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

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.