Abstract: This work approaches the automatic planning of paths
for Unmanned Aerial Vehicles (UAVs) through the application of the
Rapidly Exploring Random Tree Star-Smart (RRT*-Smart) algorithm.
RRT*-Smart is a sampling process of positions of a navigation
environment through a tree-type graph. The algorithm consists of
randomly expanding a tree from an initial position (root node) until
one of its branches reaches the final position of the path to be
planned. The algorithm ensures the planning of the shortest path,
considering the number of iterations tending to infinity. When a
new node is inserted into the tree, each neighbor node of the
new node is connected to it, if and only if the extension of the
path between the root node and that neighbor node, with this new
connection, is less than the current extension of the path between
those two nodes. RRT*-smart uses an intelligent sampling strategy
to plan less extensive routes by spending a smaller number of
iterations. This strategy is based on the creation of samples/nodes
near to the convex vertices of the navigation environment obstacles.
The planned paths are smoothed through the application of the
method called quintic pythagorean hodograph curves. The smoothing
process converts a route into a dynamically-viable one based on the
kinematic constraints of the vehicle. This smoothing method models
the hodograph components of a curve with polynomials that obey
the Pythagorean Theorem. Its advantage is that the obtained structure
allows computation of the curve length in an exact way, without the
need for quadratural techniques for the resolution of integrals.
Abstract: Finding the optimal 3D path of an aerial vehicle under
flight mechanics constraints is a major challenge, especially when
the algorithm has to produce real time results in flight. Kinematics
models and Pythagorian Hodograph curves have been widely used
in mobile robotics to solve this problematic. The level of difficulty
is mainly driven by the number of constraints to be saturated at the
same time while minimizing the total length of the path. In this paper,
we suggest a pragmatic algorithm capable of saturating at the same
time most of dimensioning helicopter 3D trajectories’ constraints
like: curvature, curvature derivative, torsion, torsion derivative, climb
angle, climb angle derivative, positions. The trajectories generation
algorithm is able to generate versatile complex 3D motion primitives
feasible by a helicopter with parameterization of the curvature and the
climb angle. An upper ”motion primitives’ concatenation” algorithm
is presented based. In this article we introduce a new way of designing
three-dimensional trajectories based on what we call the ”Dubins
gliding symmetry conjecture”. This extremely performing algorithm
will be soon integrated to a real-time decisional system dealing with
inflight safety issues.
Abstract: The PH curve can be constructed by given parameters, but the shape of the curve is not so easy to image from the value of the parameters. On the contract, Bézier curve can be constructed by the control polygon, and from the control polygon, we can image the figure of the curve. In this paper, we want to use the hodograph of Bézier curve to construct PH curve by selecting part of the control vectors, and produce other control vectors, so the property of PH curve exists.