CoPark: Learning Reactive Parking via Self-Play

arXiv:2606.04149 · cs.RO · Submitted 2026-06-02 · Read on arXiv

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Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: I'm Rosa, and with me are Dev and Taro, guest researcher.

Dev: Today's paper: "CoPark: Learning Reactive Parking via Self-Play".

Rosa: The gist Learning a single policy that reaches a goal with high geometric precision while interacting safely with nearby agents poses conflicting objectivesCoPark,

Dev: First, who's behind it and why it matters.

Paper summary: Rosa: So we've been talking about CoPark today, which is this self-play method for reactive parking that aims to balance high geometric precision with staying safe around other cars <ref:2606.04149#pg1>.

Dev: Yeah, the paper is titled "CoPark: Learning Reactive Parking via Self-Play," and the authors are focusing on this residual-policy architecture, which basically splits the task into a fixed plan and some reactive corrections <ref:2606.04149#pg1>.

Taro: What they're really doing is using that offline plan as a starting point and then having a residual head learn how to fix things when another car gets in your way, which they call partner threat modulation <ref:2606.04149#pg1>.

Rosa: It seems like the main goal here is to show that you can teach an AI both how to follow a precise path and how to react in real-time without them fighting each other <ref:2606.04149#pg2>.

Dev: And the results they got, achieving about seventy to eighty five percent success with low collision rates, are pretty compelling when you look at what they’re comparing it to <ref:2606.04149#pg1>.

Taro: The emergent behaviors they found, like reverse-yielding and mid-maneuver yielding, show that the AI isn't just following a script; it's actually learning these ways to interact dynamically <ref:2606.04149#pg1>.

Rosa: So for someone just listening here, the big picture is that this approach gives us a way to build systems that can be both incredibly accurate and surprisingly good at handling messy, real-world interactions like parking lots <ref:2606.04149#pg2>.

Dev: It's interesting because it suggests we can design architectures where the constraints of geometry and the constraints of social interaction are handled by separate parts of the system <ref:2606.04149#pg1>.

Taro: That separation is what makes it work, because you anchor one channel for precision while letting another channel handle the real-time adjustments needed when things go wrong <ref:2606.04149#pg1>.

Rosa: Exactly, so it's about structuring the learning process to handle those conflicting demands simultaneously <ref:2606.04149#pg2>.

Dev: And they did show some ablation insights that prove this design is working, like how adding that kinematic prior sharpens precision and lifts success rates by about eighteen points <ref:two thousand six hundred six point zero four one four nine#pg1.

Taro: Yeah, and they showed that the way they release the longitudinal channel—the speed control channel—while keeping the lateral channel locked onto that precomputed reference is what keeps collisions down to three point nine percent <ref:two thousand six hundred six point zero four one four nine#pg1.

Rosa: So CoPark is a specific method for reactive parking that uses a residual policy and channel-asymmetric prior release to achieve high success rates with emergent yielding behaviors <ref:2606.04149#pg1>. It’s about learning how to be precise while still being safe when things intrude.

Dev: That’s the gist of what they did here on this paper, CoPark: Learning Reactive Parking via Self-Play. The authors are proposing a method to solve the conflict between geometric precision and safety during multi-agent interactions in autonomous parking <ref:2606.04149#pg1>.

Taro: It’s important because it shows that self-play can generate robust, emergent interaction behaviors like reverse-yielding and queuing in these complex scenarios, which is something existing paradigms haven't addressed well <ref:2606.04149#pg3>.

Rosa: Ultimately, CoPark suggests that by separating the learning of the fixed geometry from the learning of the reactive corrections through a residual head, you can get high precision while still being responsive to dynamic situations in autonomous driving tasks <ref:2606.04149#pg1>.

Conclusion: Rosa: So we're wrapping up this discussion on CoPark today, which is this self-play method for reactive parking that aims to balance high geometric precision with staying safe around other cars <ref:2606.04149#pg1>.

Dev: Yeah, the paper you're looking at is titled "CoPark: Learning Reactive Parking via Self-Play," and the authors are focusing on this residual-policy architecture that splits the task into a fixed plan and some reactive corrections <ref:2606.04149#pg1>.

Rosa: It seems like the main goal here is to show that you can teach an AI both how to follow a precise path and how to react in real-time without them fighting each other <ref:2606.04149#pg2>.

Dev: And the results they got, achieving about seventy to eighty five percent success with low collision rates, are pretty compelling when you look at what they're comparing it to <ref:2606.04149#pg1>.

Rosa: Exactly, so it's about structuring the learning process to handle those conflicting demands simultaneously <ref:2606.04149#pg2>.

Dev: They also show some ablation insights proving this design works, like how adding that kinematic prior sharpens precision and lifts success rates by about eighteen points <ref:two thousand six hundred six point zero four one four nine#pg1.

Rosa: So it boils down to this CoPark method, which uses a residual policy and asymmetric prior release to get high success rates with emergent yielding behaviors <ref:2606.04149#pg1>. It’s about learning how to be precise while still being safe when things intrude.

Dev: And the limitation they pointed out is that while the lateral alignment is protected from partner noise, the longitudinal channel still depends on it for its reference, which is a trade-off they have to manage <ref:two thousand six hundred six point zero four one four nine#pg1.

Taro: That’s a good point because it shows where the system might still struggle if the conditions get too noisy or if those channels aren't perfectly balanced <ref:two thousand six hundred six point zero four one four nine#pg3.

Department of Computer Science, University of Freiburg, Germany · CARIAD SE, Germany · Technical University of Munich, Germany

cs.RO

Submitted: 2026-06-02

Updated: 2026-10-14

Code: https://github.com/Emerge-Lab/PufferDrive

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 89/100

The gist: The gist Learning a single policy that reaches a goal with high geometric precision while interacting safely with nearby agents poses conflicting objectivesCoPark, a self-play RL approach that learns

Key concepts

Residual-Policy Architecture: This architecture splits the learning task into two parts: a fixed prior and a reactive head. A precomputed offline plan provides a stable starting point, while the residual head learns only the necessary small corrections to achieve precision and react to dynamic changes during interaction.
Partner-Threat-Modulated Prior Release: This mechanism controls how much the policy relies on its fixed plan. A continuous threat signal shifts authority to the 'longitudinal' channel, enabling yielding behaviors when a partner is close, while keeping the 'lateral' channel fixed to maintain accurate slot alignment.
Closed-Loop Terminal Refinement: This final layer corrects small errors that remain after the main maneuver is planned. It uses a reward based on the distance to the target slot frame and vehicle velocity to fine-tune terminal accuracy, ensuring sub-meter precision even after the initial path is followed.

Terminology

Accuracy — 1× in this paper · explained in 1 episode
Alignment — 1× in this paper
Benchmark — 1× in this paper · explained in 2 episodes

Summary

The gist Learning a single policy that reaches a goal with high geometric precision while interacting safely with nearby agents poses conflicting objectivesCoPark, a self-play RL approach that learns reactive parking through multi-agent self-play, built on a residual-policy architectureThis approach resolves the challenge of reconciling precision and reactivity within one policy by using an offline plan as a fixed action prior and a residual head to learn reactive correctionsCoPark achieves ∼70–85% success with only 3–6% collision rate, substantially outperforming classical, imitation-learning, and large-scale RL baselinesThe results demonstrate emergent interaction behaviors such as reverse-yielding, mid-maneuver yielding, tight-corridor passing, and queuing

Problem Formulation

Reactive parking is formulated as a general-sum partially observable stochastic game (POSG) where multiple vehicles must reach assigned slots while remaining responsive to neighborsThe setting involves a parking lot L = (D,P, Oobs, G) with drivable region D and slot poses P = pm for each vehicleEach agent i takes a discrete action ai from an acceleration–steering grid and receives a partial observation oi of its state and the relative state of its K nearest neighbors (K=8)Success is defined when the Euclidean slot-frame distance e slot i,t squared ≤ ∆d for Ks consecutive stepsThe objective is to maximize the joint task distribution over parking lots, initial states, and slot assignments

CoPark Architecture

CoPark utilizes a residual-policy architecture where a precomputed offline plan provides a fixed action priorA residual head learns the reactive corrections to this priorThe key design is a partner-threat-modulated, channel-asymmetric release of the priorThis decomposition separates geometric consistency from interactionA closed-loop refinement layer corrects residual terminal error from action-grid discretization

Key Mechanisms

The core mechanism involves several interconnected components designed to handle precision and reactivity simultaneously

Offline Kinematic Prior: This is supplied by a Hybrid A∗ search with a Reeds–Shepp analytic shot, yielding a navigation route and maneuvering trajectoryThis prior is engaged only during the parking maneuver phase
Residual Policy with Prior Injection: A single parameter-sharing categorical policy acts at every step, with the offline prior engaged only during the parking maneuverThe prior is added to the policy logits via a channel-wise log-prior
Reactive Yielding under Partner Threat: The partner-threat signal modulates imitation reward and asymmetrically releases the longitudinal prior while anchoring the lateral channelThe partner-threat signal is aggregated by combining the rectified closing rate [− ˙dij]+ with an exponentially decaying range envelope
Closed-Loop Terminal Refinement: This layer continues acting beyond plan completion, using a reward toward the slot frame to correct residual terminal errorThe refinement reward is defined as r ref i,t = βred η tanh(e slot i,t-1 squared − e slot i,t 2)/η + βhold if e slot i,t ∈ Etol and vi,t ≤ ∆v

Evaluation and Results

CoPark was trained on six parking lots and evaluated zero-shot on the reactive-parking benchmark spanning Dragon Lake Parking (DLP) and DeepScenario Open 3D (DSC3D)CoPark achieves ∼70–85% success with only 3–6% collision rate, substantially outperforming classical, imitation-learning, and large-scale RL baselinesEmergent interaction behaviors such as reverse-yielding, mid-maneuver yielding, tight-corridor passing, and queuing were demonstratedIn the zero-shot benchmark results on DLP and DSC3D under both partner reaction modes, CoPark leads on SR (84.7 % / 79.7 % / 75.8 % / 69.8 %) across two datasetsCoPark is the only method reaching 0 % off-road in all conditionsThe results confirm that CoPark’s self-play training transfers to interactions with learned partners, not only to scripted onesThe channel-asymmetric prior release of Eq. 7 therefore confers an additional robustness property by construction

Ablation Insights

Cumulative components analysis showed that adding the offline kinematic prior sharpens terminal precision and lifts SR by roughly 18 pointsAdding asymmetric reliance then releases the longitudinal channel while anchoring the lateral one, returning collisions to baseline (3.9%) and lifting SR another ∼ten pointsClosed-loop refinement recovers precision and pushes SR to its 84.7% peak, with a small uptick in collisions from grazing neighbors mid-correctionThe asymmetric span of the training distribution shows that wc caps at 2.0 while wg caps at 2.0, equipping the policy with a wider safety-side margin than throughput-side marginThe degradation in success rate when replacing the stratified schedule with a uniform mixed-density distribution drops final SR on DLP-Reactive by approximately 14.5 pointsCoPark’s V–V and V–Stat split is roughly balanced (2.4% and 1.7%), confirming the design intent of the asymmetric prior releaseThe degradation in SR when tightening success criteria steepens at (0.4 m, 6◦) where the criterion bisects the terminal-error distributionThe degradation is graceful and asymmetric across the two collision channels, with V–V collisions rising from 2.4% to 5.6% as noise level climbsThe lateral slot-frame alignment is shielded from partner-perception noise even though the longitudinal channel relies on itCoPark’s distributions sit within one standard deviation of the human demonstrations on both datasets (∆Path ≤ 1.4 m, ∆Manv ≤ 0.1)The CoPark-partner row uses the same trained checkpoint as the ego on every non-ego vehicle, and collisions fall from 4.1% (IDM) to 3.6% thanks to two-sided yieldingThe training-mean default (wg, wc) = (1.25, 1.

Improvements for AI systems

Confidence in geometric grounding via an inexpensive offline plan to stabilize precision learning, as stated: To supply precision without bottlenecking self-play, an inexpensive offline plan, a Stanley tracker over a Hybrid A∗ path computed once per instance, enters the action logits as a fixed prior. This allows the policy to focus on reactive interaction rather than struggling with curricula even in the single-agent case for geometric accuracy.
Adaptive prior modulation to balance precision and reactivity, utilizing: The key design is a partner-threat-modulated, channel-asymmetric release of the prior, which enables yielding while anchoring the lateral channel: The continuous threat signal shifts authority of the longitudinal channel to the residual head to enable yielding, while the lateral channel remains anchored to the precomputed reference.
Emergent multi-agent interaction capabilities, specifically reverse-yielding, mid-maneuver yielding, and tight-corridor passing, allowing agents to exhibit sophisticated yielding behaviors without explicit behavior-specific rewards: The four behaviors in Fig. 3 arise under self-play without behavior-specific rewards, and split by the phase in which interaction occurs.
Robustness against perception errors through asymmetric channel reliance, as demonstrated by: The channel-asymmetric prior release of Eq. 7 therefore confers an additional robustness property by construction, ensuring that the lateral slot-frame alignment is shielded from partner-perception noise even though the longitudinal channel relies on it.
Deployment knob for operational style control, allowing inference time steering between safety and throughput: The single checkpoint covers an operational range from cautious-and-precise (75.3% SR at 2.0% Coll) to aggressive-and-fast (89.1% SR at 8.7% Coll) without any retraining.