Algorithmic Guardrails for Human-Interacting Robots: A Verified Shield and Lexicographic Deference Implementation of the Three Laws of Robotics

Asimov's Three Laws of Robotics are the best-known statement of machine safety, yet they have resisted implementation because their central terms (harm, inaction, human, obedience) are undefined, and because the Laws can conflict with each other and with themselves. This paper reads the Laws as a strictly ordered hierarchy of constraints to be enforced rather than as a reward to be optimized, and gives a buildable architecture that enforces them: a lexicographic decision layer and a budgeted query policy, whose selected command passes through a verified shield before it reaches the actuators. The paper distinguishes the robot (the complete physical system) from the agent (its decision-making component) and states which results depend on physical dynamics. The shield is a robust control-barrier-function filter that accounts for moving humans through an explicit speed bound; we prove that, under stated assumptions on dynamics, human speed, sensing and sampling, the robot is never in motion inside the protective separation distance of any detected human, and that the filter is always feasible because a verified braking command satisfies every barrier constraint. The decision layer enforces the First Law on non-specifiable harm, for every person separately, through a conditional-value-at-risk bound on the predictive harm distribution, evaluates inaction and stopping under the same bound as every other action, applies the Second and Third Laws strictly lexicographically, and falls back to a least-harm rule when no action satisfies the First Law. The query policy ranks questions first by the reduction in harm probability they buy and only then by decision value under a price on human attention; we show by counterexample that the classical value of information can be negative under belief-dependent constraints, which is why the first criterion is required. Human answers enter through a contamination-robust likelihood with a proven per-answer influence bound and can only add, never remove, entities from the set of humans the shield protects. We derive a five-term residual-risk bound. Finally, we prove that a complete implementation of the Laws is impossible in an open world (the First Law can be unsatisfiable, unbounded inaction-harm prediction is undecidable, and "human" has no formal specification), and we show what is achievable instead: completeness relative to a declared specification for specifiable harm, and an explicit, measurable gap for everything else.