Related papers: Minimizing Movement: Fixed-Parameter Tractability

The sequential allocation protocol is a simple and popular mechanism to allocate indivisible goods, in which the agents take turns to pick the items according to a predefined sequence. While this protocol is not strategy-proof, it has been…

This paper presents a trajectory generation method for contact-constrained robotic systems such as manipulators and legged robots. Contact-constrained systems are affected by the interaction forces between the robot and the environment. In…

Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…

The effectiveness of a robot manipulation to a large extent is determined by the speed of making this or that movement needed for carrying out the task. Accordingly to this the problem of optimal robot control is often subdivided into two…

Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…

Instabilities of robot motion are caused by topological reasons. In this paper we find a relation between the topological properties of a configuration space (the structure of its cohomology algebra) and the character of instabilities,…

We investigate the problem of monitoring multiple targets using a single mobile sensor, with the goal of minimizing the maximum estimation error among all the targets over long time horizons. The sensor can move in a network-constrained…

We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…

Task and motion planning represents a powerful set of hybrid planning methods that combine reasoning over discrete task domains and continuous motion generation. Traditional reasoning necessitates task domain models and enough information…

The task of rendezvous (also called {\em gathering}) calls for a meeting of two or more mobile entities, starting from different positions in some environment. Those entities are called mobile agents or robots, and the environment can be a…

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…

We study the algorithmic problem of optimally covering a tree with $k$ mobile robots. The tree is known to all robots, and our goal is to assign a walk to each robot in such a way that the union of these walks covers the whole tree. We…

We consider the localization problem between agents while they run a formation control algorithm. These algorithms typically demand from the agents the information about their relative positions with respect to their neighbors. We assume…

Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…

Parametric models abstract part of the specification of dynamical models by integral parameters. They are for example used in computational systems biology, notably with parametric regulatory networks, which specify the global architecture…

This paper studies the problem of detection and tracking of general objects with long-term dynamics, observed by a mobile robot moving in a large environment. A key problem is that due to the environment scale, it can only observe a subset…

We address an optimal reachability problem for a planar manipulator in a constrained environment. After introducing the optmization problem in full generality, we practically embed the geometry of the workspace in the problem, by…

The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting…

Planning motions to grasp an object in cluttered and uncertain environments is a challenging task, particularly when a collision-free trajectory does not exist and objects obstructing the way are required to be carefully grasped and moved…

Imagine we want to split a group of agents into teams in the most \emph{efficient} way, considering that each agent has their own preferences about their teammates. This scenario is modeled by the extensively studied \textsc{Coalition…