PoSafeNet: Safe Learning with Poset-Structured Neural Nets

TL;DR

The paper tackles the challenge of enforcing safety in learning-based robotic controllers when safety constraints are heterogeneous and only partially ordered. It introduces PoSafeNet, a differentiable framework that enforces poset-respecting safety by performing sequential, closed-form halfspace projections corresponding to control barrier function (CBF) constraints, organized into linear extensions of a safety poset. The approach uses a multi-head architecture where each head embodies a linear extension; outputs are combined via convex mixtures or discrete head selection, with safety preserved by construction in hard selections and under certain geometric conditions in mixtures. Empirical results across 2D navigation, constrained manipulation, and vision-based driving demonstrate improved feasibility, robustness, and scalability compared to unstructured safety layers and differentiable QP-based baselines, highlighting the practical benefits of explicit poset-based safety for complex, safety-critical tasks.

Abstract

Safe learning is essential for deploying learningbased controllers in safety-critical robotic systems, yet existing approaches often enforce multiple safety constraints uniformly or via fixed priority orders, leading to infeasibility and brittle behavior. In practice, safety requirements are heterogeneous and admit only partial priority relations, where some constraints are comparable while others are inherently incomparable. We formalize this setting as poset-structured safety, modeling safety constraints as a partially ordered set and treating safety composition as a structural property of the policy class. Building on this formulation, we propose PoSafeNet, a differentiable neural safety layer that enforces safety via sequential closed-form projection under poset-consistent constraint orderings, enabling adaptive selection or mixing of valid safety executions while preserving priority semantics by construction. Experiments on multi-obstacle navigation, constrained robot manipulation, and vision-based autonomous driving demonstrate improved feasibility, robustness, and scalability over unstructured and differentiable quadratic program-based safety layers.

Figures (11)

• Figure 1: Overview of PoSafeNet. A multi-head neural controller enforces safety through sequential projections under multiple poset-consistent constraint orderings, and adaptively combines the resulting safe executions via a soft mixture or a hard selection.
• Figure 2: Task-specific safety posets used in the experiments. Left: unicycle navigation with mutually incomparable obstacle constraints. Middle: manipulator task where joint-limit constraints take precedence over obstacle avoidance. Right: vision-based driving where collision avoidance has higher priority than lane keeping.
• Figure 3: Computational efficiency and scalability of PoSafeNet. (a) Inference cost versus batch size. (b) Training time per step versus number of heads. PoSafeNet scales near-linearly in heads and is significantly faster than QP-based safety layers.
• Figure 4: Trajectories for 2D unicycle multi-obstacle avoidance. Representative closed-loop trajectories in a planar navigation task with three circular obstacles in patches. The dashed black curve denotes the reference trajectory. Unstructured baselines exhibit either conservative detours or safety violations. In contrast, PoSafeNet produces smooth, goal-directed trajectories while maintaining safety throughout the rollout.
• Figure 5: Trajectories for safe robot manipulation under joint-space constraints. Representative end-effector trajectories for a two-link planar manipulator. The dashed black curve denotes the reference trajectory. Unstructured methods exhibit oscillatory or unstable behavior near joint limits. PoSafeNet closely tracks the reference while respecting joint-space safety throughout the rollout.

Theorems & Definitions (8)

• Definition 3.1: Poset-Respecting Safety
• Corollary 4.1: Poset consistency of linear extensions
• proof
• Theorem 4.2: Poset safety under sequential projection and antichain mixing
• Lemma 2.1: Compatibility of CBF halfspaces in control space
• proof
• Theorem 2.2: Poset safety under sequential projection and antichain mixing
• proof