The Architectural Blind Spot

In robot formations controlled by inter-agent distances, there exist configurations where an actuator signal is perfectly blocked from reaching a sensor — not by noise, not by failure, but by the mathematics of the formation itself.

Goldgraber Casspi and Zelazo (arXiv:2603.15993) call these transmission zeros: points where rigid-body and deformational modes interfere destructively at measured outputs. The surprising result is not that they exist — transmission zeros are common in linear systems — but that their geometry depends on the formation’s rigidity class.

For flexible frameworks, the blocking condition is non-generic. It requires fine-tuned configurations that occupy a measure-zero set — vanishingly unlikely in practice. But for infinitesimally rigid formations, the condition collapses onto an explicit affine hyperplane: a “spatial locus of transmission zeros” that carves out a well-defined region where sensors are architecturally blind.

The authors construct a convex polytope — the “global transmission polygon” — that maps exactly where the blindness lives. Place a sensor inside this polytope, and it will miss signals regardless of how strong they are.

This inverts the usual thinking about formation design. The standard concern is sensing quality: resolution, noise floor, dynamic range. But before any of those matter, there’s a geometric question: can the formation’s own structure carry the signal from here to there? The formation is not just the medium through which information flows. It is also the filter that selectively blocks it.

The blindness is not a bug of a particular sensor or a particular signal strength. It is architectural — built into the geometry of the formation as surely as the distances between agents. Move the formation and the blind spot moves with it, predictably, along that affine hyperplane.

This is the same structure as a bridge resonance, an acoustic dead spot in a concert hall, or a node on a vibrating string. The medium that transmits the signal is also the medium that can cancel it. The formation knows where it cannot see.