Failure-Mode Decomposition

At $N=32$, the shortfall of every planner is dominated by collisions (STLPY 34.4%, single-agent diffusion 27.5%, ours 10.9%), whereas the entire STL violation umbrella stays at or below 6.9% for every method. Joint multi-agent sampling keeps the collision channel roughly $3\times$ below both baselines, which is the source of the gap. At $N\le16$ all methods reach at least 86% success and the residual failures are about spec satisfaction rather than safety.

Setting: Dubins Car environment, mixed heterogeneous specification, where each agent samples one component (sequence, branch, cover, loop, or signal) per episode, with randomized predicate locations. The fixed-goal variant of the same sweep, at goal scale 1.0, is milder (STLPY at $N=32$ reaches 85.9% success with 8.8% collisions), so the collapse at $N=32$ is specific to randomizing predicate locations.

Every agent is attributed to exactly one outcome, so each row of the table below sums to 100%. Attribution is exclusive and follows a priority order: collision first, then resampling exhaustion, then tracking error. No agent carries two labels.

• Success. The agent never collided and its executed trajectory satisfies the specification.
• Collision. The agent collided at any point. Collision claims the agent first, so an agent that collided and later satisfied its specification still counts here, consistent with success being defined as safe and satisfied.
• STL violation. The agent stayed safe but its executed trajectory violates the specification. This is not a sibling of the two channels below, it is their union. It splits further by asking whether the plan was already bad at the moment the planner handed it over.
  • Resampling exhaustion. The reject-and-resample loop hit its iteration cap and delivered a plan that already violated the specification at plan time. This is the planner-side channel.
  • Tracking error. The delivered plan satisfied the specification and execution failed to realize it. This is the controller-side channel.

Resampling exhaustion is a diffusion concept and carries no meaning for STLPY, which has no reject-and-resample loop. The MILP delivers plans that satisfy the specification, so a safe STLPY agent that still violates the specification did so because execution failed to realize a satisfying plan. Its STL violation is therefore entirely tracking error. Either way this does not move the comparison, because STLPY's shortfall is collision (34.4% at $N=32$) and its whole STL violation umbrella is only 6.9%.