Related papers: A Discrete Topological Complexity of Discrete Moti…
Ground robots navigating in complex, dynamic environments must compute collision-free trajectories to avoid obstacles safely and efficiently. Nonconvex optimization is a popular method to compute a trajectory in real-time. However, these…
Morphological computing, the use of the physical design of a robot to ease the realization of a given task has been proven to be a relevant concept in the context of swarm robotics. Here we demonstrate both experimentally and numerically,…
We study discrete orderings in the real spectrum of a commutative ring by defining discrete prime cones and give an algebro-geometric meaning to some kind of diophantine problems over discretely ordered rings. Also for a discretely ordered…
Action planning using learned and differentiable forward models of the world is a general approach which has a number of desirable properties, including improved sample complexity over model-free RL methods, reuse of learned models across…
For successful goal-directed human-robot interaction, the robot should adapt to the intentions and actions of the collaborating human. This can be supported by musculoskeletal or data-driven human models, where the former are limited to…
The higher topological complexity of a space $X$, $\text{TC}_r(X)$, $r=2,3,\ldots$, and the topological complexity of a map $f$, $\text{TC}(f)$, have been introduced by Rudyak and Pave\v{s}i\'{c}, respectively, as natural extensions of…
In this paper, we investigate a discrete version of the homotopic distance between two $s$-Lipschitz maps for $s \geq 0$. This distance is defined by specifying a step length $r$ to which some homotopy relation corresponds. In spaces with a…
Discrete homotopy theory or A-homotopy theory is a combinatorial homotopy theory defined on graphs, simplicial complexes, and metric spaces, reflecting information about their connectivity. The present paper aims to further understand the…
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 this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well-understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is…
We focus on robot navigation in crowded environments. The challenge of predicting the motion of a crowd around a robot makes it hard to ensure human safety and comfort. Recent approaches often employ end-to-end techniques for robot control…
Motion planning is a fundamental problem in autonomous robotics that requires finding a path to a specified goal that avoids obstacles and takes into account a robot's limitations and constraints. It is often desirable for this path to also…
The complexity of a legged robot's environment or task can inform how specialised its gait must be to ensure success. Evolving specialised robotic gaits demands many evaluations - acceptable for computer simulations, but not for physical…
Recent advancements in robotics have transformed industries such as manufacturing, logistics, surgery, and planetary exploration. A key challenge is developing efficient motion planning algorithms that allow robots to navigate complex…
Motion planning under sensing uncertainty is critical for robots in unstructured environments to guarantee safety for both the robot and any nearby humans. Most work on planning under uncertainty does not scale to high-dimensional robots…
Complex motions for robots are frequently generated by switching among a collection of individual movement primitives. We use this approach to formulate robot motion plans as sequences of primitives to be executed one after the other. When…
Robot deployment in realistic dynamic environments is a challenging problem despite the fact that robots can be quite skilled at a large number of isolated tasks. One reason for this is that robots are rarely equipped with powerful…
Recent advancements in self-driving car technologies have enabled them to navigate autonomously through various environments. However, one of the critical challenges in autonomous vehicle operation is trajectory planning, especially in…
For a pair of spaces $X$ and $Y$ such that $Y \subseteq X$, we define the relative topological complexity of the pair $(X,Y)$ as a new variant of relative topological complexity. Intuitively, this corresponds to counting the smallest number…
The topological hypothesis claims that phase transitions in a classical statistical mechanical system are related to changes in the topology of the level sets of the Hamiltonian. So far, the study of this hypothesis has been restricted to…