The work considers the problem of planning and optimizing the trajectory of a mobile 2D robot processing a flat area limited by arbitrary closed boundaries. The desired trajectory must be optimized according to three criteria: minimum processing time, fuel consumption (energy) and processing resource consumption (liquid, seeds, etc.). In addition, the desired trajectory must have a parameterization that allows for further optimization and application in artificial intelligence systems. The main idea used is ternary coding of the neighborhood of a point and algorithms that exploit the connectivity of spatial regions on a lattice. The trajectory builder creates a partially optimized polyline, the construction of which generates its parameters, which are then used for optimization by a genetic algorithm. To use a genetic algorithm, parameters of different power are reduced to a system of parameters of the same power, equal to 3. The experimental construction and optimization of the trajectory confirmed the viability of the proposed algorithm and the idea of trajectory planning.