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CALCULATION OF OPTIMAL TRAJECTORY IN 3-D
STRUCTURED ENVIRONMENT BY USING GEODESY AND
MATHEMATICAL MORPHOLOGY
Santiago T. Puente, Fernando Torres, Francisco Ortiz, Pablo Gil
Department of Physics, Systems Engineering and Signal Theory. University of Alicante, P.O. Box 99, 03080 Alicante, Spain
Keywords: 3-D mathematical morphology; disassembly trajectory; geodesic paths.
Abstract: A new method for obtaining the optimal path to disassembly an object in a 3-D structure is presented in this
paper. To obtain
the optimal path, we use an extension of the mathematical morphology and the geodesic
distance to 3-D sets. The disassembly algorithm is based on the search for a path of minimum cost by using
the wave-front of the geodesic distance. Cost is considered to be the number of changes in trajectory
required to be able to remove the object. The new method will be applied to disassembly objects in several
3-D environments. The result path for removing an object in a concrete 3-D set will be shown.
1 INTRODUCTION
A method for obtaining the optimal trajectory from
an initial point to a final point in a 3-D space is
presented in this paper. When the trajectory is
computed from the initial point to the final
destination, the following factors must be taken into
consideration:
• Avoiding collisions with the environment: as
there is a structure
d environment, the path between
the two points must avoid any collisions between the
moving object and the environment.
• The shortest path: when this is taken into
consideration, the displace
ment is reduced to a
minimum. It must be noted that there may be more
than one path with the same distance between the
two points. Such paths are all correct and must be
taken into consideration.
• Minimizing changes in direction: From all the
pos
sible paths, only those that require the minimum
number of direction changes along the path will be
chosen.
Another characteristic of the proposed trajectory
is th
at it allows paths in the 3-D space, which
implies an important characteristic gain over the 2-D
trajectories, which are the ones used in traditional
robot navigation. In the traditional navigation of
robots, the movement is defined in a 2-D
environment although the real movement is in 3-D.
Furthermore, in the case of air robots or submarine
navigation, a trajectory in a 3-D environment is
necessary, since the robots can move with more
freedom.
Another area where the use of 3-D trajectories is
necessa
ry is in manipulator robots. When a
manipulator needs to move within a complex
environment with obstacles, it has to define the
trajectory to be followed from the starting point to
the target, as for example, in the pick and place
application in a structured environment (McAvoy et
alt, 2000). Furthermore, this type of trajectory is
necessary when we must have access to the inside of
a product to manipulate it, and we must move the
manipulator between the other components of the
product without colliding with them (Puente et alt,
2003).
The techniques for the generation of trajectories
can be di
vided into three categories: global, local or
mixed (Puente, 2002), according to the environment
in which the solution is required. The global
techniques are the most interesting ones, since a
complete representation of the work area is used.
In this paper, geodesic techniques for computing
t
he trajectory between two points are used (Belta
and Kumar, 2002) (Tchon and Duleba, 1993). The
geodesic techniques used have been extended to
work in 3-D spaces. The use of geodesic techniques
affords a simple way of defining security parameters
153
T. Puente S., Torres F., Ortiz F. and Gil P. (2006).
CALCULATION OF OPTIMAL TRAJECTORY IN 3-D STRUCTURED ENVIRONMENT BY USING GEODESY AND MATHEMATICAL MORPHOLOGY.
In Proceedings of the First International Conference on Computer Vision Theory and Applications, pages 153-156
DOI: 10.5220/0001365001530156
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