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An Active Perception Game for Robust Information Gathering

Siming He, Yuezhan Tao, Igor Spasojevic, Vijay Kumar, Pratik Chaudhari

TL;DR

Active perception systems rely on estimates of future information gain, which can be misleading in critical tasks; the paper develops an online estimator of the discrepancy between the estimated gain and the true gain by framing active perception as a game between the robot and an adversary, and introduces an improvement function $f(s,r)$ to predict the specific gain $r^*$ from the horizon index $s$ and the observed gain $r$. The estimator is represented as a matrix in $\mathbb{R}^{\Delta t \times b}$ with updates that balance past data and current discrepancy, yielding regret guarantees of $O(T^{3/4})$ for the gain estimation and $O(T^{3/4} + \lambda T + \Delta)$ for the full active perception pipeline under near-optimal path planning. The authors validate the approach through extensive simulations (quadrotor in Habitat-Sim with NeRF maps) and real-world ground-robot experiments across indoor/outdoor environments, showing reductions in estimation error and improvements in PSNR, depth consistency, and object localization. The work provides a general framework for improving active perception with online learning and offers clear directions for future improvements in improvement-function design and regret analysis.

Abstract

Active perception approaches select future viewpoints by using some estimate of the information gain. An inaccurate estimate can be detrimental in critical situations, e.g., locating a person in distress. However the true information gained can only be calculated post hoc, i.e., after the observation is realized. We present an approach to estimate the discrepancy between the estimated information gain (which is the expectation over putative future observations while neglecting correlations among them) and the true information gain. The key idea is to analyze the mathematical relationship between active perception and the estimation error of the information gain in a game-theoretic setting. Using this, we develop an online estimation approach that achieves sub-linear regret (in the number of time-steps) for the estimation of the true information gain and reduces the sub-optimality of active perception systems. We demonstrate our approach for active perception using a comprehensive set of experiments on: (a) different types of environments, including a quadrotor in a photorealistic simulation, real-world robotic data, and real-world experiments with ground robots exploring indoor and outdoor scenes; (b) different types of robotic perception data; and (c) different map representations. On average, our approach reduces information gain estimation errors by 42%, increases the information gain by 7%, PSNR by 5%, and semantic accuracy (measured as the number of objects that are localized correctly) by 6%. In real-world experiments with a Jackal ground robot, our approach demonstrated complex trajectories to explore occluded regions.

An Active Perception Game for Robust Information Gathering

TL;DR

Active perception systems rely on estimates of future information gain, which can be misleading in critical tasks; the paper develops an online estimator of the discrepancy between the estimated gain and the true gain by framing active perception as a game between the robot and an adversary, and introduces an improvement function to predict the specific gain from the horizon index and the observed gain . The estimator is represented as a matrix in with updates that balance past data and current discrepancy, yielding regret guarantees of for the gain estimation and for the full active perception pipeline under near-optimal path planning. The authors validate the approach through extensive simulations (quadrotor in Habitat-Sim with NeRF maps) and real-world ground-robot experiments across indoor/outdoor environments, showing reductions in estimation error and improvements in PSNR, depth consistency, and object localization. The work provides a general framework for improving active perception with online learning and offers clear directions for future improvements in improvement-function design and regret analysis.

Abstract

Active perception approaches select future viewpoints by using some estimate of the information gain. An inaccurate estimate can be detrimental in critical situations, e.g., locating a person in distress. However the true information gained can only be calculated post hoc, i.e., after the observation is realized. We present an approach to estimate the discrepancy between the estimated information gain (which is the expectation over putative future observations while neglecting correlations among them) and the true information gain. The key idea is to analyze the mathematical relationship between active perception and the estimation error of the information gain in a game-theoretic setting. Using this, we develop an online estimation approach that achieves sub-linear regret (in the number of time-steps) for the estimation of the true information gain and reduces the sub-optimality of active perception systems. We demonstrate our approach for active perception using a comprehensive set of experiments on: (a) different types of environments, including a quadrotor in a photorealistic simulation, real-world robotic data, and real-world experiments with ground robots exploring indoor and outdoor scenes; (b) different types of robotic perception data; and (c) different map representations. On average, our approach reduces information gain estimation errors by 42%, increases the information gain by 7%, PSNR by 5%, and semantic accuracy (measured as the number of objects that are localized correctly) by 6%. In real-world experiments with a Jackal ground robot, our approach demonstrated complex trajectories to explore occluded regions.
Paper Structure (22 sections, 7 theorems, 23 equations, 3 figures, 2 tables)

This paper contains 22 sections, 7 theorems, 23 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Problem Formulation
  5. Estimating the specific information gain
  6. Analysis
  7. Bound on regret of online estimation with full feedback
  8. Bound on regret of online estimation with bandit feedback
  9. Regret of active perception
  10. Experimental Validation
  11. Simulation experiments
  12. Setup
  13. Baselines and Metrics
  14. Results
  15. M3ED Dataset
  16. ...and 7 more sections

Key Result

Theorem IV.1

For the "follow the regularized leader" learning rate $\eta_{a} = \beta/\sqrt{\alpha_a}$ in eq:fupdate, the regret is where the robot selects from among $N$ candidate viewpoints at each timestep. The bound on $\rho$ is in worst case $\Delta t b \beta (N\sqrt{T}+1)$.

Figures (3)

  • Figure 1: Comparison of our approach for active perception against a baseline for a quadrotor exploring an indoor environment in a photorealistic simulator. Our approach reduces estimation errors (a), leads to a higher information gain (b), better reconstruction with higher peak signal-to-noise-ratio (PSNR) and lower depth mean square error (MSE) in the learned neural radiance field (NeRF) (c), and leads to an increase the total number of objects that are correctly localized in the scene (d).
  • Figure 2: Viewpoint selection comparison. Given a set of candidate trajectories, our method selects trajectory (b), which leads to an underexplored room, while the baseline selects trajectory (a), which remains within the same room.
  • Figure 3: Reconstructed Occupancy Map and Exploration of Occluded Areas in Real-World Experiment. The robot navigates to occluded areas, highlighted by orange circles, in indoor (a) and outdoor (b) environments.

Theorems & Definitions (8)

  • Theorem IV.1
  • Theorem IV.2
  • Theorem IV.3
  • Theorem IV.4
  • Remark IV.1
  • Lemma VII.1
  • Lemma VII.2
  • Lemma VII.3