On the Application of Model Predictive Control to a Weighted Coverage Path Planning Problem

TL;DR

This work tackles static Weighted Coverage Path Planning by formulating it as a Model Predictive Control problem with Coverage Constraints that enforce one-time reward collection in a continuous space. A Gaussian Mixture Model–based heuristic identifies key reward-rich points to initialize the solver via a TSP tour, which markedly improves MPC performance over a naive setup. The approach is demonstrated on UAV/SAR-like scenarios, showing that CCs and smart initialization yield higher rewards with manageable computation time, validating the method's practical viability. The study highlights potential future integration of initialization steps into a single optimal-control formulation and exploration of alternative CCs and MPC variants.

Abstract

This paper considers the application of Model Predictive Control (MPC) to a weighted coverage path planning (WCPP) problem. The problem appears in a wide range of practical applications, including search and rescue (SAR) missions. The basic setup is that one (or multiple) agents can move around a given search space and collect rewards from a given spatial distribution. Unlike an artificial potential field, each reward can only be collected once. In contrast to a Traveling Salesman Problem (TSP), the agent moves in a continuous space. Moreover, he is not obliged to cover all locations and/or may return to previously visited locations. The WCPP problem is tackled by a new Model Predictive Control (MPC) formulation with so-called Coverage Constraints (CCs). It is shown that the solution becomes more effective if the solver is initialized with a TSP-based heuristic. With and without this initialization, the proposed MPC approach clearly outperforms a naive MPC formulation, as demonstrated in a small simulation study.

Figures (5)

• Figure 1: Solution of the MPC for the same scenario as in Figure \ref{['fig:results:1']}, but without an initial guess.
• Figure 2: Key points found using Gaussian mixtures with $n=20$ ($m=10$) and $n=40$ ($m=20$) components respectively.
• Figure 3: A travelling salesman tour through all key points (orange), starting from the initial position $x_{0}$ (red). The tour also ends in $x_{0}$, which is ommitted here.
• Figure 4: The resulting open-loop trajectory of the MPC controller based on the initial solution obtained from the tour in Figure \ref{['fig:tour']}.
• Figure 5: Results for three different scenarios, with increased horizon length on the right side. The red marker denotes the initial position of the UAV.