相关论文: A Topologist's View of Kinematic Maps and Manipula…

The purpose of this work is twofold: to present mathematical expressions for the kinematics of an articulated mechanism and to perform numerical experiments with the implemented code. The system of rigid parts is made of two slender bars…

Topological complexity $\TC{B}$ of a space $B$ is introduced by M. Farber to measure how much complex the space is, which is first considered on a configuration space of a motion planning of a robot arm. We also consider a stronger version…

Given a compact manifold with boundary with unknown Riemannian metric. The problem is to reconstruct the metric in a class of conformal metrics from knowledge of lengths of all closed geodesics (kinematic data). An integral inequality is…

Planning for multi-robot teams in complex environments is a challenging problem, especially when these teams must coordinate to accomplish a common objective. In general, optimal solutions to these planning problems are computationally…

We study a probabilistic variant of the r-th sequential parametrized topological complexity, which bounds this classical invariant from below and measures the difficulty in constructing permissive parametrized motion planning algorithms. On…

Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in…

This paper considers the task of locating articulated poses of multiple robots in images. Our approach simultaneously infers the number of robots in a scene, identifies joint locations and estimates sparse depth maps around joint locations.…

A map is a connected topological graph cellularly embedded in a surface and a complete map is a cellularly embedded complete graph in a surface. In this paper, all automorphisms of complete maps of order n are determined by permutations on…

Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold…

In this paper, we introduce relative LS category of a map and study some of its properties. Then we introduce `higher topological complexity' of a map, a homotopy invariant. We give a cohomological lower bound and compare it with previously…

We consider the maximal number of arbitrary points in a special fibre that can be simultaneously approached by points in one sequence of general fibres. Several results about this topological invariant and their applications describe the…

While soft robot manipulators offer compelling advantages over rigid counterparts, including inherent compliance, safe human-robot interaction, and the ability to conform to complex geometries, accurate forward modeling from low-dimensional…

Task planning and motion planning are two of the most important problems in robotics, where task planning methods help robots achieve high-level goals and motion planning methods maintain low-level feasibility. Task and motion planning…

Many mechanical systems exhibit changes in their kinematic topology altering the mobility. Ideal contact is the best known cause, but also stiction and controlled locking of parts of a mechanism lead to topology changes. The latter is…

Autonomous robotic inspection, where a robot moves through its environment and inspects points of interest, has applications in industrial settings, structural health monitoring, and medicine. Planning the paths for a robot to safely and…

We study an extensive class of movement minimization problems which arise from many practical scenarios but so far have little theoretical study. In general, these problems involve planning the coordinated motion of a collection of agents…

Topological complexity is a numerical homotopy invariant that measures the instability of motion planning in a space. To study the topological complexity of non-simply connected spaces, Costa and Farber introduced a cohomology class whose…

A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…

The present paper aims at analyzing the topological content of the complex trajectories that weeder-autonomous robots follow in operation. We will prove that the topological descriptors of these trajectories are affected by the robot…

Motion planning schemes are used for planning motions of a manipulator from an initial pose to a final pose during a task execution. A motion planning scheme generally comprises of a trajectory planning method and an inverse kinematic…