Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A modified Bellman-Ford Algorithm for Application in Symbolic Optimal Control and Plan and Goal Recognition

Marcus Kreuzer, Alexander Weber, Alexander Knoll

TL;DR

This work tackles the computation of value functions for symbolic optimal control on hyper-graphs by introducing a modified generalized Bellman-Ford algorithm that reduces per-iteration node processing. It also integrates Plan and Goal Recognition (PGRM) with model-based online simulation to eliminate the need for an initial task-allocation guess in UAV missions, enabling dynamic trajectory and subtask prediction. Empirical results show substantial reductions in processed nodes per iteration without sacrificing overall run-time performance, and the UAV firefighting scenario demonstrates robustness to positional uncertainty and near-identical trajectory hypotheses. Together, the contributions advance autonomous, robust control and monitoring in cyber-physical UAV systems with improved scalability and resilience to uncertainty.

Abstract

The contributions of this short technical note are two-fold. Firstly, we introduce a modified version of a generalized Bellman-Ford algorithm calculating the value function of optimal control problems defined on hyper-graphs. Those Bellman-Ford algorithms can be used in particular for the synthesis of near-optimal controllers by the principle of symbolic control. Our modification causes less nodes of the hyper-graph being iterated during the execution compared to our initial version of the algorithm published in 2020. Our second contribution lies in the field of Plan recognition applied to drone missions driven by symbolic controllers. We address and resolve the Plan and Goal Recognition monitor's dependence on a pre-defined initial guess for a drone's task allocation and mission execution. To validate the enhanced implementation, we use a more challenging scenario for UAV-based aerial firefighting, demonstrating the practical applicability and robustness of the system architecture.

A modified Bellman-Ford Algorithm for Application in Symbolic Optimal Control and Plan and Goal Recognition

TL;DR

This work tackles the computation of value functions for symbolic optimal control on hyper-graphs by introducing a modified generalized Bellman-Ford algorithm that reduces per-iteration node processing. It also integrates Plan and Goal Recognition (PGRM) with model-based online simulation to eliminate the need for an initial task-allocation guess in UAV missions, enabling dynamic trajectory and subtask prediction. Empirical results show substantial reductions in processed nodes per iteration without sacrificing overall run-time performance, and the UAV firefighting scenario demonstrates robustness to positional uncertainty and near-identical trajectory hypotheses. Together, the contributions advance autonomous, robust control and monitoring in cyber-physical UAV systems with improved scalability and resilience to uncertainty.

Abstract

The contributions of this short technical note are two-fold. Firstly, we introduce a modified version of a generalized Bellman-Ford algorithm calculating the value function of optimal control problems defined on hyper-graphs. Those Bellman-Ford algorithms can be used in particular for the synthesis of near-optimal controllers by the principle of symbolic control. Our modification causes less nodes of the hyper-graph being iterated during the execution compared to our initial version of the algorithm published in 2020. Our second contribution lies in the field of Plan recognition applied to drone missions driven by symbolic controllers. We address and resolve the Plan and Goal Recognition monitor's dependence on a pre-defined initial guess for a drone's task allocation and mission execution. To validate the enhanced implementation, we use a more challenging scenario for UAV-based aerial firefighting, demonstrating the practical applicability and robustness of the system architecture.

Paper Structure

This paper contains 8 sections, 10 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. The definition of Plant and Optimal Control Problem
  3. The modified Algorithm
  4. Experimental evaluation
  5. Application to Mission Monitoring
  6. Plan Recognition for prediction of trajectory and mission (sub-)tasks
  7. Multi-UAV firefighting scenario
  8. Conclusions from the new scenario

Figures (2)

  • Figure 1: Timeline for mission execution of U1 and the PGRM's processes to monitor correct trajectory alignment and (sub-)task assignment. Qualitative illustration of sequences including reference to figures.
  • Figure 2: Mission execution shown in scenes.