Related papers: An Analytic Solution to the 3D CSC Dubins Path Pro…
The $k$ disjoint shortest paths problem ($k$-DSPP) on a graph with $k$ source-sink pairs $(s_i, t_i)$ asks for the existence of $k$ pairwise edge- or vertex-disjoint shortest $s_i$-$t_i$-paths. It is known to be NP-complete if $k$ is part…
Motion planning seeks a collision-free path in a configuration space (C-space), representing all possible robot configurations in the environment. As it is challenging to construct a C-space explicitly for a high-dimensional robot, we…
This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be…
We formulate a novel planar motion planning problem for a Dubins-Laser system that consists of a Dubins vehicle with an attached controllable laser. The vehicle moves with unit speed and the laser, having a finite range, can rotate in a…
The constrained path optimization (CPO) problem takes the following input: (a) a road network represented as a directed graph, where each edge is associated with a "cost" and a "score" value; (b) a source-destination pair and; (c) a budget…
Consider a 2D coordinate space with a set of red and a set of blue points. We define a scenic point as a point that is equidistant to a red point and a blue point. The set of contiguous scenic points form a scenic path. The perpendicular…
Using a path integral approach, we derive an analytical solution of a nonlinear and singular Langevin equation, which has been introduced previously by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion of a solid…
Methods for inverse kinematics computation and path planning of a three degree-of-freedom (DOF) manipulator using the algorithm for quantifier elimination based on Comprehensive Gr\"obner Systems (CGS), called CGS-QE method, are proposed.…
We consider the Adaptive Regularization with Cubics approach for solving nonconvex optimization problems and propose a new variant based on inexact Hessian information chosen dynamically. The theoretical analysis of the proposed procedure…
We study the quadratic $k$-vertex-disjoint paths problem (Q-$k$-VDP), which seeks $k$ vertex-disjoint paths in a directed graph that minimize a nonconvex quadratic objective function. We formulate the problem as a binary quadratic program…
This article studies the time-optimal path planning problem for a convexified Reeds-Shepp (CRS) vehicle on a unit sphere, capable of both forward and backward motion, with speed bounded in magnitude by 1 and turning rate bounded in…
Path planning in the presence of dynamic obstacles is a challenging problem due to the added time dimension in search space. In approaches that ignore the time dimension and treat dynamic obstacles as static, frequent re-planning is…
The detection of curved lanes is still challenging for autonomous driving systems. Although current cutting-edge approaches have performed well in real applications, most of them are based on strict model assumptions. Similar to other…
The trajectory derived from RRT and RRT* is zagged. A holonomic drive is able to follow this trajectory. But real-life vehicle which has dynamical constraints cannot follow this trajectory. In this work, we are going to modify the RRT and…
This paper presents a triple optimization algorithm of two-dimensional space, driving path and driving speed, and iterates in the time dimension to obtain the local optimal solution of path and speed in the optimal driving area. Design…
We present a multi-UAV Coverage Path Planning (CPP) framework for the inspection of large-scale, complex 3D structures. In the proposed sampling-based coverage path planning method, we formulate the multi-UAV inspection applications as a…
This paper investigates the singular curves in two-dimensional slices of the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points…
Through the development of efficient algorithms, data structures and preprocessing techniques, real-world shortest path problems in street networks are now very fast to solve. But in reality, the exact travel times along each arc in the…
In this work, we solve the problem of finding non-intersecting paths between points on a plane with a new approach by borrowing ideas from geometric topology, in particular, from the study of polygonal schema in mathematics. We use a…
Stochastic Optimal Control (SOC) problems arise in systems influenced by uncertainty, such as autonomous robots or financial models. Traditional methods like dynamic programming are often intractable for high-dimensional, nonlinear systems…