The path planning problem for a controlled moving object with a nonuniform radiation pattern is considered for the case in which the necessary path optimality conditions are
degenerate. Additional constraints are introduced, and two optimization problems are formalized, one of finding an optimal speed mode for a given path of the object and the other of finding
an optimal path when moving at a constant speed. Methods and algorithms for constructing
optimal paths and finding speed modes are proposed; for the second problem, the analytical
domain of existence of a solution for arbitrary parameters is found. The analytical results are
illustrated with examples.
