Related papers: Motion planning algorithms for Configuration Space…
This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…
In this paper we develop theory of sequential parametrized motion planning which generalises the approach of parametrized motion planning, which was introduced recently in [3]. A sequential parametrized motion planning algorithm produced a…
We consider practical aspects of reconstructing planar curves with prescribed Euclidean or affine curvatures. These curvatures are invariant under the special Euclidean group and the equi-affine groups, respectively, and play an important…
We present a hierarchical framework for motion planning of a large collection of agents. The proposed framework starts from low level motion primitives over a gridded workspace and provides a set of rules for constructing higher level…
This paper presents a new approach to learning for motion planning (MP) where critical regions of an environment are learned from a given set of motion plans and used to improve performance on new environments and problem instances. We…
This paper presents a novel method to generate spatial constraints for motion planning in dynamic environments. Motion planning methods for autonomous driving and mobile robots typically need to rely on the spatial constraints imposed by a…
Motion planning is a key tool that allows robots to navigate through an environment without collisions. The problem of robot motion planning has been studied in great detail over the last several decades, with researchers initially focusing…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
This paper presents an approach for learning motion planners that are accompanied with probabilistic guarantees of success on new environments that hold uniformly for any disturbance to the robot's dynamics within an admissible set. We…
We introduce the digital projective product spaces based on Davis' projective product spaces. We determine an upper bound for the digital LS-category of the digital projective product spaces. In addition, we obtain an upper bound for the…
We consider planning problems on a punctured Euclidean spaces, $\mathbb{R}^D - \widetilde{\mathcal{O}}$, where $\widetilde{\mathcal{O}}$ is a collection of obstacles. Such spaces are of frequent occurrence as configuration spaces of robots,…
Randomized sampling based algorithms are widely used in robot motion planning due to the problem's intractability, and are experimentally effective on a wide range of problem instances. Most variants bias their sampling using various…
Motion planning in uncertain environments like complex urban areas is a key challenge for autonomous vehicles (AVs). The aim of our research is to investigate how AVs can navigate crowded, unpredictable scenarios with multiple pedestrians…
We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and…
An application design is offered, which students of physics can use when authoring a solver for mechanical systems with constraints. A 'chainlist' concept is introduced to capture a constrained mechanical system configuration and to pass…
Planning the motion for humanoid robots is a computationally-complex task due to the high dimensionality of the system. Thus, a common approach is to first plan in the low-dimensional space induced by the robot's feet---a task referred to…
Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…
We design an algorithm writing down presentations of graph braid groups. Generators are represented in terms of actual motions of robots moving without collisions on a given graph. A key ingredient is a new motion planning algorithm whose…
Sampling based methods are widely used for robotic motion planning. Traditionally, these samples are drawn from probabilistic ( or deterministic ) distributions to cover the state space uniformly. Despite being probabilistically complete,…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…