Continuous curvature wayline generation using quadratic optimisation for agricultural machine guidance

Abstract

Navigation systems are widely used in precision agriculture to improve efficiencies and yields. These systems guide agricultural machines to follow waylines calculated based on specific traffic patterns, including straight and curved waylines. While generating straight waylines is relatively straightforward, generating curved waylines presents challenges due to the variation in their shape and curvature during propagation, which can lead to skips and overlaps between adjacent waylines.In this paper, we present a novel method to curved wayline generation by formulating the problem as a non-linear optimisation problem, as opposed to using geometry operations like existing methods. With the designed objective function and constraints, the problem is reduced to a quadratic optimisation problem that can be efficiently solved, and the generated waylines satisfy the curvature constraint, while minimising skips and overlaps. The functionality and applicability of the method were demonstrated with a simulation experiment, the comparison tests with geometric methods, and a field test. Our algorithm achieved coverage over 97%, with overlap and skip rates lower than 0.8% and 2.3%, respectively. The results indicate that our algorithm can generate smooth, continuous curvature waylines with high coverage and low skip/overlap. Furthermore, our algorithm can also generate straight waylines when the input reference line is a straight AB line. This algorithm can be used as a wayline planning component of navigation system for agricultural machines and robots. The code and boundary data utilised in the "Results and Discussion" section are accessible online at https://github.com/prefect-of-gryffindor/curve-wayline-generation.