An abstract theory of sensor eventification

TL;DR

The paper develops an abstract theory of sensor eventification, generalizing the notion of event cameras to arbitrary sensors through generalized output simulation modulo relations. It introduces observation variators to model differencing in structured signal spaces and derives conditions under which a derivative of a sensor exists, including NP-hardness results for minimization of the variator. The authors further extend the framework to data acquisition modes via monoidal variators, establishing constructs like the monoid-integrator and collapser/disaggregator to achieve stable, chatter-free derivatives. These contributions provide a formal foundation for designing eventified sensors aligned with robotic tasks, with implications for sensor design, signal processing, and robust perception in dynamic environments.

Abstract

Unlike traditional cameras, event cameras measure changes in light intensity and report differences. This paper examines the conditions necessary for other traditional sensors to admit eventified versions that provide adequate information despite outputting only changes. The requirements depend upon the regularity of the signal space, which we show may depend on several factors including structure arising from the interplay of the robot and its environment, the input-output computation needed to achieve its task, as well as the specific mode of access (synchronous, asynchronous, polled, triggered). Further, there are additional properties of stability (or non-oscillatory behavior) that can be desirable for a system to possess and that we show are also closely related to the preceding notions. This paper contributes theory and algorithms (plus a hardness result) that addresses these considerations while developing several elementary robot examples along the way.

Figures (14)

• Figure 1: A small $F_{\text{rgb}}$, with $Y(F_\text{rgb}) = \{a,b\}$, and $C = \{\text{red},\text{green},\text{blue}\}$.
• Figure 2: An iRobot Create drives down a corridor its wall sensor $w$ generating output values as it proceeds.
• Figure 3: Two describing the scenario in Example \ref{['ex:create-binary-beam']}: (a) A model of the rather trivial transduction of the Create's wall sensor, and (b) its derivative under the observation variator $\set{D_2}$.
• Figure 4: A self-driving car, with on-board sensors to detect whether the vehicle changes to the left or right, or stays at the current lane.
• Figure 5: A Boston Dynamics Minispot quadraped is equipped with a compass to give its heading. To simplify the control challenge, the Minispot is programmed with motion primitives to step forward and backward, and to turn in place by $\pm\ang{45}$ (illustrated on the right).

Theorems & Definitions (46)

• definition 1: setlabelrss
• definition 2: deterministic
• definition 3: direct product
• remark 1
• definition 4: output simulation o2017concise
• definition 5: output simulation modulo a relation
• remark 2
• remark 3
• remark 4
• remark 5