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Online Trajectory Optimization for Persistent Monitoring Problems in Partitioned Environments

Jonas Hall, Christos G. Cassandras, Sean B. Andersson

TL;DR

The paper addresses persistent monitoring of multiple targets in partitioned environments with region-dependent hybrid dynamics, and formalizes the problem with a Kalman-Bucy covariance model and a periodic average cost $J = \frac{1}{T} \int_0^T \sum_{i=1}^M \mathrm{tr}(\Omega_i(t)) \; dt$. It proposes a two-stage approach: an offline RRBT-based global planner to determine a target visiting sequence, and an online trajectory optimization framework to realize that sequence via locally optimized monitoring and switching segments, with cost decomposed into local terms. A bilevel optimization is developed to minimize the average steady-state estimation error by jointly tuning monitoring durations and trajectory parameters, leveraging duality-based gradients and two online update schemes. Numerical experiments on partitioned environments demonstrate convergence to efficient loops and scalability to larger problem instances, validating the practical viability of the approach.

Abstract

We consider the problem of using an autonomous agent to persistently monitor a collection of dynamic targets distributed in an environment. We generalize existing work by allowing the agent's dynamics to vary throughout the environment, leading to a hybrid dynamical system. This introduces an additional layer of complexity towards the planning portion of the problem: we must not only identify in which order to visit the points of interest, but also in which order to traverse the regions. We design an offline high-level sequence planner together with an online trajectory optimizer realizing the computed visiting sequence. We provide numerical experiments to illustrate the performance of our approach.

Online Trajectory Optimization for Persistent Monitoring Problems in Partitioned Environments

TL;DR

The paper addresses persistent monitoring of multiple targets in partitioned environments with region-dependent hybrid dynamics, and formalizes the problem with a Kalman-Bucy covariance model and a periodic average cost . It proposes a two-stage approach: an offline RRBT-based global planner to determine a target visiting sequence, and an online trajectory optimization framework to realize that sequence via locally optimized monitoring and switching segments, with cost decomposed into local terms. A bilevel optimization is developed to minimize the average steady-state estimation error by jointly tuning monitoring durations and trajectory parameters, leveraging duality-based gradients and two online update schemes. Numerical experiments on partitioned environments demonstrate convergence to efficient loops and scalability to larger problem instances, validating the practical viability of the approach.

Abstract

We consider the problem of using an autonomous agent to persistently monitor a collection of dynamic targets distributed in an environment. We generalize existing work by allowing the agent's dynamics to vary throughout the environment, leading to a hybrid dynamical system. This introduces an additional layer of complexity towards the planning portion of the problem: we must not only identify in which order to visit the points of interest, but also in which order to traverse the regions. We design an offline high-level sequence planner together with an online trajectory optimizer realizing the computed visiting sequence. We provide numerical experiments to illustrate the performance of our approach.
Paper Structure (13 sections, 1 theorem, 23 equations, 6 figures, 1 algorithm)

This paper contains 13 sections, 1 theorem, 23 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Trajectory Decomposition
  4. The Target Visiting Sequence
  5. The Monitoring Trajectories
  6. The Switching Trajectories
  7. The Monitoring Durations
  8. The Switching Points
  9. Global Planning
  10. Optimizing the Average Steady-State Cost
  11. Numerical Results
  12. Conclusion and Future Work
  13. Proof of Thm \ref{['thm:probabilistic:optimality:convergence']}

Key Result

Theorem 1

Let us assume that Then, for any $\varepsilon > 0$, it holds

Figures (6)

  • Figure 1: An example of a partitioned environment with four targets and ten regions. The left plot shows the initial trajectory, the optimal trajectory, and the TSP solution. The right plot illustrates the decomposition.
  • Figure 2: Illustration of global paths (blue) generated via the rrbt algorithm for one root node (red).
  • Figure 3: Illustration of travel duration from each location to the root node (red) using the rrbt algorithm.
  • Figure 4: Illustrating the requirement of Assumption \ref{['assumption:prob:completeness:finite:number:switching:points']}.
  • Figure 5: Optimizing the monitoring durations $\tau$ utilizing both variant \ref{['item:opti:variant:1']} (yellow, vertical lines indicate steady-state) and \ref{['item:opti:variant:2']} (blue). The first plot shows the cost per loop, and the second plot shows the evolution of $\tau_1$.
  • ...and 1 more figures

Theorems & Definitions (10)

  • Theorem 1
  • Remark 1: Interpretation of Assumption \ref{['assumption:prob:completeness:finite:number:switching:points']}
  • Remark 2: Interpretation of Assumption \ref{['assumption:prob:completeness:lipschitz']}
  • proof
  • Claim 1
  • proof
  • Claim 2
  • proof
  • Claim 3
  • proof