Related papers: Optimal online escape path against a certificate
A watchman path is a path such that a direct line of sight exists between each point in some region and some point along the path. Here, we study the online watchman path problem outside a convex polygon, i.e., in $\mathbb{R}^2\setminus…
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…
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 the problem of planning a safe (i.e., collision-free) trajectory from an initial state to a goal region when the obstacle space is a-priori unknown and is incrementally revealed online, e.g., through line-of-sight…
Recent papers have shown optimally-competitive on-line strategies for a robot traveling from a point $s$ to a point $t$ in certain unknown geometric environments. We consider the question: Having gained some partial information about the…
We study online competitive algorithms for the \emph{line chasing problem} in Euclidean spaces $\reals^d$, where the input consists of an initial point $P_0$ and a sequence of lines $X_1,X_2,...,X_m$, revealed one at a time. At each step…
In this paper, we propose a new method for path planning to a point for robot in environment with obstacles. The resulting algorithm is implemented as a simple variation of Dijkstra's algorithm. By adding a constraint to the shortest-path,…
We consider how to directly extract a road map (also known as a topological representation) of an initially-unknown 2-dimensional environment via an online procedure that robustly computes a retraction of its boundaries. In this article, we…
The classical setting of optimal control theory assumes full knowledge of the process dynamics and the costs associated with every control strategy. The problem becomes much harder if the controller only knows a finite set of possible…
While maximizing line-of-sight coverage of specific regions or agents in the environment is a well-explored path planning objective, the converse problem of minimizing exposure to the entire environment during navigation is especially…
This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport…
Pedestrians often need to decide between different routes they can use to reach their intended destinations, both during emergencies and in their daily lives. This route-choice behavior is important in determining traffic management,…
We consider a perimeter defense problem in a rooted full tree graph environment in which a single defending vehicle seeks to defend a set of specified vertices, termed as the perimeter from mobile intruders that enter the environment…
Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in…
The optimal strategies to catch a randomly walking cat in various environments are presented. All games have a player that opens a box at step $i$. If the cat is in this box the player wins, if not, the cat moves randomly to an adjacent…
Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…
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…
Define an environment as a set of convex constraint functions that vary arbitrarily over time and consider a cost function that is also convex and arbitrarily varying. Agents that operate in this environment intend to select actions that…
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…
In this paper, we study the problem of coverage planning by a mobile robot with a limited energy budget. The objective of the robot is to cover every point in the environment while minimizing the traveled path length. The environment is…