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We present a fixed-parameter tractable (FPT) algorithm to find a shortest curve that encloses a set of k required objects in the plane while paying a penalty for enclosing unwanted objects. The input is a set of interior-disjoint simple…
We describe an algorithm for solving an important geometric problem arising in computer-aided manufacturing. When cutting away a region from a solid piece of material -- such as steel, wood, ceramics, or plastic -- using a rough tool in a…
We consider the problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We…
As robots are being increasingly used in close proximity to humans and objects, it is imperative that robots operate safely and efficiently under real-world conditions. Yet, the environment is seldom known perfectly. Noisy sensors and…
Multi-robot systems are increasingly being used for critical applications such as rescuing injured people, delivering food and medicines, and monitoring key areas. These applications usually involve navigating at high speeds through…
Decentralized multi-robot systems typically perform coordinated motion planning by constantly broadcasting their intentions as a means to cope with the lack of a central system coordinating the efforts of all robots. Especially in complex…
Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem…
We study computationally-hard fundamental motion planning problems where the goal is to translate $k$ axis-aligned rectangular robots from their initial positions to their final positions without collision, and with the minimum number of…
Given a set of $n$ points in the plane, and a parameter $k$, we consider the problem of computing the minimum (perimeter or area) axis-aligned rectangle enclosing $k$ points. We present the first near quadratic time algorithm for this…
Coordinating the motion of multiple robots in cluttered environments remains a computationally challenging task. We study the problem of minimizing the execution time of a set of geometric paths by a team of robots with state-dependent…
Trajectory retiming is the task of computing a feasible time parameterization to traverse a path. It is commonly used in the decoupled approach to trajectory optimization whereby a path is first found, then a retiming algorithm computes a…
Building structures can allow a robot to surmount large obstacles, expanding the set of areas it can reach. This paper presents a planning algorithm to automatically determine what structures a construction-capable robot must build in order…
Effective evacuation policies in emergency situations are important to save lives. To develop such policies, simulation models based on cellular automata have been used for crowd evacuation dynamics. In most previous studies of crowd…
We study the problem of tracking multiple moving targets using a team of mobile robots. Each robot has a set of motion primitives to choose from in order to collectively maximize the number of targets tracked or the total quality of…
Decentralized control of robots has attracted huge research interests. However, some of the research used unrealistic assumptions without collision avoidance. This report focuses on the collision-free control for multiple robots in both…
For enabling efficient, large-scale coordination of unmanned aerial vehicles (UAVs) under the labeled setting, in this work, we develop the first polynomial time algorithm for the reconfiguration of many moving bodies in three-dimensional…
In this paper, we have considered two fully synchronous $\mathcal{OBLOT}$ robots having no agreement on coordinates entering a finite unoriented grid through a door vertex at a corner, one by one. There is a resource that can move around…
We study the problem of optimal multi-robot path planning on graphs (MPP) over four distinct minimization objectives: the total arrival time, the makespan (last arrival time), the total distance, and the maximum (single-robot traveled)…
Nowadays, robots are increasingly operated in environments shared with humans, where conflicts between human and robot behaviors may compromise safety. This paper presents a proactive behavioral conflict avoidance framework based on the…
The current best approximation algorithms for $k$-median rely on first obtaining a structured fractional solution known as a bi-point solution, and then rounding it to an integer solution. We improve this second step by unifying and…