Protected-Prior Greedy Large-Language-Model-Seeded Grey Wolf Optimization for Low-Budget Legible Motion

Legible robot motion should reveal the intended goal early while remaining collision-free and reasonably short. Under a small function-evaluation budget, however, continuous trajectory search leaves little room to discover intent-expressive motions through optimization alone. Standard population optimizers typically begin with random candidates, which provide numerical diversity but no scene-specific guidance for communicating intent. We evaluate a three-prior protected-greedy design under a shared low function-evaluation budget. We propose Protected-Prior Greedy Large-Language-Model-Seeded Grey Wolf Optimization (PPG-LLM-GWO). One structured large-language-model query returns confusion-aware, early-discrimination, and corridor-handling priors; after deterministic geometry repair, these trajectories occupy the three initial GWO leader roles, and 17 feasible-random trajectories complete the population. Subsequent sweeps protect the entering leaders, update only ordinary wolves, accept only feasibility-first improvements, and re-rank all survivors. We evaluate the method on a 24-map development bank at BFE∈{50,150}, using batch-aligned area under the best-so-far curve (AUC) after population initialization as the primary metric. Against original GWO, the development mean differences are +0.00222 [−0.00076, 0.00508] and +0.01040 [0.00543, 0.01616], respectively. The interval includes zero at BFE=50 but is above zero at BFE=150; PPG-LLM-GWO has the largest batch-aligned mean among the tested population optimizers at both settings. At BFE=50, the paired AUC differences versus PSO, DE, and GA are +0.02621, +0.01529, and +0.03349, respectively, with all three intervals above zero. At BFE=150, the differences are +0.01721, +0.02565, and +0.04954, respectively, and all four intervals, including the comparison with GWO, are above zero. Against a three-prior shared-carrier goal-aware analytic control on the frozen bank, the differences are +0.00509 [0.00004, 0.01197] and +0.00314 [−0.00049, 0.00864]. Secondary seed-first anytime AUC preserves the same mean direction, all reported optimizer comparisons retain 100% final sampled-path feasibility, and three PyBullet scenes confirm collision-free simulation execution. The results support the complete design within the tested scope; they do not isolate gains from the prior combination or protected update individually. Human-observer validation remains future work.