Timed Rule-Based Supervision of an End-to-End Autonomous Parking Policy

Kejia Gao; Liguo Zhou; Lei Yu; Alois Knoll

cs.ROSep 24, 2026

Timed Rule-Based Supervision of an End-to-End Autonomous Parking Policy

Authors: Kejia Gao, Liguo Zhou, Lei Yu, Alois Knoll

Abstract

We study whether a manually specified runtime supervisor can correct recurring failures of an existing end-to-end parking policy in a fixed CARLA parking lot. The vision-based Transformer architecture is inherited from Yang et al.; our contribution is a timed, rule-based Parametric Safety Shield (PSS) applied to its control outputs. The PSS uses hand-calibrated speed, position, and duration thresholds to intervene in observed failure modes, including boundary exits, delayed braking, and stalled or oscillatory control. In the reported closed-loop evaluation, 16 held-out target slots and six initial poses are each evaluated in four rounds (384 attempts per configuration). Target success increases from 327/384 (85.16%) for the retrained policy to 375/384 (97.66%) with the PSS; mean position and orientation errors among successful attempts are 0.21m and 0.33 degrees. These results show an improvement within this simulator setup. The repeated attempts share one map, vehicle, and sensor configuration, and the PSS uses simulator world coordinates; thus the results do not establish generalization to other lots or real vehicles, or a formal safety guarantee.

Figures & tables

Panel of Figure 1 — Fig. 1: Complete closed-loop architecture. Blue boxes are inherited from E2E Parking [ 2 ] ; the red box is the hand-designed component introduced here. The PSS uses CARLA world coordinates and vehicle velocity in addition to the nominal command.

Panel of Figure 2 — Fig. 2: Schematic of the inherited E2E Parking nominal policy, adapted from Yang et al. [ 2 ] . Auxiliary depth and segmentation losses are described in the text. The new PSS is shown separately in Fig. 1 .

Fig. 3: Topology of the PSS structured as a finite-state supervisor.

Parameter	Description	Calibrated Value
$v_{\text{limit}}$	Kinematic velocity upper bound	$7.5\ \mathrm{km/h}$
$v_{\text{stall}}$	Low-velocity stall threshold	$2.0\ \mathrm{km/h}$
$\delta_{x}$	Longitudinal alignment tolerance	$0.075\ \mathrm{m}$
$Y_{\text{boundary}}$	Spatial boundary of the parking lot	$-239.4\ \mathrm{m}$
$v_{y,\text{th}}$	Lateral velocity run-off threshold	$-0.01\ \mathrm{km/h}$
$\epsilon_{\text{f}}$	Numerical deadband floating zero	$1\times 10^{-5}$

TABLE I: Parameter Calibration of the PSS

Fig. 4: Top view of the parking lot in CARLA.

Panel of Figure 6 — Fig. 5: (a) Scene with random seed = 11, when target slot is 3-8 with shadow. (b) Scene with random seed = 27, when target slot is 3-8 with shadow. (c) Scene with random seed = 12, when target slot is 3-10 with shadow. (d) Scene with random seed = 28, when target slot is 3-10 with shadow.

Fig. 6: Pareto frontier showcasing the trade-off between TSR and APT under different physical speed limits $v_{\text{limit}}$ .

TaskIdx	TSR (%)	TFR (%)	NTSR (%)	CR (%)	TR (%)	APE (m)	AOE (deg)	APT (s)	AIT (s)
2-1	87.500	4.167	4.167	4.167	0.000	0.199	0.600	21.156	0.077
2-3	95.833	0.000	0.000	0.000	4.167	0.158	0.232	20.126	0.077
2-5	100.000	0.000	0.000	0.000	0.000	0.232	0.206	20.357	0.077
2-7	95.833	0.000	0.000	4.167	0.000	0.247	0.204	21.181	0.077
2-9	100.000	0.000	0.000	0.000	0.000	0.219	0.383	22.443	0.077
2-11	100.000	0.000	0.000	0.000	0.000	0.235	0.416	20.686	0.078

TABLE II: Closed-loop results for the retrained policy with PSS: 384 repeated attempts (

16

slots

\times

6

initial-pose trials

\times

4

rounds) in one CARLA lot.

Panel of Figure 9 — Fig. 7: Visualization of four failure cases.

Fig. 8: Visualization of a corrected trajectory.

Panel of Figure 11 — Fig. 9: BEV features of a timeout case.

Panel of Figure 12 — Fig. 10: BEV features of an outbound case.

Fig. 11: Comparison of abnormal and corrected control signal.

Panel of Figure 14 — Fig. 12: BEV features corrected by rules.

Panel of Figure 15 — Fig. 13: BEV features before collision at target slot 3-9.

Panel of Figure 16 — Fig. 14: BEV features during forced brake at target slot 3-9.

Panel of Figure 17 — Fig. 15: Abnormal BEV features during forced brake at target slot 3-9.

Method	Core decision mechanism	Output and inputs	Reported evaluation scope
ParkingE2E [ 7 ]	Learned target-query Transformer	Future waypoints from surround-view cameras	Four real garages and real-vehicle tests; 87.8% mean parking success under its own protocol
HOPE [ 8 ]	Reinforcement learning plus Reeds–Shepp curves and action masking	Parking path from its planner state representation	Difficulty-stratified parking scenarios and real-world experiments
This work	Inherited E2E Parking Transformer plus hand-coded timed output supervisor	Low-level controls from cameras, target, vehicle state, and CARLA world coordinates	One CARLA lot, one vehicle/sensor setup; 16 slots $\times$ 6 initial poses $\times$ 4 rounds

TABLE III: Methodological comparison with recent peer-reviewed parking work. Published evaluations use different protocols; this table is not a head-to-head performance comparison.

TaskIdx	TSR (%)	TFR (%)	CR (%)	APE (m)	AOE (deg)	APT (s)
E2E Parking [ 2 ] Unreleased Model	91.41	2.08	2.08	0.30	0.87	15.72
E2E Parking [ 2 ] Released Model	75.00	1.56	10.42	0.25	0.63	18.41
Model trained on Gen 2B [ 1 ] (Baseline)	85.16	0.00	2.87	0.24	0.34	22.08
Model trained on Gen 2B [ 1 ] + Rule-based Correction	97.66	0.26	1.04	0.21	0.33	21.34
Original Expert [ 2 ]	100.00	0.00	0.00	0.23	0.48	14.96
New Expert	100.00	0.00	0.00	0.13	0.05	16.95

TABLE IV: Reported policy and expert results for context. Only the two Gen 2B policy rows are the within-study comparison of the PSS.

Fig. 16: Example of a closed-loop failure after target-slot overshoot.

Configuration	TSR (%)	APT (s)
(i) w/o Target Alignment	93.49	21.66
(ii) w/o Speed Limit	91.93	18.07
(iii) w/o Geofencing	89.84	21.54
(iv) Complete PSS	97.66	21.34

TABLE V: PSS component ablations over 384 repeated attempts per configuration in one CARLA lot

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End-to-End Autonomous Driving Autonomous Parking Autonomous Driving Autonomous Driving Planning

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End-to-end autonomous parking has emerged as a critical task within the realm of autonomous driving. However, existing methods suffer from black-box characteristics, lacking high-level semantic understanding and interpretability, which impedes the realization of seamless long-distance autonomous parking from the road to the target spot. To address these limitations, we propose ParkingTransformer, a novel framework that leverages multi-view perception and the scene understanding capability of Large Language Models (LLMs). By combining trajectory queries with LLMs implicit state features, our method interacts directly with historical information and raw sensor data to output planning trajectories, eliminating the need for dense Bird's-View (BEV) representations. To compensate for the inadequate spatial reasoning ability of LLMs, we introduce 3D positional encoding to explicitly inject spatial geometric awareness. Furthermore, a fixed-window streaming mechanism is designed for historical information processing, significantly improving long-term temporal processing efficiency and inference speed. Additionally, a coarse-to-fine decoding strategy is employed to progressively enhance trajectory precision. Extensive closed-loop experiments are conducted on the CARLA simulator and real-world vehicle platforms. The results demonstrate that our method achieves a driving score of 61.32 in CARLA simulator and an average success rate of 88.70% in real-world experiments, validating the feasibility and effectiveness of the proposed algorithms.

Abstract

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