Emmanuel A. Mechan-Cruz, Alan S.
Morris
IEEE Transactions on Robotics, VOL.
22, NO.4, August 2006
Summary
Artificial
Potential Fields (APF) are useful in describing workspace of manipulators for implementation
of fuzzy collision-avoidance strategies. APF is capable of collision avoidance
and trajectory planning simultaneously, but has a high risk of being stuck in
local minima conditions in certain conditions, therefore in the literature,
following Khatib studies, many solutions to avoid local minima have been
performed. The authors present a novel fuzzy genetic algorithm (GA) approach to
make trajectory planning of two manipulators sharing a common workspace. The
application of fuzzy logic for information generation to drive a manipulator to
a certain goal was first investigated by Althoefer (1996), but the system
appear to no be feasible for two manipulators working simultaneously with a one
of them in static condition nearby the goal.
·
Model
The
fuzzy-GA-based trajectory planner (FuGABTP) is a simple Genetic Algorithm (GA)
trajectory planner (GABTP) where individual fuzzy units provide correction to
the displacement of each articulation. Manipulators are modeled as obstacles
using a APF method, calculated only for the near vicinity (being a local
approach).
The
outline see initial configurations being input in both manipulators, which in
parallel start first the GABTP and then implement the fuzzy corrections, at
that point trajectories are updated and goal is verified if check or not,
repeating the sequence if goal is not reached.
The
GABTP carries an initial estimation of the motion without considering the
presence of possible obstacles, in free
workspace the degree of extension of the manipulator is considered in order to
minimize unnecessary displacements of the links (refer to Appendix A): f=1/(e(error/R)),
where the error is the distance between goal coordinated and actual coordinate,
R is the distance between initial coordinates and actual current coordinates.
Fuzzy
correction is achieved by individual Mamdami-type
fuzzy units that provide collision avoidance. The obstacle direction can be
right is the APF increased or left in the other case. μi are
the fuzzy sets, used for mapping μp(d): D à
[0;1]. The
function to represent the fuzzy sets is asymmetrical triangular functions since
these are easily computable. The correction is given according to the fuzzy
rules: 1) obstacle on the left and small
APF then SN correction, 2) obstacle on the left and med APF then MN
correction; 3) obstacle on the left and medbig APF then MBN correction; 4) if
obstacle is on the left and APF is big then BN correction; 5) if obstacle is on
the left and APF is 0 then zero correction; 6) if obstacle is on the right and
APF is small then correction is SP; 7) if the obstacle is on the right and APF
is small then correction is MP; 8) if the obstacle is right and APF is medbig
then correction is MBP; 9) is obstacle is right and APF is bit then correction
is BP; 10) if obstacle is right and APF is 0 then correction is 0; 11) if
obstacle is left and error is 0 then correction is 0; 12) if obstacle is right
and error is 0 then correction is 0. The fuzzy set for output correction
showing the each acronym graph is report at page 616.
Key
Concepts
Fuzzy-GA-Based
Trajectory Planner, Planning, Workspace sharing
Key Results
The simulation has been
carried on with a 3 d.o.f. and a 7 d.o.f. manipulator both in static and
dynamic case, showing success in reaching the goal. The FuGABTP took generally
more segment movement but an overall less time to reach the goals if compared
with simple GABTP.
The approach demonstrates
to be robust and stable, from the set of outputs coming from the model it is
further own easy to computer trajectory, velocity and acceleration through
kinematics. The parallel planning avoids the need of any further planning.
No comments:
Post a Comment