Related papers: Oriented robot motion planning in Riemannian manif…
We introduce variational obstacle avoidance problems on Riemannian manifolds and derive necessary conditions for the existence of their normal extremals. The problem consists of minimizing an energy functional depending on the velocity and…
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 do not sample uniformly at random, and…
This study investigates the exact geometry of the configuration space in three-dimensional rotational motion planning. A parameterization of configuration space obstacles is derived for a given triangulated or ball-approximated scene with…
This paper presents a novel on-line path planning method that enables aerial robots to interact with surfaces. We present a solution to the problem of finding trajectories that drive a robot towards a surface and move along it. Triangular…
This paper is concerned with problems relevant to motion planning in robotics. Configuration spaces are of practical relevance in designing safe control schemes for robots moving on a track. The topological complexity of a configuration…
In this series of papers, we present a motion planning framework for planning comfortable and customizable motion of nonholonomic mobile robots such as intelligent wheelchairs and autonomous cars. In Part I, we presented the mathematical…
We put in a general framework the situations in which a Riemannian manifold admits a family of compatible complex structures, including hyperkahler metrics and the Spin-rotations of arxiv:1302.2846. We determine the (polystable) holomorphic…
We discuss some specializations of the frames of flat orthonormal frame bundles over geometries of indefinite signature, and the resulting symmetries of families of embedded Riemannian or pseudo-Riemannian geometries. The specializations…
Constrained robot motion planning is a widely used technique to solve complex robot tasks. We consider the problem of learning representations of constraints from demonstrations with a deep neural network, which we call Equality Constraint…
We present a decoupled algorithm for motion planning for a collection of unit-balls moving among polyhedral obstacles in $\mathbb{R}^d$, for any $d \ge 2$. We assume that the robots have revolving areas in the vicinity of their start and…
Motion planning and control are key problems in a collection of robotic applications including the design of autonomous agile vehicles and of minimalist manipulators. These problems can be accurately formalized within the language of affine…
Robot motion planning involves computing a sequence of valid robot configurations that take the robot from its initial state to a goal state. Solving a motion planning problem optimally using analytical methods is proven to be PSPACE-Hard.…
We define a simpler notion of symmetric topological complexity more ad hoc to the motion planning problem which was the original motivation for the definition of topological complexity. This is a homotopy invariant that we call…
This paper deals with a path planning and intelligent control of an autonomous robot which should move safely in partially structured environment. This environment may involve any number of obstacles of arbitrary shape and size; some of…
Headland maneuvering is a crucial aspect of unmanned field operations for autonomous agricultural vehicles (AAVs). While motion planning for headland turning in open fields has been extensively studied and integrated into commercial…
We prove that a locally compact space with an upper curvature bound is a topological manifold if and only if all of its spaces of directions are homotopy equivalent and not contractible. We discuss applications to homology manifolds, limits…
We give a simple upper bound for the upper box dimension of a backward invariant set of a $C^{1}$-diffeomorphism of a Riemannian manifold. We also estimate an upper bound for the box dimension of a forward invariant set of a $C^{1}$-mapping…
We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on…
We consider path planning for a rigid spatial robot moving amidst polyhedral obstacles. Our robot is either a rod or a ring. Being axially-symmetric, their configuration space is R^3 x S^2 with 5 degrees of freedom (DOF). Correct, complete…
We study the problem of motion planning for a collection of $n$ labeled unit disc robots in a polygonal environment. We assume that the robots have revolving areas around their start and final positions: that each start and each final is…