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We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. For the unweighted case, we prove that a local search algorithm yields a \PTAS. For the weighted case,…
In this paper, we present a novel approach to efficiently generate collision-free optimal trajectories for multiple non-holonomic mobile robots in obstacle-rich environments. Our approach first employs a graph-based multi-agent path planner…
We consider the speed planning problem for a robotic manipulator. In particular, we present an algorithm for finding the time-optimal speed law along an assigned path that satisfies velocity and acceleration constraints and respects the…
This paper introduces an optimization problem (P) and a solution strategy to design variable-speed-limit controls for a highway that is subject to traffic congestion and uncertain vehicle arrival and departure. By employing a finite…
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…
We propose distributed algorithms to automatically deploy a team of mobile robots to partition and provide coverage of a non-convex environment. To handle arbitrary non-convex environments, we represent them as graphs. Our partitioning and…
We consider the problem of computing shortest paths in a dense motion-planning roadmap $\mathcal{G}$. We assume that~$n$, the number of vertices of $\mathcal{G}$, is very large. Thus, using any path-planning algorithm that directly searches…
Let $\mathcal{W} \subset \mathbb{R}^2$ be a planar polygonal environment (i.e., a polygon potentially with holes) with a total of $n$ vertices, and let $A,B$ be two robots, each modeled as an axis-aligned unit square, that can translate…
This paper considers three related mobile robot multi-target sensory coverage and inspection planning problems in 2-D environments. In the first problem, a mobile robot must find the shortest path to observe multiple targets with a limited…
Robust motion planning is a well-studied problem in the robotics literature, yet current algorithms struggle to operate scalably and safely in the presence of other moving agents, such as humans. This paper introduces a novel framework for…
To operate reactively in uncertain environments, robots need to be able to quickly estimate the risk that they will collide with their environment. This ability is important for both planning (to ensure that plans maintain acceptable levels…
This paper addresses an Optimal Transport (OT)-based efficient multi-robot exploration problem, considering the energy constraints of a multi-robot system. The efficiency in this problem implies how a team of robots (agents) covers a given…
If we give a robot the task of moving an object from its current position to another location in an unknown environment, the robot must explore the map, identify all types of obstacles, and then determine the best route to complete the…
In this paper, we present a polynomial-time algorithm that approximates sufficiently high-value Max 2-CSPs on sufficiently dense graphs to within $O(N^{\varepsilon})$ approximation ratio for any constant $\varepsilon > 0$. Using this…
We study the demand-robust fleet size vehicle routing problem with time windows and compatibility constraints. Unlike traditional robust optimization, which considers uncertainty in the data, demand-robust optimization considers uncertainty…
Mobility-on-demand (MoD) ridesharing is a promising way to improve the occupancy rate of personal vehicles and reduce traffic congestion and emissions. Maximizing the number of passengers served and maximizing a profit target are major…
We consider the following problem of labeling points in a dynamic map that allows rotation. We are given a set of points in the plane labeled by a set of mutually disjoint labels, where each label is an axis-aligned rectangle attached with…
We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…
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 task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…