CaDiS: Canonical Distributional Skill Planning under Physical Resource Interlocks

Deploying generalist robot policies over extended horizons requires managing persistent physical reserves whose saturation clipping and path-dependent consumption break standard unconstrained additive accounting in dynamic programming, causing neural simulators to compound prediction errors and reactive safeguards to trigger too late. We introduce CADIS, a planning framework that decouples deterministic resource algebra from stochastic physical dynamics without modifying frozen foundation policies. CADIS abstracts execution ledgers into an identifiable monoid of canonical capped affine contracts, collapsing multi-stage trajectory feasibility into a single scalar threshold comparison and enabling closed-form downstream demand pull-backs for proactive recovery. A persistent-context generative world model preserves inter-skill physical coupling, while an independent post-selection validation protocol provides provable finite-sample risk certification under the fitted rollout law. Mechanistic evaluations across 3.64 million queries confirm zero-error accounting, alongside rigorous false-acceptance control. On LIBERO-Long manipulation with a frozen π0.5 policy, CADIS achieves 71.6% safe success and curtails interlocks to 0.8%, while threshold sorting delivers a 38.5-fold query speedup. This architecture establishes a principled foundation for deploying unconstrained motor policies under rigid hardware capacity limits.