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An Algebraic Collision Avoidance Approach for Unmanned Aerial
Vehicle
Adriana Dapena
1
, Mar
´
ıa Jos
´
e Souto-Salorio
2
, Ana Dorotea Tarr
´
ıo-Tobar
3
and Paula M. Castro
1
1
Department of Computer Engineering, Universidade da Coru
˜
na, Coru
˜
na, Spain
2
Department of Computer Science, Universidade da Coru
˜
na, Coru
˜
na, Spain
3
Department of Mathematics, Universidade da Coru
˜
na, Coru
˜
na, Spain
Keywords:
Collision Avoidance, Control and Supervision Systems, Characteristic Polynomial, Engineering Applications,
Hyperboloid Structure, Modelling and Simulation, Unmanned Aerial Vehicle.
Abstract:
In this paper we address the problem of avoidancing collisions between an Unmanned Aerial Vehicle (UAV)
and a rigid surface. The UAV is modelled as an unique sphere envolving the UAV or as multiple spheres only
envolving the motors. The UAV flies inside a rigid hyperboloid structure typically used in architecture. The
collision is detected by means of the study of the characteristic polynomial associated to quadric surfaces.
Computer simulation results included in this paper will show both the accuracy and the low computational
cost exhibited by the proposed method.
1 INTRODUCTION
Collision detection between two or more rigid bodies
is based on determining whether any of the solids
makes contact at one or more points (Brozos-V
´
azquez
et al., 2016), (Choi et al., 2006). This problem has
a great interest in many fields such as robotics (Choi
et al., 2006), (Steinbach et al., 2006), computer graph-
ics (Jia et al., 2006), animation and computer simu-
lated environments (C. O’Sullivan, 1999), etc.
From a mathematical point of view, the contact
between rigid bodies can be determined by saying that
the surfaces are in contact when their intersection is
not an empty set of points. Then, given two surfaces,
the question is to know whether they intersect or not.
Most work in the literature devoted to the study
of collision detection only considers convex bodies
(Choi et al., 2006), (Jia et al., 2006). Moreover,
most of the proposed algorithms are indeed valid
only under that condition of convexity. Recently, in
(Brozos-V
´
azquez et al., 2016), the authors have pre-
sented a study in which one of the bodies was not
convex (in fact, that was a hyperboloid). Since hyper-
boloid structures are doubly ruled surfaces, this type
of architectural structures is very strong against buck-
ling and cheaper than other singly ruled surfaces, like
cylinders or cones. For this reason, the hyperboloid
structure is used in architecture to design cooling tow-
ers, water towers, cathedrals, air traffic control towers,
and so on.
Because of its potential for commercial, military,
law-enforcement, research, and other purposes, Un-
manned Aerial Vehicles (UAVs) have received con-
siderable attention in recent years. The fast develop-
ment of this field has required the design of robust
collision avoidance systems which are based, in gene-
ral, on the combination of information acquired from
several sensors, which implies processing latency and
complexity (Giancarmine et al., 2008). If the surface
shape changes in height (like occurs with the hyper-
boloid structure) those sensors must be used for the
registration of this information in all directions. Col-
lision avoidance methods based on computing the dis-
tance from the UAV to the surface are adequate in
most situations where that surface shape is similar for
all height positions.
The method presented in this paper is oriented to
predict collisions when an UAV is flying inside a hy-
perboloid structure. We propose to model the UAV
using multiples spheres adapted to its shape. Using
the results presented in (Brozos-V
´
azquez et al., 2016),
we propose several algorithms for collision avoidance
by means of the study of the roots of a character-
istic polynomial associated to quadric surfaces. In
those algorithms, the conditions for collision detec-
tion are evaluated before any UAV movement so that
only valid movements are allowed thus avoiding such
262
Dapena, A., Souto-Salorio, M., Tarrío-Tobar, A. and Castro, P.
An Algebraic Collision Avoidance Approach for Unmanned Aerial Vehicle.
DOI: 10.5220/0006410002620269
In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 2, pages 262-269
ISBN: Not Available
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