Core Concepts
The boundary of the reachability set can be accessed by time optimal solutions, extending to 3D curvature-bounded paths.
Abstract
This paper explores the equivalence relation between optimal control problems and reachability sets, focusing on 3D curvature-bounded paths. It presents a construction method for the boundary of reachability sets, considering terminal directions and without them. The results generalize existing literature on 2D curves, offering insights into time optimal solutions and reachability sets.
Abstract
Equivalence relation between optimal control problems and reachability sets.
Construction method for reachability set boundaries in 3D curves.
Introduction
Importance of reachability analysis in optimal control.
Previous studies on constructing reachability sets for curvature-bounded paths.
Data Extraction
"The findings facilitate the use of solution structures from a certain class of optimal control problems to address problems in corresponding equivalent classes."
"These advancements in understanding the reachability of curvature bounded paths in R3 hold significant practical implications."
Quotations
"The analysis of reachability, or attainability, of dynamical systems is crucial in a wide range of applications."
"The emphasis on the curvature-bounded paths is due to the dynamics of planar curves with a prescribed curvature bound."
Further Questions
How does the equivalence theorem impact the practical applications of reachability analysis?
What counterarguments exist against the association of time optimal problems with reachability?
How can the concept of equivalence in optimal control be applied to other fields beyond reachability analysis?
Stats
"The findings facilitate the use of solution structures from a certain class of optimal control problems to address problems in corresponding equivalent classes."
"These advancements in understanding the reachability of curvature bounded paths in R3 hold significant practical implications."
Quotes
"The analysis of reachability, or attainability, of dynamical systems is crucial in a wide range of applications."
"The emphasis on the curvature-bounded paths is due to the dynamics of planar curves with a prescribed curvature bound."