Related papers: Oriented robot motion planning in Riemannian manif…
In this paper we generalize the discrete r-homotopy to the discrete (s, r)-homotopy. Then by this notion, we introduce the discrete motion planning for robots which can move discreetly. Moreover, in this case the number of motion planning,…
In this paper, we deal with the robot motion planning problem in multi-valued function theory. We first enrich the multi-homotopy studies by introducing a multi-homotopy lifting property and a multi-fibration. Then we compute both a…
Solving the inverse kinematics problem is a fundamental challenge in motion planning, control, and calibration for articulated robots. Kinematic models for these robots are typically parametrized by joint angles, generating a complicated…
We study the topological complexity of work maps with respect to some subspaces of the configuration space and a workspace considered as the target set of the motion of robots. The motivation is to optimize and reduce the number of motion…
In this paper we study symmetric motion planning algorithms, i.e. such that the motion from one state A to another B, prescribed by the algorithm, is the time reverse of the motion from B to A. We experiment with several different notions…
We give an explicit formula for the holonomy of the orientation bundle of a family of real Cauchy-Riemann operators. A special case of this formula resolves the orientability question for spaces of maps from Riemann surfaces with Lagrangian…
Multi-robot motion planning (MRMP) is the problem of finding collision-free paths for a set of robots in a continuous state space. The difficulty of MRMP increases with the number of robots and is exacerbated in environments with narrow…
Autonomous motion of a system (robot) is controlled by a motion planning algorithm. A sequential parametrized motion planning algorithm \cite{FP22} works under variable external conditions and generates continuous motions of the system to…
In many robot motion planning problems, task objectives and physical constraints induce non-Euclidean geometry on the configuration space, yet many planners operate using Euclidean distances that ignore this structure. We address the…
In this paper we combine a survey of the most important topological properties of kinematic maps that appear in robotics, with the exposition of some basic results regarding the topological complexity of a map. In particular, we discuss…
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…
Motion planning is a difficult problem in robot control. The complexity of the problem is directly related to the dimension of the robot's configuration space. While in many theoretical calculations and practical applications the…
We study certain topological problems that are inspired by applications to autonomous robot manipulation. Consider a continuous map $f\colon X\to Y$, where $f$ can be a kinematic map from the configuration space $X$ to the working space $Y$…
We address the problem of planning robot motions in constrained configuration spaces where the constraints change throughout the motion. The problem is formulated as a fixed sequence of intersecting manifolds, which the robot needs to…
Despite the attention that the problem of path planning for tethered robots has garnered in the past few decades, the approaches proposed to solve it typically rely on a discrete representation of the configuration space and do not exploit…
Task And Motion Planning (TAMP) is the problem of finding a solution to an automated planning problem that includes discrete actions executable by low-level continuous motions. This field is gaining increasing interest within the robotics…
This is a continuation of our recent paper in which we developed the theory of sequential parametrized motion planning. A sequential parametrized motion planning algorithm produced a motion of the system which is required to visit a…
We compute the higher topological complexity of ordered configuration spaces of orientable surfaces, thus extending Cohen-Farber's description of the ordinary topological complexity of those spaces.
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…
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…