Related papers: Discrete Dubins Paths
We study the problem of finding curves of minimum pointwise-maximum arc-length derivative of curvature, here simply called curves of minimax spirality, among planar curves of fixed length with prescribed endpoints and tangents at the…
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…
This paper gives a partial confirmation of a conjecture of P. Agarwal, S. Har-Peled, M. Sharir, and K. Varadarajan that the total curvature of a shortest path on the boundary of a convex polyhedron in the 3-dimensional Euclidean space…
Tubular structure tracking is a crucial task in the fields of computer vision and medical image analysis. The minimal paths-based approaches have exhibited their strong ability in tracing tubular structures, by which a tubular structure can…
In this paper, we propose a new method for path planning to a point for robot in environment with obstacles. The resulting algorithm is implemented as a simple variation of Dijkstra's algorithm. By adding a constraint to the shortest-path,…
Some problems founds in teaching physics related to curved paths that are unfortunately only described as illustration. A simple way to introduce the path is presented, which can help students to test their concept numerically. The…
We consider the set E of curves with positive algebraic curvature, whose extremities and tangents in their extremities are given. For each of the curves of E, we define the minimum of the radius of curvature. We first prove that there…
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…
The motion of a mechanical system can be defined as a path through its configuration space. Computing such a path has a computational complexity scaling exponentially with the dimensionality of the configuration space. We propose to reduce…
When designing path tracking controllers for car-like vehicles, two main aspects are the tracking performance and the characteristics of the actuation signal. Our work bases on an existing variable structure controller that was designed…
We consider the set E of curves with positive algebraic curvature, whose extremities and tangents in their extremities are given. For each of the curves of E, we define the minimum of the radius of curvature. There exists a unique curve of…
We develop the structure theory for transformations of weakly geometric rough paths of bounded $1 < p$-variation and their controlled paths. Our approach differs from existing approaches as it does not rely on smooth approximations. We…
We study the problem of determining optimal coordinated motions for two disc robots in an otherwise obstacle-free plane. Using the total path length traced by the two disc centres as a measure of distance, we give an exact characterization…
This paper addresses the problem of finding shortest paths homotopic to a given disjoint set of paths that wind amongst point obstacles in the plane. We present a faster algorithm than previously known.
In this article, two methods of addressing path planning for a Dubins vehicle moving on a sphere are considered, wherein either spherical coordinates or a moving frame are considered to describe the vehicle's motion. The primary…
In this paper, we introduced a novel approach to computing the fewest-turn map directions or routes based on the concept of natural roads. Natural roads are joined road segments that perceptually constitute good continuity. This approach…
This paper establishes a comprehensive theory of geometric rough paths for mixed fractional Brownian motion (MFBM) and its generalized multi-component extensions. We prove that for a generalized MFBM of the form $M_t^H(a) = \sum_{k=1}^N a_k…
We propose a simple, geometrically-motivated construction of smooth random paths in the plane. The construction is such that, with probability one, the paths have finite curvature everywhere (and the realizations are visually pleasing when…
To perform autonomous driving maneuvers, such as parallel or perpendicular parking, a vehicle requires continual speed and steering adjustments to follow a generated path. In consequence, the path's quality is a limiting factor of the…
The kinematic approximation of Dubin's Vehicle has been largely exploited in the formulation of various motion planning methods. In the majority of these methods, planning and control phases are decoupled, and the burden of rejecting…