Related papers: Parameterization of configuration space obstacles …
In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and…
Unforeseen events are frequent in the real-world environments where robots are expected to assist, raising the need for fast replanning of the policy in execution to guarantee the system and environment safety. Inspired by human behavioural…
Optimal motion planning involves obstacles avoidance where path planning is the key to success in optimal motion planning. Due to the computational demands, most of the path planning algorithms can not be employed for real-time based…
Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…
Motion path planning is an intrinsically geometric problem which is central for design of robot systems. Since the early years of AI, robotics together with computer vision have been the areas of computer science that drove its development.…
Teleoperation systems map operator commands from an input device into some coordinate frame in the remote environment. This frame, which we call a control coordinate system, should be carefully chosen as it determines how operators should…
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…
We propose here a geometric and topological setting for the study of branching effects arising in various fields of research, e.g. in statistical mechanics and turbulence theory. We describe various aspects that appear key points to us, and…
Path planning is a classic problem for autonomous robots. To ensure safe and efficient point-to-point navigation an appropriate algorithm should be chosen keeping the robot's dimensions and its classification in mind. Autonomous robots use…
This work addresses the problem of predicting the motion trajectories of dynamic objects in the environment. Recent advances in predicting motion patterns often rely on machine learning techniques to extrapolate motion patterns from…
Geometric motion planning offers effective and interpretable gait analysis and optimization tools for locomoting systems. However, due to the curse of dimensionality in coordinate optimization, a key component of geometric motion planning,…
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…
Formation control deals with the design of decentralized control laws that stabilize mobile, autonomous agents at prescribed distances from each other. We call any configuration of the agents a target configuration if it satisfies the…
This paper proposes a new set of conditions for exactly representing collision avoidance constraints within optimization-based motion planning algorithms. The conditions are continuously differentiable and therefore suitable for use with…
We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…
The main objective of this paper is to introduce a new method for qualitative analysis of various designs of robot arms. To this end we define the complexity of a map, examine its main properties and develop some methods of computation. In…
In a recent paper (arXiv:math-ph/0609076) the authors investigated the basic global geometry of congruence moduli curves and shape curves of 3-body motions with vanishing angular momentum. Here the study is extended to the case of planary…
This paper develops a new approach for robot motion planning and control in obstacle-laden environments that is inspired by fundamentals of fluid mechanics. For motion planning, we propose a novel transformation between motion space, with…
In this thesis, we propose an alternative characterization of the notion of Configuration Space, which we call Visual Configuration Space (VCS). This new characterization allows an embodied agent (e.g., a robot) to discover its own body…
The parameterisation of rotations in three dimensional Euclidean space is an area of applied mathematics that has long been studied, dating back to the original works of Euler in the 18th century. As such, many ways of parameterising a…