CUSP: CUSUM-Governed Survival Hazard Alarms at the Perception Onset for Off-Road Navigation

Inuk Kang; Seung-Woo Seo

cs.ROOct 6, 2026

CUSP: CUSUM-Governed Survival Hazard Alarms at the Perception Onset for Off-Road Navigation

Authors: Inuk Kang, Seung-Woo Seo

Organizations: Seoul National University

Abstract

Off-road navigation exposes a robot to potentially hazardous terrain en route. Although learning-based navigation uses safety supervision to choose which path to drive, it provides no runtime alarm when the robot following that path is heading into danger. Such an alarm must be learned from field logs, where human intervention preempts the failure and the failure itself is therefore never observed. The human judges driving unsafe early but typically intervenes only once failure is clearly near, so the intervention marks that judgment late. That earlier judgment is what a runtime alarm must detect, yet no prior intervention-supervised method has targeted it. To address this problem, we introduce CUSP (CUSUM-governed Survival model of the Perception onset), a model-agnostic runtime hazard alarm that learns this moment from intervention-terminated logs. "Cusp" is a word for the point at which one state is about to turn into another, and the moment we target is exactly such a cusp: the point at which safe driving turns unsafe in a human's judgment. We call this point the perception onset and annotate it separately from the intervention. A visual hazard head is trained on the annotated onset with a discrete-time survival objective so that driving with and without an onset both supervise the head, and a CUSUM accumulates the predicted onset risk into alarms. We evaluate CUSP at five unseen sites, two autonomous and three teleoperated, with 142 events and every method tuned to the same rate of ten false alarms per hour. CUSP detected 85 events compared to 26 for the best of nine adapted baselines, and the margin comes from hazards to which every signal in the navigation model is blind.

Figures & tables

Fig. 1: The challenge this paper addresses. (Left) The autonomy model keeps proposing candidate paths as the robot approaches a deteriorating slope, and nothing in the model raises an alarm. (Middle) The human perceives the safe-to-dangerous transition, marked as the onset $o_{i}$ (red box), and takes over before failure. (Right) CUSP learns this perception. It accumulates evidence of the transition over time and raises an alarm once that evidence exceeds a threshold, here shortly after the onset.

Fig. 2: CUSP overview. (a) Training. Each episode is annotated with the perception onset $o_{i}$ and the $\mathrm{end}_{i}$ just before intervention. Frozen DINOv3 features are pooled over the committed-path corridor with temporal differences and global context and FiLM-conditioned on path curvature and speed. Survival targets and masks are anchored on $o_{i}$ , and per-event weights $w_{i}$ are graded by IMU tilt around the onset (training only). (b) Runtime. The onset-risk score is robust-standardized and accumulated by a one-sided CUSUM under a per-site false-alarm budget.

Fig. 3: Example detections at Sites II, III, and V. (a) Four vegetation intrusion events at Site II, where the path is visibly impassable and the baselines also detect the events. (b) Mounting a right cross-slope (Site V). (c) Sliding into a downward right cross-slope (Site III). (d) Entering a left cross-slope overgrown with dense bushes (Site III). In (b)–(d) nothing in the view marks the path as impassable, and CUSP is the only method that alarms. Each plot shows the score $s_{t}$ (grey) and the CUSUM statistic $C_{t}$ (blue) against time from onset, with the threshold $h$ as a dashed line, the perception-to-action window $[o_{i},\mathrm{end}]$ shaded in green, and the alarm time marked by the orange vertical line. Frames above each plot are sampled at the indicated times from onset.

Method	Native output	Hazard score
Traversability
STERLING [ 2 ]	terrain feature	roughness head
CAHSOR [ 8 ]	terrain feature	roughness head (speed-cond.)
SALON [ 36 ]	visual feature	Mahalanobis to normal
WVN [ 1 ]	roughness, confidence	roughness $+$ RND novelty
Obstacle proximity

TABLE I: Baselines: native output

\rightarrow

per-frame hazard score.

Method	det. ( $\uparrow$ )/142 (I–V)	margin ( $\uparrow$ ) $>$ 0.5/1/2 (s)	$C({+}3)$ ( $\uparrow$ )	delay ( $\downarrow$ ) [IQR] (s)
events	142 (11/50/28/13/40)
NavDP [ 10 ]	3 (0/3/0/0/0)	3/2/2	0.014	$+$ 2.04 [1.8–5.7]
CARE [ 11 ]	10 (0/5/1/1/3)	10/10/10	0.021	$+$ 4.59 [1.7–5.7]
LaND [ 17 ]	12 (0/0/3/3/6)	11/11/10	0.049	$+$ 2.58 [1.4–3.8]
FIPER [ 14 ]	21 (1/10/6/0/4)	19/16/12	0.028	$+$ 5.24 [3.2–8.4]
PAAD [ 18 ]	26 (0/14/3/1/8)	25/22/19	0.056	$+$ 5.13 [2.8–7.7]

TABLE II: Five-site results under a common 10/h budget.

Fig. 4: Detection rate against realized FAR on Sites III–V as $h$ varies. The dashed line marks the 10/h operating point.

Objective	Hor.	Mask	$w_{i}$	det./142 (I–V)	$\Delta$ [95% CI]
Binary [ 17 , 18 ]	$H$	—	—	9 (2/1/3/0/3)	$-76$ [ $-89$ , $-64$ ]
Per-bin binary	$B$ bins	no	—	4 (0/1/1/0/2)	$-81$ [ $-92$ , $-70$ ]
Time-to-onset regr.	cont.	—	—	11 (0/3/2/1/5)	$-74$ [ $-85$ , $-63$ ]
Survival	$B$ bins	yes	uniform	45 (0/8/15/3/19)	$-40$ [ $-49$ , $-32$ ]
Survival (CUSP)	$B$ bins	yes	graded	85 (4/40/16/4/21)	—

TABLE III: Training objective ablation.

$\eta$ (s)	0	$+$ 1	$+$ 2	$+$ 4	$+$ 6	$+$ 10	end
det./142	85	72	72	69	62	60	58
I/II	4/40	0/31	1/33	3/30	2/30	2/29	2/28
III/IV/V	16/4/21	16/5/20	15/4/19	13/4/19	9/4/17	10/4/15	8/5/15

TABLE IV: Positive label extended to

[o_{i},\,o_{i}{+}\eta]

Scheme	$w_{i}$	$w_{i}{>}0$ /163	det./142 (I–V)	$\Delta$ [95% CI]
Soft ramp	$\mathrm{clip}(z_{i}/2,0,1)$	146	41 (0/3/15/5/18)	$-44$ [ $-51$ , $-36$ ]
Uniform (evidence off)	$1$	163	45 (0/8/15/3/19)	$-40$ [ $-49$ , $-32$ ]
Sigmoid	$\sigma(z_{i}{-}1)$	163	48 (0/9/15/4/20)	$-37$ [ $-46$ , $-28$ ]
Gate	$\mathbf{1}[z_{i}{\geq}1.5]$	89	62 (2/23/14/5/18)	$-23$ [ $-32$ , $-14$ ]
Clipped ramp (CUSP)	Eq. ( 7 ), $(1,2)$	114	85 (4/40/16/4/21)	—

TABLE V: Evidence-weight mapping

z_{i}\!\to\!w_{i}

Decision statistic	det./142 (I–V)	$\Delta$ [95% CI]	site- $\sigma$ (/h)	FAR (/h, I–V)
Conformal martingale	16 (1/3/4/5/3)	$-69$ [ $-81$ , $-57$ ]	5.9	5.9/8.4/6.4/19.6/2.4
Sliding sum	26 (2/2/8/7/7)	$-59$ [ $-69$ , $-48$ ]	3.3	7.9/9.8/12.9/14.7/5.7
EWMA	37 (2/12/8/6/9)	$-48$ [ $-59$ , $-38$ ]	4.0	13.8/9.8/6.4/15.9/5.7
Instantaneous	53 (2/20/10/6/15)	$-32$ [ $-43$ , $-22$ ]	6.4	17.8/9.8/0.0/15.9/6.5
CUSUM (CUSP)	85 (4/40/16/4/21)	—	2.2	7.9/9.8/12.9/12.2/7.3

TABLE VI: Decision statistic on the frozen CUSP score. Site-

\sigma

is the population SD of the five FARs.

Conditioning	det./61 (I/II)	$\Delta$ [95% CI]	FAR (/h) [95% upper]
FiLM off	8 (0/8)	$-36$ [ $-43$ , $-28$ ]	8.2 [ $\leq$ 18.2]
concat. $[\mathrm{curv},\mathrm{spd}]$	36 (0/36)	$-8$ [ $-14$ , $-3$ ]	8.2 [ $\leq$ 19.5]
FiLM (CUSP)	44 (4/40)	—	9.0 [ $\leq$ 19.5]

TABLE VII: Kinematic conditioning on autonomous Sites I–II.

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