A new motion planning algorithm for the so-called Dubins Travelling Salesperson Problem is derived, and compared via simulations with a number of existing algorithms from the literature. In its general form, the new algorithm is dubbed "k-step look-ahead algorithm" and stems naturally from the formulation of the Dubins Travelling Salesperson Problem as a minimum-time control problem. When the minimum turning radius of the Dubins vehicle is comparable to the average intercity distance, the simulations yield a comparison favourable to the new algorithm. The examples in the paper are confined to small instances of the Dubins Travelling Salesperson Problem, however the main idea behind the k-step look-ahead algorithm can be combined with different optimisation methods, if larger instances of the DTSP are to be considered.
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