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The number of multi-robot systems deployed in field applications has increased dramatically over the years. Despite the recent advancement of navigation algorithms, autonomous robots often encounter challenging situations where the control…
Safe reinforcement learning aims to learn the optimal policy while satisfying safety constraints, which is essential in real-world applications. However, current algorithms still struggle for efficient policy updates with hard constraint…
We study the path planning problem for continuum-arm robots, in which we are given a starting and an end point, and we need to compute a path for the tip of the continuum arm between the two points. We consider both cases where obstacles…
In this paper a search algorithm is proposed to find a sub optimal path for a non-holonomic system. For this purpose the algorithm starts sampling the front part of the vehicle and moves towards the destination with a cost function. The…
This paper studies a class of multi-robot coordination problems where a team of robots aim to reach their goal regions with minimum time and avoid collisions with obstacles and other robots. A novel numerical algorithm is proposed to…
The quantum query complexity of subgraph-containment problems, which ask whether a given subgraph $H$ is present in an input graph $G$, has been the subject of considerable study. However, even for relatively simple subgraphs, such as paths…
Efficient motion planning algorithms are of central importance for deploying robots in the real world. Unfortunately, these algorithms often drastically reduce the dimensionality of the problem for the sake of feasibility, thereby foregoing…
We propose a novel centralized and decoupled algorithm, DDM, for solving multi-robot path planning problems in grid graphs, targeting on-demand and automated warehouse-like settings. Two settings are studied: a traditional one whose…
We consider the rooted orienteering problem in Euclidean space: Given $n$ points $P$ in $\mathbb R^d$, a root point $s\in P$ and a budget $\mathcal B>0$, find a path that starts from $s$, has total length at most $\mathcal B$, and visits as…
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ to minimize the radius of the resulting graph. Previously, a similar problem for minimizing the diameter of the graph…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…
We study the computational complexity of optimally solving multi-robot path planning problems on planar graphs. For four common time- and distance-based objectives, we show that the associated path optimization problems for multiple robots…
We study the approximability of two related problems on graphs with $n$ nodes and $m$ edges: $n$-Pairs Shortest Paths ($n$-PSP), where the goal is to find a shortest path between $O(n)$ prespecified pairs, and All Node Shortest Cycles…
Designing good heuristic functions for graph search requires adequate domain knowledge. It is often easy to design heuristics that perform well and correlate with the underlying true cost-to-go values in certain parts of the search space…
We consider the motion-planning 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…
Fastest-path queries between two points in a very large road map is an increasingly important primitive in modern transportation and navigation systems, thus very efficient computation of these paths is critical for system performance and…
Approximate computing is a computation domain which can be used to trade time and energy with quality and therefore is useful in embedded systems. Energy is the prime resource in battery-driven embedded systems, like robots. Approximate…