Related papers: A randomized greedy algorithm for piecewise linear…
Using the notion of contiguity of simplicial maps, we adapt Farber's topological complexity to the realm of simplicial complexes. We show that, for a finite simplicial complex $K$, our discretized concept recovers the topological complexity…
The Topological complexity a la Farber $\text{TC}(-)$ is a homotopy invariant which have interesting applications in Robotics, specifically, in the robot motion planning problem. In this work we calculate the topological complexity of the…
We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of…
In this paper we develop theory of sequential parametrized motion planning which generalises the approach of parametrized motion planning, which was introduced recently in [3]. A sequential parametrized motion planning algorithm produced a…
We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as…
This paper proposes a method for solving multivariate regression and classification problems using piecewise linear predictors over a polyhedral partition of the feature space. The resulting algorithm that we call PARC (Piecewise Affine…
We propose a randomized greedy search algorithm to find a point estimate for a random partition based on a loss function and posterior Monte Carlo samples. Given the large size and awkward discrete nature of the search space, the…
This is a continuation of our recent paper in which we developed the theory of sequential parametrized motion planning. A sequential parametrized motion planning algorithm produced a motion of the system which is required to visit a…
Greedy Sampling Methods (GSMs) are widely used to construct approximate solutions of Configuration Optimization Problems (COPs), where a loss functional is minimized over finite configurations of points in a compact domain. While effective…
We present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its…
A greedy algorithm is proposed for sparse-sensor selection in reduced-order sensing that contains correlated noise in measurement. The sensor selection is carried out by maximizing the determinant of the Fisher information matrix in a…
In robotics, a topological theory of motion planning was initiated by M. Farber. The multitasking motion planning problem is new and its theoretical part via topological complexity has hardly been developed, but the concrete implementations…
Probabilistic variants of Model Order Reduction (MOR) methods have recently emerged for improving stability and computational performance of classical approaches. In this paper, we propose a probabilistic Reduced Basis Method (RBM) for the…
In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…
This letter presents a novel coarse-to-fine motion planning framework for robotic manipulation in cluttered, unmodeled environments. The system integrates a dual-camera perception setup with a B-spline-based model predictive control (MPC)…
We consider optimal sensor placement for a family of linear Bayesian inverse problems characterized by a deterministic hyper-parameter. The hyper-parameter describes distinct configurations in which measurements can be taken of the observed…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
In this paper we study paramertized motion planning algorithms which provide universal and flexible solutions to diverse motion planning problems. Such algorithms are intended to function under a variety of external conditions which are…
This paper studies motion planning of a mobile robot under uncertainty. The control objective is to synthesize a {finite-memory} control policy, such that a high-level task specified as a Linear Temporal Logic (LTL) formula is satisfied…
We present a centralized algorithmic framework for solving multi-robot path planning problems in general, two-dimensional, continuous environments while minimizing globally the task completion time. The framework obtains high levels of…