Related papers: The Parameterized Complexity of Motion Planning fo…
Snake robots are inspired by the ability of biological snakes to move over rock, grass, leaves, soil, up trees, along pavement and more. Their ability to move in multiple distinct environments is due to their legless locomotion strategy,…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
This paper proposes Gait Decomposition (G.D), a method of mathematically decomposing snake movements, and Gait Parameter Gradient (GPG), a method of optimizing decomposed gait parameters. G.D is a method that can express the snake gait…
We discuss approximability and inapproximability in FPT-time for a large class of subset problems where a feasible solution $S$ is a subset of the input data and the value of $S$ is $|S|$. The class handled encompasses many well-known…
The concept of $k$-planarity is extensively studied in the context of Beyond Planarity. A graph is $k$-planar if it admits a drawing in the plane in which each edge is crossed at most $k$ times. The local crossing number of a graph is the…
We study verification problems for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. In particular, we focus in this paper on the model proposed by Suzuki and Yamashita of anonymous robots…
We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems. For the first problem, {\sc $k$-Leaf…
Given a graph $G = (V,E)$, a threshold function $t~ :~ V \rightarrow \mathbb{N}$ and an integer $k$, we study the Harmless Set problem, where the goal is to find a subset of vertices $S \subseteq V$ of size at least $k$ such that every…
We present a fully parallelized grid-based parameter estimation algorithm for investigating multidimensional likelihoods called Snake, and apply it to cosmological parameter estimation. The basic idea is to map out the likelihood grid-cell…
In this paper, we study the back-end of simultaneous localization and mapping (SLAM) problem in deforming environment, where robot localizes itself and tracks multiple non-rigid soft surface using its onboard sensor measurements. An…
This paper proposes a novel method of coverage path planning for the purpose of scanning an unstructured environment autonomously. The method uses the morphological skeleton of the prior 2D navigation map via SLAM to generate a sequence of…
Snakes can traverse almost all types of environments by bending their elongate bodies in 3-D to interact with the terrain. Similarly, a snake robot is a promising platform to perform critical tasks in various environments. Understanding how…
Robot navigation within complex environments requires precise state estimation and localization to ensure robust and safe operations. For ambulating mobile robots like robot snakes, traditional methods for sensing require multiple embedded…
Multi-robot motion planning is a hard problem. We investigate restricted variants of the problem where square robots are allowed to slide over an arbitrary curve to a new position only a constant number of times each. We show that the…
We study the Steiner Tree problem on the intersection graph of most natural families of geometric objects, e.g., disks, squares, polygons, etc. Given a set of $n$ objects in the plane and a subset $T$ of $t$ terminal objects, the task is to…
We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their…
Robotic and animal mapping systems share many challenges and characteristics: they must function in a wide variety of environmental conditions, enable the robot or animal to navigate effectively to find food or shelter, and be…
This paper presents an optimization-based motion planning methodology for snake robots operating in constrained environments. By using a reduced-order model, the proposed approach simplifies the planning process, enabling the optimizer to…
Path planning for multiple robots is well studied in the AI and robotics communities. For a given discretized environment, robots need to find collision-free paths to a set of specified goal locations. Robots can be fully anonymous,…
Over the years, much research involving mobile computational entities has been performed. From modeling actual microscopic (and smaller) robots, to modeling software processes on a network, many important problems have been studied in this…