Aerospace Science and Technology 71 (2017) 1–11 Contents lists available at ScienceDirect Aerospace Science and Technology www.elsevier.com/locate/aescte A mixed probabilistic–geometric strategy for UAV optimum flight path identification based on bit-coded basic manoeuvres Luciano Blasi ∗ , Simeone Barbato, Egidio D’Amato Dipartimento di Ingegneria Industriale e dell’Informazione, Università degli Studi della Campania “Luigi Vanvitelli”, Via Roma 29, 81031 Aversa, Italy a r t i c l e i n f o a b s t r a c t Article history: Received 22 March 2017 Received in revised form 1 September 2017 Accepted 5 September 2017 Available online 13 September 2017 Keywords: Path planning Trajectory optimization Unmanned Aerial Vehicles Particle Swarm Optimization This paper presents a novel algorithm identifying optimal flight trajectories for Unmanned Aerial Vehicles compliant with environmental constraints. Such constraints are defined in terms of obstacles, fixed way- points and selected destination points. Optimality is evaluated taking the minimum path length as the specific objective function. The proposed path planning strategy is based on an original trajectory modelling coupled with a Particle Swarm optimizer (PSO). Flight paths starting from a specified point and ending at a selected destination point are divided into a finite number of segments made up of circular arcs and straight lines. In the proposed approach such a geometrical sequence is replaced with a finite sequence of binary-coded basic manoeuvres. This novel formulation allows to easily handle the manoeuvres sequence with a fixed number of integer variables taking advantage of PSO capability in handling discrete variables; moreover the use of mixed-type variables provides the optimization procedure a useful flexibility in the “decision making” modelling and operational scenarios definition as well. Specific geometric-based linear obstacle avoidance models have been implemented in addition to suitable penalty functions. The use of these models forces each path to be consistent with the environmental constraints favouring the identification of feasible trajectories with a reduced number of iterations and particles. The path planning model has been developed with particular care devoted to reduce computational effort as well as to improve algorithm capability in handling general-shaped obstacles both in 2-D and 3-D environments. Various applications have been performed in order to test the effectiveness of the proposed flight path generator. Applicability of the proposed optimization model also to vehicles with VTOL and hovering capabilities has been preliminarily assessed.  2017 Elsevier Masson SAS. All rights reserved. 0. Introduction Unmanned air vehicles (UAVs) are being extensively used for different civil and military applications especially to replace the presence of human pilot aboard in dangerous/dull missions or to reduce operational costs. In the frame of a careful mission plan- ning, identification of feasible flight trajectories, consistent with mission objectives, operational scenarios and vehicles performance, certainly plays an important role. A wide literature exists regarding trajectory optimization methodologies applied to different operational scenarios and ve- hicles. The variational approach is the most rigorous one for this class of problems though unfit to solve complex problems. Numer- ical methods based on the solution of Non Linear Programming (NLP) problems are presented by Betts [1]. Feasible trajectories can be also generated following a geometrical approach based on topo- * Corresponding author. E-mail address: luciano.blasi@unicampania.it (L. Blasi). logical techniques creating a sequence of waypoints. This sequence can derive from probabilistic or potential methods [2]. A classical geometric approach guaranteeing optimality conditions in terms of paths length and smooth trajectories compliant with curvature constraint was proposed by Dubins [3] and refined by Anderson et al. [4], Chitsaz and LaValle [5] and Shanmugavel et al. [6]. An interesting technique, taking into account flight dynamics, is based on the so called “motion primitives” [7], where flight paths are defined through a sequence of trim conditions and manoeuvres. Recently, novel path planning strategies work by quickly sampling the 3-D free space to get a grid of points which are connected with specific smooth curves. An interesting paper is proposed by Ching-Huei Huang et al. [8], where Rapidly Random Tree (RRT) technique is employed with A* algorithm to get the optimal trajec- tory connecting the starting and the ending points. Bezier curves are used to get the final smooth path. A variant of the classical RRT method uses 3-D Dubins curves for tree expansion [9]. An im- proved RRT, using D* Lite algorithm for solving the dynamic path planning problem, is proposed by Liu Yang et al. [10]. Probabilistic Roadmap Method (PRM) together with A* algorithm used to as- http://dx.doi.org/10.1016/j.ast.2017.09.007 1270-9638/ 2017 Elsevier Masson SAS. All rights reserved.