




















Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Course title is Embedded Intelligent Robotics. This course is for Electrical engineering students. Though good thing is everyone can learn about robotics in this course. This lecture includes: Generalized Voronoi Graphs, Sensor Based Exploration, Distance Function, Equidistant Face, Hierarchical Gvg, Gvg Tracing Function, Simulations, Hierarchical Voronoi Diagrams, Basic Motion Problem
Typology: Slides
1 / 28
This page cannot be seen from the preview
Don't miss anything!
full knowledge of the world
environments and into environments that are too difficult to
model
may have only a coarse knowledge of the world
unexpected changes
(GVD):for planar environment only.
(GVG): a generalization of
the GVD into higher dimensions.
One dimensional.
A more concise representation
of the workspace or configuration space.
m
equidistant face is formed, which is a one dimensional set of
points.
meet point.
m+1-equidistant faces(meet point).
Equidistant Face
recursively defined on lower dimensional equidistant faces.
GVG.
We will focus on R^3 only in the rest of this paper.
Hierarchical GVG
kl fij
trace the roots of the expression
as is varied.
x : point on the GVG.
z 1 : in the tangent direction of x.
At x , let the hyperplane
spanned by local coordinates
z 2 - z m be termed the normal
plane. The tracing function
This function assumes a zero
value only on the GVG.
G 1 ( y ,) (^0)
( )( , )
( )( , )
( )( , )
( , )
1
1 3
1 2
1
d d y
d d y
d d y
G y
m
direction of the GVG
This is achieved through the Newton method:
It can be proved that the Jacobian matrix is always nonsingular.
( ) 1 ( , )
1 1
1 k k y
k k
the direction of the gradients to the m closest obstacles.
Some Details
Accessibility: using gradient ascent on the multi-object
distance function, moving in a direction to which the
sensor with the smallest value is facing.
trace the edges of second-order GVG.
( )( , )
( )( , )
( )( , )
( , )
3
3 4
1 2
2
d d y
d d y
d d y
G y
m
19
Simulations