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Abstract(s)
In the last twenty years genetic algorithms (GAs) were applied in a plethora of fields such as: control,
system identification, robotics, planning and scheduling, image processing, and pattern and speech
recognition (Bäck et al., 1997). In robotics the problems of trajectory planning, collision avoidance
and manipulator structure design considering a single criteria has been solved using several techniques
(Alander, 2003).
Most engineering applications require the optimization of several criteria simultaneously. Often the
problems are complex, include discrete and continuous variables and there is no prior knowledge about
the search space. These kind of problems are very more complex, since they consider multiple design
criteria simultaneously within the optimization procedure. This is known as a multi-criteria (or multiobjective)
optimization, that has been addressed successfully through GAs (Deb, 2001). The overall
aim of multi-criteria evolutionary algorithms is to achieve a set of non-dominated optimal solutions
known as Pareto front. At the end of the optimization procedure, instead of a single optimal (or near
optimal) solution, the decision maker can select a solution from the Pareto front. Some of the key issues
in multi-criteria GAs are: i) the number of objectives, ii) to obtain a Pareto front as wide as possible
and iii) to achieve a Pareto front uniformly spread.
Indeed, multi-objective techniques using GAs have been increasing in relevance as a research area.
In 1989, Goldberg suggested the use of a GA to solve multi-objective problems and since then other
researchers have been developing new methods, such as the multi-objective genetic algorithm (MOGA)
(Fonseca & Fleming, 1995), the non-dominated sorted genetic algorithm (NSGA) (Deb, 2001), and
the niched Pareto genetic algorithm (NPGA) (Horn et al., 1994), among several other variants (Coello,
1998).
In this work the trajectory planning problem considers: i) robots with 2 and 3 degrees of freedom (dof ),
ii) the inclusion of obstacles in the workspace and iii) up to five criteria that are used to qualify the
evolving trajectory, namely the: joint traveling distance, joint velocity, end effector / Cartesian distance,
end effector / Cartesian velocity and energy involved. These criteria are used to minimize the joint and end effector traveled distance, trajectory ripple and energy required by the manipulator to reach at
destination point.
Bearing this ideas in mind, the paper addresses the planning of robot trajectories, meaning the development
of an algorithm to find a continuous motion that takes the manipulator from a given starting
configuration up to a desired end position without colliding with any obstacle in the workspace.
The chapter is organized as follows. Section 2 describes the trajectory planning and several approaches
proposed in the literature. Section 3 formulates the problem, namely the representation adopted to
solve the trajectory planning and the objectives considered in the optimization. Section 4 studies the
algorithm convergence. Section 5 studies a 2R manipulator (i.e., a robot with two rotational joints/links)
when the optimization trajectory considers two and five objectives. Sections 6 and 7 show the results for
the 3R redundant manipulator with five goals and for other complementary experiments are described,
respectively. Finally, section 8 draws the main conclusions.
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InTech