arXiv subjects

Jun-Yong Lee

Publications and source records attributed to Jun-Yong Lee.

3 recordsLinked to original sources

arXiv2025

On the Reachability of 3-Dimensional Paths with a Prescribed Curvature Bound

This paper presents the reachability analysis of curves in $\mathbb{R}^3$ with a prescribed curvature bound. Based on Pontryagin Maximum Principle, we leverage the existing knowledge on the structure of solutions to minimum-time problems, or Markov-Dubins problem, to reachability considerations. Based on this development, two types of reachability are discussed. First, we prove that any boundary point of the reachability set, with the directional component taken into account as well as geometric coordinates, can be reached via curves of H, CSC, CCC, or their respective subsegments, where H denotes a helicoidal arc, C a circular arc with maximum curvature, and S a straight segment. Second, we show that the reachability set when directional component is not considered\textemdash{}the position reachability set\textemdash{}is simply a solid of revolution of its two-dimensional counterpart, the Dubins car. These findings extend the developments presented in literature on Dubins car into spatial curves in $\mathbb{R}^3$.

math.OC↗

arXiv2025

Hybridization of colloidal handlebodies with singular defects and topological solitons in chiral liquid crystals

Topology can manifest itself in colloids when quantified by invariants like Euler characteristics of nonzero-genus colloidal surfaces, albeit spherical colloidal particles are most often studied, and colloidal particles with complex topology are rarely considered. On the other hand, singular defects and topological solitons often define the physical behavior of the molecular alignment director fields in liquid crystals. Interestingly, nematic liquid crystalline dispersions of colloidal particles allow for probing the interplay between topologies of surfaces and fields, but only a limited number of such cases have been explored so far. Here, we study the hybridization of topological solitons, singular defects, and topologically nontrivial colloidal particles with the genus of surfaces different from zero in a chiral nematic liquid crystal phase. Hybridization occurs when distortions separately induced by colloidal particles and LC solitons overlap, leading to energy minimization-driven redistribution of director field deformations and defects. As a result, hybrid director configurations emerge, combining topological features from both components. We uncover a host of director field configurations complying with topological theorems, which can be controlled by applying electric fields. Rotational and translational dynamics arise due to the nonreciprocal evolution of the director fields in response to alternating electric fields of different frequencies. These findings help define a platform for controlling topologically hyper-complex colloidal structures and dynamics with electrically reconfigurable singular defects and topological solitons induced by colloidal handlebodies.

cond-mat.soft↗

arXiv2024

Constraint-Aware Mesh Refinement Method by Reachability Set Envelope of Curvature Bounded Paths

This paper presents an enhanced direct-method-based approach for the real-time solution of optimal control problems to handle path constraints, such as obstacles. The principal contributions of this work are twofold: first, the existing methods for constructing reachability sets in the literature are extended to derive the envelope of these sets, which determines the region swept by all feasible trajectories between adjacent sample points. Second, we propose a novel method to guarantee constraint violation-free between discrete states in two dimensions through mesh refinement approach. To illustrate the effectiveness of the proposed methodology, numerical simulations are conducted on real-time path planning for fixed-wing unmanned aerial vehicles.

eess.SY↗