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92 I.K. Nikolos et al.
4 Coordinated UAV Path Planning

This section describes the development and implementation of an off-line
path planner for Unmanned Aerial Vehicles (UAVs) coordinated navigation
and collision avoidance in known static maritime environments. The problem
formulation is described, including assumptions, objectives, constraints, objec-
tive function definition and path modeling.

4.1 Constraints and Objectives
The path planner was designed for navigation and collision avoidance of a
small team of autonomous UAVs in maritime environments. Known and static
environments are considered, characterized by the existence of a number of
islands with short distances between them. The flight height is assumed to
be almost constant, close to the sea-level, and the path-planning problem
is formulated as a 2-D one. Having N UAVs launched from different known
initial locations, the issue is to produce N 2-D trajectories, formed by B-Spline
curves, with a desirable velocity distribution along each trajectory, aiming at
reaching a predetermined target location, while ensuring collision avoidance
either with the environmental obstacles or with the UAVs. Additionally the
produced flight paths should satisfy specific route and coordination objectives
and constraints. Each vehicle is assumed to be a point, while its actual size is
taken into account by equivalent obstacle – ground growing.
The general constraint of the problem is the collision avoidance between
UAVs and the ground. The route constraints are:

(a) Predefined initial and target coordinates for all UAVs
(b) Predefined initial and final velocity magnitudes for all UAVs, and
(c) Predefined minimum and maximum UAV velocity magnitudes during their
flights.

Additionally, a single route objective is imposed: minimum path lengths,
for maximizing the effective range of each vehicle. All three route constraints
are explicitly taken into account by the optimization algorithm. The route
objective is implicitly handled by the algorithm, through the definition of the
objective function.
Besides route constraints and objective, coordination-relative constraints
and objectives are imposed, which are implicitly handled by the algorithm,
through the objective function definition. The coordination objectives used in
this work are the following:
(a) Each UAV should arrive at the target, using a different path and a different
approach vector, but the time of arrival for all UAVs should be as close
as possible.