Latency vs precision: Stability preserving perception scheduling

TL;DR

This work addresses the latency-precision trade-off in robotic perception by modeling the closed-loop as a discrete-time switching system with mode-dependent latencies and noise. It introduces SP$^2$, a stability-preserving scheduling framework that constructs admissible sets of finite-length perception schedules and uses Lyapunov-like gauge functions to guarantee asymptotic stability while balancing a latency-precision cost. A non-conservative admissibility check via a nonlinear program and a subdivision into regular/non-regular points enables offline construction of admissible schedule sets, which can then be leveraged in a dynamic-programming-based optimizer to approach the best possible performance under computational constraints. The approach is demonstrated on a double-integrator and a particle mobile robot, showing reduced cost and CPU load relative to static configurations, and indicating that increasing the number of admissible schedule sets improves performance. Overall, the framework provides a principled way to switch perception modes online while preserving stability and managing resource usage, with potential applicability to varied perception-latency models and networked-control scenarios.

Abstract

In robotic systems, perception latency is a term that refers to the computing time measured from the data acquisition to the moment in which perception output is ready to be used to compute control commands. There is a compromise between perception latency, precision for the overall robotic system, and computational resource usage referred to here as the latency-precision trade-off. In this work, we analyze a robot model given by a linear system, a zero-order hold controller, and measurements taken by several perception mode possibilities with different noise levels. We show that the analysis of this system is reduced to studying an equivalent switching system. Our goal is to schedule perception modes such that stability is attained while optimizing a cost function that models the latency-precision trade-off. Our solution framework comprises three main tools: the construction of perception scheduling policy candidates, admissibility verification for policy candidates, and optimal strategies based on admissible policies.

Figures (3)

• Figure 1: Set $\mathbb{S}_{\Gamma}^\text{$\star$}$ for the set of schedules $\Gamma$ described in Section \ref{['ex:double']} as well as $\mathbb{S}_0$ to show admissibility.
• Figure 2: Resulting histograms for the sample path cost $\mathcal{J}_{\mathsf{sp}}$ for example of Section \ref{['ex:double']} using the balanced $\textsf{\footnotesize SP}^2$ strategy with $m=5,m=10,m=20$ and static schedules $\{1,1,\dots\}, \{2,2,\dots\}$.
• Figure 3: Resulting histograms for the sample path cost $\mathcal{J}_{\mathsf{sp}}$ for the example of Section \ref{['ex:double']} using the balanced $\textsf{\footnotesize SP}^2$ strategy with $m=20$ and static schedules $\{1,1,\dots\}, \{2,2,\dots\}$.