相关论文: A Topologist's View of Kinematic Maps and Manipula…
This paper formally defines a robot system, including its sensing and actuation components, as a general, topological dynamical system. The focus is on determining general conditions under which various environments in which the robot can…
We present an algorithm to compute planar linkage topology and geometry, given a user-specified end-effector trajectory. Planar linkage structures convert rotational or prismatic motions of a single actuator into an arbitrarily complex…
In this paper, we study three relative LS categories of a map and study some of their properties. Then we introduce the `higher topological complexity' and `weak higher topological complexity' of a map. Each of them are homotopy invariants.…
In the present work, irregular complex joints of the human arm are modelled in the computer-aided design environment. Accurately the geometric models of the joints and surrounding bony regions are developed from computed tomography data set…
Autonomous navigation of a mobile robot is a challenging task which requires ability of mapping, localization, path planning and path following. Conventional mapping methods build a dense metric map like an occupancy grid, which is affected…
This paper addresses the problem of picking up only one object at a time avoiding any entanglement in bin-picking. To cope with a difficult case where the complex-shaped objects are heavily entangled together, we propose a topology-based…
Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external conditions, which are viewed as parameters and form part of the input of the underlying…
In this paper, we develop the theory of constrained motion spaces of robotic arms. We compute their homology groups in two cases: when the constraint is a horizontal line and when it is a smooth curve whose motion space is a smooth…
A precise meaning is given to the notion of continuous iteration of a mapping. Usual discrete iterations are extended into a dynamical flow which is a homotopy of them all. The continuous iterate reveals that a dynamical map is formend by…
In order for a bimanual robot to manipulate an object that is held by both hands, it must construct motion plans such that the transformation between its end effectors remains fixed. This amounts to complicated nonlinear equality…
We construct "higher" motion planners for automated systems whose space of states are homotopy equivalent to a polyhedral product space $Z(K,\{(S^{k_i},\star)\})$, e.g. robot arms with restrictions on the possible combinations of…
Topological conjugateness of one dimensional unimodal dynamical systems, which are generated by interval [0, 1] into itself maps are studied. We study the smoothness and differentiability of the conjugacy of symmetrical and non-symmetrical…
Mapping is one of the crucial tasks enabling autonomous navigation of a mobile robot. Conventional mapping methods output a dense geometric map representation, e.g. an occupancy grid, which is not trivial to keep consistent for prolonged…
This article surveys the use of configuration space integrals in the study of the topology of knot and link spaces. The main focus is the exposition of how these integrals produce finite type invariants of classical knots and links. More…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
Parametrized topological complexity is a homotopy invariant that represents the degree of instability of motion planning problem that involves external constraints. We consider the parametrized topological complexity in the case of…
State-of-the-art generalist manipulation policies have enabled the deployment of robotic manipulators in unstructured human environments. However, these frameworks struggle in cluttered environments primarily because they utilize auxiliary…
We introduce a compactification of the group of rigid motions in 3-space derived from the Study model for this group. We use this compactifi-cation in robot kinematics, by considering the boundary of the configuration space of a robot. We…
Maps have always been an essential component of autonomous driving. With the advancement of autonomous driving technology, both the representation and production process of maps have evolved substantially. The article categorizes the…