Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Adaptive Self-Calibration for Minimalistic Collective Perception by Imperfect Robot Swarms

Khai Yi Chin, Carlo Pinciroli

TL;DR

Estimation performance by a swarm with correctly known accuracy is superior to that by a swarm unaware of its accuracy, and the ASDF drastically mitigates the damage, even reaching the performance levels of robots aware a priori of their correct accuracy.

Abstract

Collective perception is a fundamental problem in swarm robotics, often cast as best-of-$n$ decision-making. Past studies involve robots with perfect sensing or with small numbers of faulty robots. We previously addressed these limitations by proposing an algorithm, here referred to as Minimalistic Collective Perception (MCP) [arxiv:2209.12858], to reach correct decisions despite the entire swarm having severely damaged sensors. However, this algorithm assumes that sensor accuracy is known, which may be infeasible in reality. In this paper, we eliminate this assumption to (i) investigate the decline of estimation performance and (ii) introduce an Adaptive Sensor Degradation Filter (ASDF) to mitigate the decline. We combine the MCP algorithm and a hypothesis test to enable adaptive self-calibration of robots' assumed sensor accuracy. We validate our approach across several parameters of interest. Our findings show that estimation performance by a swarm with correctly known accuracy is superior to that by a swarm unaware of its accuracy. However, the ASDF drastically mitigates the damage, even reaching the performance levels of robots aware a priori of their correct accuracy.

Adaptive Self-Calibration for Minimalistic Collective Perception by Imperfect Robot Swarms

TL;DR

Estimation performance by a swarm with correctly known accuracy is superior to that by a swarm unaware of its accuracy, and the ASDF drastically mitigates the damage, even reaching the performance levels of robots aware a priori of their correct accuracy.

Abstract

Collective perception is a fundamental problem in swarm robotics, often cast as best-of- decision-making. Past studies involve robots with perfect sensing or with small numbers of faulty robots. We previously addressed these limitations by proposing an algorithm, here referred to as Minimalistic Collective Perception (MCP) [arxiv:2209.12858], to reach correct decisions despite the entire swarm having severely damaged sensors. However, this algorithm assumes that sensor accuracy is known, which may be infeasible in reality. In this paper, we eliminate this assumption to (i) investigate the decline of estimation performance and (ii) introduce an Adaptive Sensor Degradation Filter (ASDF) to mitigate the decline. We combine the MCP algorithm and a hypothesis test to enable adaptive self-calibration of robots' assumed sensor accuracy. We validate our approach across several parameters of interest. Our findings show that estimation performance by a swarm with correctly known accuracy is superior to that by a swarm unaware of its accuracy. However, the ASDF drastically mitigates the damage, even reaching the performance levels of robots aware a priori of their correct accuracy.

Paper Structure

This paper contains 28 sections, 2 theorems, 30 equations, 8 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Minimalistic Collective Perception (MCP)
  5. Adaptive Sensor Degradation Filter (ASDF)
  6. Sensor Accuracy Update
  7. Adaptive Filter Activation
  8. Simulated Experiments
  9. General Setup and Metrics
  10. Setup
  11. Metrics
  12. Factors Affecting Behaviors of Individual Robots
  13. Baseline Performance
  14. Dynamic robots
  15. Fully connected robots
  16. ...and 13 more sections

Key Result

Theorem 1

Let $\hat{\theta}$ denote the MLE of $\theta$. We assume the following regularity conditions on $p(x \mid \theta)$: Then, $\hat{\theta}$ is a consistent and asymptotically efficient estimator of $\theta$. That is, $\sqrt{n}(\hat{\theta} - \theta)$ converges in distribution to a zero-mean Gaussian distributed variable with an asymptotic variance equal to the Cramér-Rao lower bound:

Figures (8)

  • Figure 1: A top-down view of a robotic swarm (orange circles) in a black-and-white tile environment with a focus on the interaction between two robots. Communication links between robots (green lines) are established if neighbors enter the communication range of a robot (red dotted line, drawn for a single robot). The expanded panels show the two robots using the MCP algorithm to perform collective perception (steps 1-3), in which the assumed accuracy information is obtained with the ASDF (step 4).
  • Figure 2: With a constant $n/t$, a higher $\hat{b}$ robot has a local confidence value $>100\times$ greater than that of a lower $\hat{b}$ robot (\ref{['eq:local_confidence']}). Here we assume $\hat{w} = \hat{b}$.
  • Figure 3: Comparison of informed estimation performance across various nominal filtering periods $\tau$ (box colors), where each box represents 30 trial scores, $H$, from \ref{['eq:overall_score']}. Higher $H$ is preferred as it indicates better performance. Scores of experiments with different flawed assumed accuracies $\hat{b}$ are shown (secondary $x$-axis) as deviations from $b$, plotted for each $P$ (primary $x$-axis). At $P = 0\%$, all robots have correct assumed accuracies, hence the absence of a secondary $x$-axis label. The No Filtering data is identical in both (a) and (b). Both sets of scores are computed with $K_{max} = 40000$, $e_{max} = 0.45$.
  • Figure 4: Comparison of informed estimation performance in terms of convergence and accuracy, where each point represents the $h_K$ and $h_e$ scores (from \ref{['eq:consensus_scaling']}) for a single trial. Higher $h_K$ (rightward) and $h_e$ (upward) scores are preferred as they indicate better performance. Both sets of scores are computed with $K_{max} = 40000$, $e_{max} = 0.45$.
  • Figure 5: Comparison of informed estimation performance between fully connected and dynamic robots (box colors), where each box represents 30 trial scores, $H$, from \ref{['eq:overall_score']}. Higher $H$ is preferred as it indicates better performance. Scores of experiments with different flawed assumed accuracies $\hat{b}$ are shown (secondary $x$-axis) as deviations from $b$, plotted for each $P$ (primary $x$-axis). At $P = 0\%$, all robots have correct assumed accuracies, hence the absence of a secondary $x$-axis label. The No Filtering data is identical in both (a) and (b). Both sets of scores are computed with $K_{max} = 40000$, $e_{max} = 0.45$.
  • ...and 3 more figures

Theorems & Definitions (3)

  • Theorem 1: Asymptotic efficiency of MLEs
  • Theorem 2: Continuous mapping theorem
  • proof