Related papers: Computing Feasible Trajectories for an Articulated…
In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the…
We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by…
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We present a simple randomized scheme for triangulating a set $P$ of $n$ points in the plane, and construct a kinetic data structure which maintains the triangulation as the points of $P$ move continuously along piecewise algebraic…
The Distance Geometry Problem asks for a realization of a given weighted graph in $\mathbb{R}^K$. Two variants of this problem, both originating from protein conformation, are based on a given vertex order (which abstracts the protein…
We study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem. For the problem of finding the closest point in the…
Consider two entities with constant but not necessarily equal velocities, moving on two given piece-wise linear trajectories inside a simple polygon $P$. The Trajectory Range Visibility problem deals with determining the sub-trajectories on…
Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$…
An extremity is a vertex such that the removal of its closed neighbourhood does not increase the number of connected components. Let $Ext_{\alpha}$ be the class of all connected graphs whose quotient graph obtained from modular…
The paper is devoted to studying the performance of a computational pipeline, the number of simultaneously executing stages of which at each time is bounded from above by a fixed number. A look at the restriction as a structural hazard…
Safety is a critical concern for the success of urban air mobility, especially in dynamic and uncertain environments. This paper proposes a path planning algorithm based on RRT in conjunction with chance constraints in the presence of…
We propose an algorithm for an optimal adaptive selection of points from the design domain of input random variables that are needed for an accurate estimation of failure probability and the determination of the boundary between safe and…
A combinatorial optimization problem (COP) has a finite groundset $E(\left|E\right|=N$), a weight vector $c=\left(c^e:e\in E\right)$ and a family $T\in E$ of feasible subsets with objective to find $t\in T$ with maximal weight:…
Collision-free mobile robot navigation is an important problem for many robotics applications, especially in cluttered environments. In such environments, obstacles can be static or dynamic. Dynamic obstacles can additionally be…
Generating safe motion plans in real-time is necessary for the wide-scale deployment of robots in unstructured and human-centric environments. These motion plans must be safe to ensure humans are not harmed and nearby objects are not…
High-speed trajectory planning through unknown environments requires algorithmic techniques that enable fast reaction times while maintaining safety as new information about the operating environment is obtained. The requirement of…
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…
Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…
In this work, we propose a trajectory generation method for robotic systems with contact force constraint based on optimal control and reachability analysis. Normally, the dynamics and constraints of the contact-constrained robot are…
We study the problem of planning paths for $p$ distinguishable pebbles (robots) residing on the vertices of an $n$-vertex connected graph with $p \le n$. A pebble may move from a vertex to an adjacent one in a time step provided that it…