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ASPIRe: An Informative Trajectory Planner with Mutual Information Approximation for Target Search and Tracking

Kangjie Zhou, Pengying Wu, Yao Su, Han Gao, Ji Ma, Hangxin Liu, Chang Liu

TL;DR

This paper develops a novel sigma point-based approximation to accurately estimate mutual information (MI) for general, non-Gaussian distributions utilizing particle representation of the belief state, while simultaneously maintaining high computational efficiency.

Abstract

This paper proposes an informative trajectory planning approach, namely, \textit{adaptive particle filter tree with sigma point-based mutual information reward approximation} (ASPIRe), for mobile target search and tracking (SAT) in cluttered environments with limited sensing field of view. We develop a novel sigma point-based approximation to accurately estimate mutual information (MI) for general, non-Gaussian distributions utilizing particle representation of the belief state, while simultaneously maintaining high computational efficiency. Building upon the MI approximation, we develop the Adaptive Particle Filter Tree (APFT) approach with MI as the reward, which features belief state tree nodes for informative trajectory planning in continuous state and measurement spaces. An adaptive criterion is proposed in APFT to adjust the planning horizon based on the expected information gain. Simulations and physical experiments demonstrate that ASPIRe achieves real-time computation and outperforms benchmark methods in terms of both search efficiency and estimation accuracy.

ASPIRe: An Informative Trajectory Planner with Mutual Information Approximation for Target Search and Tracking

TL;DR

This paper develops a novel sigma point-based approximation to accurately estimate mutual information (MI) for general, non-Gaussian distributions utilizing particle representation of the belief state, while simultaneously maintaining high computational efficiency.

Abstract

This paper proposes an informative trajectory planning approach, namely, \textit{adaptive particle filter tree with sigma point-based mutual information reward approximation} (ASPIRe), for mobile target search and tracking (SAT) in cluttered environments with limited sensing field of view. We develop a novel sigma point-based approximation to accurately estimate mutual information (MI) for general, non-Gaussian distributions utilizing particle representation of the belief state, while simultaneously maintaining high computational efficiency. Building upon the MI approximation, we develop the Adaptive Particle Filter Tree (APFT) approach with MI as the reward, which features belief state tree nodes for informative trajectory planning in continuous state and measurement spaces. An adaptive criterion is proposed in APFT to adjust the planning horizon based on the expected information gain. Simulations and physical experiments demonstrate that ASPIRe achieves real-time computation and outperforms benchmark methods in terms of both search efficiency and estimation accuracy.
Paper Structure (17 sections, 19 equations, 4 figures, 2 tables, 2 algorithms)

This paper contains 17 sections, 19 equations, 4 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. System Models
  4. Belief MDP Formulation with Particle Filter
  5. Sigma Point-Based Mutual Information Approximation
  6. Reward Function Definition
  7. Sigma Point-Based Entropy Approximation
  8. Adaptive Particle Filter Tree for Planning
  9. Algorithm Overview
  10. Adaptive Criterion for Efficient Tree Search
  11. Simulation
  12. Approximation Accuracy and Efficiency
  13. Benchmark Comparisons
  14. Unimodal Case
  15. Multimodal Case
  16. ...and 2 more sections

Figures (4)

  • Figure 1: (a) Comparison of different planning methods in mobile target SAT with prior uncertainty (green particles show the initial target state distribution). Suffering from the myopic horizon, the next-best-view method tends to randomly explore the environment. Although the sampling-based method can make long-term planning, ASPIRe generates a smoother and shorter trajectory. (b) ASPIRe combines SP-based MI approximation with an adaptive planning horizon instead of a fixed one in the policy tree, enabling the maintenance of abundant particles for precise distribution representation, accurate reward approximation, and efficient planning.
  • Figure 2: Quantitative comparisons in the unimodal (left column) and multimodal case (right column). NBV-ASPIRe and IIG-ASPIRe in the first row represent the difference in search time using the NBV strategy and IIG-tree, respectively, compared to ASPIRe.
  • Figure 3: Qualitative comparisons in the unimodal case (top row) and multimodal case (bottom row). (a) Initialization. (b) The NBV policy. (c) IIG-tree. (d) ASPIRe. The blue circle represents the moment when the target is detected. ASPIRe shows shorter search time and more stable tracking performance with smoother trajectories, even under distracting prior information.
  • Figure 4: Indoor experiments with inaccurate prior information. The red circle and green star show the current positions of the robot and the target, and the squares represent their starting positions.