Closed-form Action Projection for Constrained World Model Planning in Robotics

Physical control systems face hard constraints at every manipulation step, such as strict bounds on contact force and velocity. However, existing reward-driven reinforcement learning struggles to enforce these limits. This challenge is compounded in practice because constraint satisfaction depends not only on the high-level predicted action, but also on the low-level controller's live state during execution. To bridge this gap, we introduce CAP (Closed-form Action Projection), a modular layer that imposes hard, state-dependent action constraints on learned policies and world-model planners. At each control step, CAP derives an admissible action set in closed form from the live controller state and projects the proposed action onto it without any online optimization or a learned constraint model, provably guaranteeing constraint satisfaction. To resolve the geometric ambiguity inherent in pure proprioception, we integrate a world model that processes environmental observations, such as wrist depth, during impedance control. Evaluations on three representative contact-rich manufacturing tasks, peg insertion, gear meshing and nut threading, demonstrate that CAP strictly prevents force limit violations at every step while maintaining high task success rates, achieving significant improvement against the state-of-the-art neural baselines.