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Topological complexity for spaces was introduced by M. Farber as a minimal number of continuity domains for motion planning algorithms. It turns out that this notion can be extended to the case of not necessarily commutative C*-algebras.…
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…
We present a new approach to equivariant version of the topological complexity, called a symmetric topological complexity. It seems that the presented approach is more adequate for the analysis of an impact of symmetry on the the motion…
We compute the Lusternik-Schnirelmann category and the topological complexity of no $k$-equal manifolds $M^{(k)}_d(n)$ for certain values of $d$, $k$ and $n$. This includes instances where $M^{(k)}_d(n)$ is known to be rationally…
This work addresses the problem of multi-robot coordination under unknown robot transition models, ensuring that tasks specified by Time Window Temporal Logic are satisfied with user-defined probability thresholds. We present a bi-level…
This study examines the problem of hopping robot navigation planning to achieve simultaneous goal-directed and environment exploration tasks. We consider a scenario in which the robot has mandatory goal-directed tasks defined using Linear…
This paper explores topological complexity in the finite equivariant setting. We first define and study an equivariant version of Tanaka's combinatorial complexity for finite topological spaces. We explore the relationships between this…
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.…
In order to solve complex, long-horizon tasks, intelligent robots need to carry out high-level, abstract planning and reasoning in conjunction with motion planning. However, abstract models are typically lossy and plans or policies computed…
This paper studies motion planning of a mobile robot under uncertainty. The control objective is to synthesize a {finite-memory} control policy, such that a high-level task specified as a Linear Temporal Logic (LTL) formula is satisfied…
This paper addresses two intertwined needs for collaborative robots operating in shop-floor environments. The first is the ability to perform complex manipulation operations, such as those on articulated or even flexible objects, in a way…
This survey focuses on the computational complexity of some of the fundamental decision problems in 3-manifold theory. The article discusses the wide variety of tools that are used to tackle these problems, including normal and almost…
In this paper we introduce the concepts of higher equivariant and invariant topological complexity; and study their properties. Then we compare them with equivariant LS-category. We give lower and upper bounds for these new invariants. We…
This is a glossary of notions and methods related with the topological theory of collections of affine planes, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial resolutions, complexes of…
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 paper considers multi-goal motion planning in unstructured, obstacle-rich environments where a robot is required to reach multiple regions while avoiding collisions. The planned motions must also satisfy the differential constraints…
We develop a homotopical framework for small categories that extends classical invarints of algebraic topology to the categorical setting. Our approach is based on the construction of genuine path category, obtained trough a localization…
When designing a motion planner for autonomous robots there are usually multiple objectives to be considered. However, a cost function that yields the desired trade-off between objectives is not easily obtainable. A common technique across…
We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on…
Automation applications are pushing the deployment of many high DoF manipulators in warehouse and manufacturing environments. This has motivated many efforts on optimizing manipulation tasks involving a single arm. Coordinating multiple…