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We present a fully distributed collision avoidance algorithm based on convex optimization for a team of mobile robots. This method addresses the practical case in which agents sense each other via measurements from noisy on-board sensors…
Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or…
The set of 2-dimensional packing problems builds an important class of optimization problems and Strip Packing together with 2-dimensional Bin Packing and 2-dimensional Knapsack is one of the most famous of these problems. Given a set of…
We propose factor graph optimization for simultaneous planning, control, and trajectory estimation for collision-free navigation of autonomous systems in environments with moving objects. The proposed online probabilistic motion planning…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
We deal with the problem of planning collision-free trajectories for robots operating in a shared space. Given the start and destination position for each of the robots, the task is to find trajectories for all robots that reach their…
We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…
We present a fast algorithm for the design of smooth paths (or trajectories) that are constrained to lie in a collection of axis-aligned boxes. We consider the case where the number of these safe boxes is large, and basic preprocessing of…
We consider the NP-hard problem of MAP-inference for undirected discrete graphical models. We propose a polynomial time and practically efficient algorithm for finding a part of its optimal solution. Specifically, our algorithm marks some…
To identify the robust settings of the control factors, it is very important to understand how they interact with the noise factors. In this article, we propose space-filling designs for computer experiments that are more capable of…
We present an efficient algorithm to compute tight upper bounds of collision probability between two objects with positional uncertainties, whose error distributions are represented with non-Gaussian forms. Our approach can handle noisy…
Exploration is a fundamental problem in robot autonomy. A major limitation, however, is that during exploration robots oftentimes have to rely on on-board systems alone for state estimation, accumulating significant drift over time in large…
This paper presents a distributed method for robots moving in rigid formations while ensuring probabilistic collision avoidance between the robots. The formation is parametrised through the transformation of a base configuration. The robots…
Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input-output data. Based on a density result,…
This paper introduces a numerical algorithm to compute the $L_2$ optimal transport map between two measures $\mu$ and $\nu$, where $\mu$ derives from a density $\rho$ defined as a piecewise linear function (supported by a tetrahedral mesh),…
This paper presents a framework for fast and robust motion planning designed to facilitate automated driving. The framework allows for real-time computation even for horizons of several hundred meters and thus enabling automated driving in…
Localization is an essential component for autonomous robots. A well-established localization approach combines ray casting with a particle filter, leading to a computationally expensive algorithm that is difficult to run on…
In this paper we present a method for automatically planning optimal paths for a group of robots that satisfy a common high level mission specification. Each robot's motion in the environment is modeled as a weighted transition system. The…
While multi-joint continuum robots are highly dexterous and flexible, designing an optimal robot can be challenging due to its kinematics involving curvatures. Hence, the current work presents a computational method developed to find…
In this paper, we address the problem of time-optimal coordination of mobile robots under kinodynamic constraints along specified paths. We propose a novel approach based on time discretization that leads to a mixed-integer linear…