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Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external conditions, which are viewed as parameters and form part of the input of the underlying…

Algebraic Topology · Mathematics 2021-10-15 Daniel C. Cohen , Michael Farber , Shmuel Weinberger

r-gathering problem is a variant of facility location problems. In this problem, we are given a set of users and a set of facilities on same metric space. We open some of the facilities and assign each user to an open facility, so that at…

Data Structures and Algorithms · Computer Science 2019-07-10 Soh Kumabe , Takanori Maehara

We suggest necessary conditions of soficness of multidimensional shifts formulated in termsof resource-bounded Kolmogorov complexity. Using this technique we provide examples ofeffective and non-sofic shifts on $\mathbb{Z}^2$ with very low…

Discrete Mathematics · Computer Science 2022-05-24 Julien Destombes , Andrei Romashchenko

The complexity of algorithms solving the motion planning problem is measured by a homotopy invariant TC(X) of the configuration space X of the system. Previously known lower bounds for TC(X) use the structure of the cohomology algebra of X.…

Algebraic Topology · Mathematics 2007-07-07 Michael Farber , Mark Grant

We present an algorithm determining where to relocate objects inside a cluttered and confined space while rearranging objects to retrieve a target object. Although methods that decide what to remove have been proposed, planning for the…

Robotics · Computer Science 2020-03-25 Sang Hun Cheong , Brian Y. Cho , Jinhwi Lee , ChangHwan Kim , Changjoo Nam

In warehouse and manufacturing environments, manipulation platforms are frequently deployed at conveyor belts to perform pick and place tasks. Because objects on the conveyor belts are moving, robots have limited time to pick them up. This…

Robotics · Computer Science 2021-01-19 Fahad Islam , Oren Salzman , Aditya Agarwal , Maxim Likhachev

Modern parcel logistic networks are designed to ship demand between given origin, destination pairs of nodes in an underlying directed network. Efficiency dictates that volume needs to be consolidated at intermediate nodes in typical…

Discrete Mathematics · Computer Science 2023-11-10 Madison Van Dyk , Kim Klause , Jochen Koenemann , Nicole Megow

This work introduces PokeRRT, a novel motion planning algorithm that demonstrates poking as an effective non-prehensile manipulation skill to enable fast manipulation of objects and increase the size of a robot's reachable workspace. Our…

Robotics · Computer Science 2022-03-10 Anuj Pasricha , Yi-Shiuan Tung , Bradley Hayes , Alessandro Roncone

We analyze Solo Chess puzzles, where the input is an $n \times n$ board containing some standard Chess pieces of the same color, and the goal is to make a sequence of capture moves to reduce down to a single piece. Prior work analyzes this…

Computational Complexity · Computer Science 2023-02-06 Josh Brunner , Lily Chung , Michael Coulombe , Erik D. Demaine , Timothy Gomez , Jayson Lynch

In this paper, we present a planner that plans a sequence of base positions for a mobile manipulator to efficiently and robustly collect objects stored in distinct trays. We achieve high efficiency by exploring the common areas where a…

Robotics · Computer Science 2020-10-05 Jingren Xu , Yukiyasu Domae , Toshio Ueshiba , Weiwei Wan , Kensuke Harada

We study the computational complexity of the popular board game backgammon. We show that deciding whether a player can win from a given board configuration is NP-Hard, PSPACE-Hard, and EXPTIME-Hard under different settings of known and…

Computational Complexity · Computer Science 2021-12-15 R. Teal Witter

We present a method that finds locomanipulation plans that perform simultaneous locomotion and manipulation of objects for a desired end-effector trajectory. Key to our approach is to consider a generic locomotion constraint manifold that…

Robotics · Computer Science 2019-09-24 Steven Jens Jorgensen , Mihir Vedantam , Ryan Gupta , Henry Cappel , Luis Sentis

Motion planning trajectories for a multi-limbed robot to climb up walls requires a unique combination of constraints on torque, contact force, and posture. This paper focuses on motion planning for one particular setup wherein a six-legged…

Robotics · Computer Science 2023-08-16 Xuan Lin , Jingwen Zhang , Junjie Shen , Gabriel Fernandez , Dennis W Hong

Manipulation planning and control are relevant building blocks of a robotic system and their tight integration is a key factor to improve robot autonomy and allows robots to perform manipulation tasks of increasing complexity, such as those…

We consider a set of challenging sequential manipulation puzzles, where an agent has to interact with multiple movable objects and navigate narrow passages. Such settings are notoriously difficult for Task-and-Motion Planners, as they…

Robotics · Computer Science 2024-05-06 Svetlana Levit , Joaquim Ortiz-Haro , Marc Toussaint

The paper surveys topological problems relevant to the motion planning problem of robotics and includes some new results and constructions. First we analyse the notion of topological complexity of configuration spaces which is responsible…

Algebraic Topology · Mathematics 2017-01-10 Michael Farber

We consider the computational complexity of winning this turn (mate-in-1 or "finding lethal") in Hearthstone as well as several other single turn puzzle types introduced in the Boomsday Lab expansion. We consider three natural…

Computational Complexity · Computer Science 2020-10-20 Michael Hoffmann , Jayson Lynch , Andrew Winslow

It has recently been shown that the problem of testing global convexity of polynomials of degree four is {strongly} NP-hard, answering an open question of N.Z. Shor. This result is minimal in the degree of the polynomial when global…

Optimization and Control · Mathematics 2019-03-14 Amir Ali Ahmadi , Georgina Hall

Path planning and collision avoidance are challenging in complex and highly variable environments due to the limited horizon of events. In literature, there are multiple model- and learning-based approaches that require significant…

Robotics · Computer Science 2022-06-22 Carlo Tiseo , Vladimir Ivan , Wolfgang Merkt , Ioannis Havoutis , Michael Mistry , Sethu Vijayakumar

Aerial manipulation combines the maneuverability of multirotors with the dexterity of robotic arms to perform complex tasks in cluttered spaces. Yet planning safe, dynamically feasible trajectories remains difficult due to whole-body…

Robotics · Computer Science 2026-05-18 Lin Yang , Jinwoo Lee , Domenico Campolo , H. Jin Kim , Jeonghyun Byun