles, CA 90095, USA

Imitation Learning Robot Imitation Learning

Open paper AskPDF arXiv

In behavioral cloning (BC), policy performance is fundamentally limited by demonstration data quality. Real-world datasets contain trajectories of varying quality due to operator skill differences, teleoperation artifacts, and procedural inconsistencies, yet standard BC treats all demonstrations equally. Existing curation methods require costly policy training in the loop or manual annotation, limiting scalability. We propose RINSE (Ranking and INdexing Smooth Examples), a lightweight framework for scoring demonstrations based on trajectory smoothness that is policy-architecture-agnostic and operates on trajectory data alone, with TED additionally using a phase-boundary/contact signal. Grounded in motor control theory, which establishes smoothness as a hallmark of skilled movement, RINSE uses two complementary metrics: Spectral Arc Length (SAL), a spectral measure of frequency-domain regularity, and Trajectory-Envelope Distance (TED), a spatial measure of contact-aware geometric deviation. We show that smoothness filtering can reduce the conditional action variance of the retained data distribution, with downstream effects that can be amplified by action chunking and compounding error. On RoboMimic benchmarks, SAL filtering achieves 16% higher success using one-sixth of the data. On real-world manipulation, TED filtering achieves 20% improvement with half the data. As a retrieval-stage filter within STRAP on LIBERO-10, RINSE re-ranking improves mean success by 5.6%. As soft weights in Re-Mix domain reweighting, RINSE scores produce domain allocations highly correlated with the learned Re-Mix allocations (Spearman

ρ\geq 0.89

). These results support smoothness as a useful quality signal across filtering, retrieval, and reweighting settings, especially in noisy or heterogeneous data regimes.

Abstract

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