Related papers: A Discrete Topological Complexity of Discrete Moti…
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…
We introduce the geodesic complexity of a metric space, inspired by the topological complexity of a topological space. Both of them are numerical invariants, but, while the TC only depends on the homotopy type, the GC is an invariant under…
This paper presents Latent Sampling-based Motion Planning (L-SBMP), a methodology towards computing motion plans for complex robotic systems by learning a plannable latent representation. Recent works in control of robotic systems have…
Planning of any motion starts by planning the trajectory of the CoM. It is of the highest importance to ensure that the robot will be able to perform planned trajectory. With increasing capabilities of the humanoid robots, the case when…
We introduce the digital projective product spaces based on Davis' projective product spaces. We determine an upper bound for the digital LS-category of the digital projective product spaces. In addition, we obtain an upper bound for the…
This paper addresses the problem of coordination of a fleet of mobile robots - the problem of finding an optimal set of collision-free trajectories for individual robots in the fleet. Many approaches have been introduced during the last…
Effective motion planning in high dimensional spaces is a long-standing open problem in robotics. One class of traditional motion planning algorithms corresponds to potential-based motion planning. An advantage of potential based motion…
In this short note we observe that the higher topological complexity of an iterated connected sum of real projective spaces is maximal possible. Unlike the case of regular TC, the result is accessible through easy mod 2 zero-divisor…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
We describe and implement a randomized algorithm that inputs a polyhedron, thought of as the space of states of some automated guided vehicle $\mathcal{R}$, and outputs an explicit system of piecewise linear motion planners for…
Trajectory prediction in a cluttered environment is key to many important robotics tasks such as autonomous navigation. However, there are an infinite number of possible trajectories to consider. To simplify the space of trajectories under…
This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…
In terms of Rudyak's generalization of Farber's topological complexity of the path motion planning problem in robotics, we give a complete description of the topological instabilities in any sequential motion planning algorithm for a system…
Robotic manipulation in complex, constrained spaces is vital for widespread applications but challenging, particularly when navigating narrow passages with elongated objects. Existing planning methods often fail in these low-clearance…
Continuum robots, characterized by their high flexibility and infinite degrees of freedom (DoFs), have gained prominence in applications such as minimally invasive surgery and hazardous environment exploration. However, the intrinsic…
The problem of planning for a robot that operates in environments containing a large number of objects, taking actions to move itself through the world as well as to change the state of the objects, is known as task and motion planning…
Most animal and human locomotion behaviors for solving complex tasks involve dynamic motions and rich contact interaction. In fact, complex maneuvers need to consider dynamic movement and contact events at the same time. We present a…
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 present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…
Sequential parametrized topological complexity is a numerical homotopy invariant of a fibration, which arose in the robot motion planning problem with external constraints. In this paper, we study sequential parametrized topological…