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Discrete approximations to continuous curves Sean B. Andersson
 

Summary: Discrete approximations to continuous curves
Sean B. Andersson
Department of Aerospace and Mechanical Engineering
Boston University, Boston, MA 02215
Email: sanderss@bu.edu
Abstract-- We consider the problem of approximating a con-
tinuous curve by a piecewise linear one whose segments are
assumed to be connected by universal joints. Rather than taking
a least-squares approach, we require that the endpoints of the line
segments lie on the continuous curve. We show that under these
assumptions a single rotational degree of freedom remains. An
algorithm is derived to determine the set of angles characterizing
the relative orientation of each consecutive pair of line segments
as a function of this rotational degree of freedom. Two examples
are given to illustrate the procedure. The motivating application
for this work is the control of a snake-like robot using a set of
gaits designed from shape primitives.
I. INTRODUCTION
In this paper we consider the problem of approximating a
continuous parameterized 3-D curve with a piecewise linear

  

Source: Andersson, Sean B. - Department of Aerospace and Mechanical Engineering, Boston University

 

Collections: Engineering