24 research outputs found
A New Algorithm for Optimizing Dubins Paths to Intercept a Moving Target
This paper is concerned with determining the shortest path for a pursuer
aiming to intercept a moving target travelling at a constant speed. We
introduce an intuitive and efficient mathematical model outlined as an optimal
control problem to address this challenge. The proposed model is based on
Dubins path where we concatenate two possible paths: a left-circular curve or a
right-circular curve followed by a straight line. We develop and explore this
model, providing a comprehensive geometric interpretation, and design an
algorithm tailored to implement the proposed mathematical approach efficiently.
Extensive numerical experiments involving diverse target positions highlight
the strength of the model. The method exhibits a remarkably high convergence
rate in finding solutions. For experiment purposes, we utilized the modelling
software AMPL, employing a range of solvers to solve the problem. Subsequently,
we simulated the obtained solutions using MATLAB, demonstrating the efficiency
of the model in intercepting a moving target. The proposed model distinguishes
itself by employing fewer parameters and making fewer assumptions, setting the
model simplifies the complexities, and thus, makes it easier for experts to
design optimal path plans
Spartan Daily, February 15, 1990
Volume 94, Issue 14https://scholarworks.sjsu.edu/spartandaily/7944/thumbnail.jp
Spartan Daily, February 15, 1990
Volume 94, Issue 14https://scholarworks.sjsu.edu/spartandaily/7944/thumbnail.jp
An Optimal Control Theory for the Traveling Salesman Problem and Its Variants
We show that the traveling salesman problem (TSP) and its many variants may
be modeled as functional optimization problems over a graph. In this
formulation, all vertices and arcs of the graph are functionals; i.e., a
mapping from a space of measurable functions to the field of real numbers. Many
variants of the TSP, such as those with neighborhoods, with forbidden
neighborhoods, with time-windows and with profits, can all be framed under this
construct. In sharp contrast to their discrete-optimization counterparts, the
modeling constructs presented in this paper represent a fundamentally new
domain of analysis and computation for TSPs and their variants. Beyond its
apparent mathematical unification of a class of problems in graph theory, the
main advantage of the new approach is that it facilitates the modeling of
certain application-specific problems in their home space of measurable
functions. Consequently, certain elements of economic system theory such as
dynamical models and continuous-time cost/profit functionals can be directly
incorporated in the new optimization problem formulation. Furthermore, subtour
elimination constraints, prevalent in discrete optimization formulations, are
naturally enforced through continuity requirements. The price for the new
modeling framework is nonsmooth functionals. Although a number of theoretical
issues remain open in the proposed mathematical framework, we demonstrate the
computational viability of the new modeling constructs over a sample set of
problems to illustrate the rapid production of end-to-end TSP solutions to
extensively-constrained practical problems.Comment: 24 pages, 8 figure