The Law of Task-Achieving Body Motion: Axiomatizing Success of Robot Manipulation Actions

Autonomous agents that perform everyday manipulation actions need to ensure that their body motions are semantically correct with respect to a task request, causally effective within their environment, and feasible for their embodiment. In order to enable robots to verify these properties, we introduce the Law of Task-Achieving Body Motion as an axiomatic correctness specification for body motions. To that end we introduce scoped Task-Environment-Embodiment (TEE) classes that represent world states as Semantic Digital Twins (SDTs) and define applicable physics models to decompose task achievement into three predicates: SatisfiesRequest for semantic request satisfaction over SDT state evolution; Causes for causal sufficiency under the scoped physics model; and CanPerform for safety and feasibility verification at the embodiment level. This decomposition yields a reusable, implementation-independent interface that supports motion synthesis and the verification of given body motions. It also supports typed failure diagnosis (semantic, causal, embodiment and out-of-scope), feasibility across robots and environments, and counterfactual reasoning about robot body motions. We demonstrate the usability of the law in practice by instantiating it for articulated container manipulation in kitchen environments on three contrasting mobile manipulation platforms