Safety-Filtered Distributed Koopman-MPC

Abstract

Distributed model predictive control (DMPC) often constructs both predictions and collision constraints from neighbor trajectories, so packet loss can remove both. We separate these roles: received trajectories drive Koopman-MPC, while local sensing and shelf geometry define a hard-constrained quadratic program (QP) that projects the applied input. Its radial demand is the least constant acceleration that keeps a supporting-plane clearance nonnegative throughout one zero-order-hold interval. Complementary pair rows recover the coupled demand without exchanging safety decisions. We give an intersample separation theorem under bounded snapshot and directional plant errors, an exact max-min test for simultaneous local feasibility, and a sensing-radius condition for switching interaction graphs. Anticipatory high-order rows may be relaxed for performance, but the finite-hold rows contain no safety slack. Matched eight-robot warehouse simulations use a frozen Koopman model, nonlinear drift, bounded inputs and speed, shelf constraints, a 120 ms control period, and packet dropout. The full controller is collision-free in 20/20 matched trials and reaches 160/160 robot goals; predictive Koopman-MPC without the final projection is collision-free in 1/20 trials. All 38,400 full-method hard-row sets pass the online feasibility test, and every local QP solves. Five-stream fleet sweeps are collision-free and hard-row feasible through 16 robots; the 20-robot boundary fails only after the online margin turns negative, while the reconstructed per-agent critical path remains below the sampling period. Bounded-sensing and differential-drive tests provide additional deployment stress.

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