Boundary Approximation and Area Coverage Using Fourier Analysis and Lissajous Curves

In this paper, we discuss the area coverage of a closed and connected region of arbitrary shape using Lissajous curves. We approximate the boundary of the region using Fourier analysis and justify the benefits of doing so compared to other approaches. We then generate coverage paths inside the region using Lissajous curves. The radius of the circular field-of-view of the covering agent is determined analytically, along with the time required to ensure complete coverage of the region. We demonstrate extensions of our solution to problems demanding non-uniform coverage and coverage using multiple agents by splitting up a large region. The effectiveness of our strategy is ascertained by proposing two performance metrics, representing completeness and uniformity.