Time integration and steady-state continuation for 2d lubrication equations

Lubrication equations allow to describe many structurin processes of thin liquid films. We develop and apply numerical tools suitable for their analysis employing a dynamical systems approach. In particular, we present a time integration algorithm based on exponential propagation and an algorithm for steady-state continuation. In both algorithms a Cayley transform is employed to overcome numerical problems resulting from scale separation in space and time. An adaptive time-step allows to study the dynamics close to hetero- or homoclinic connections. The developed framework is employed on the one hand to analyse different phases of the dewetting of a liquid film on a horizontal homogeneous substrate. On the other hand, we consider the depinning of drops pinned by a wettability defect. Time-stepping and path-following are used in both cases to analyse steady-state solutions and their bifurcations as well as dynamic processes on short and long time-scales. Both examples are treated for two- and three-dimensional physical settings and prove that the developed algorithms are reliable and efficient for 1d and 2d lubrication equations, respectively.Comment: 33 pages, 16 figure

Collision-aware Task Assignment for Multi-Robot Systems

We propose a novel formulation of the collision-aware task assignment (CATA) problem and a decentralized auction-based algorithm to solve the problem with optimality bound. Using a collision cone, we predict potential collisions and introduce a binary decision variable into the local reward function for task bidding. We further improve CATA by implementing a receding collision horizon to address the stopping robot scenario, i.e. when robots are confined to their task location and become static obstacles to other moving robots. The auction-based algorithm encourages the robots to bid for tasks with collision mitigation considerations. We validate the improved task assignment solution with both simulation and experimental results, which show significant reduction of overlapping paths as well as deadlocks

Decentralized collaborative transport of fabrics using micro-UAVs

Small unmanned aerial vehicles (UAVs) have generally little capacity to carry payloads. Through collaboration, the UAVs can increase their joint payload capacity and carry more significant loads. For maximum flexibility to dynamic and unstructured environments and task demands, we propose a fully decentralized control infrastructure based on a swarm-specific scripting language, Buzz. In this paper, we describe the control infrastructure and use it to compare two algorithms for collaborative transport: field potentials and spring-damper. We test the performance of our approach with a fleet of micro-UAVs, demonstrating the potential of decentralized control for collaborative transport.Comment: Submitted to 2019 International Conference on Robotics and Automation (ICRA). 6 page

Decentralized Connectivity-Preserving Deployment of Large-Scale Robot Swarms

We present a decentralized and scalable approach for deployment of a robot swarm. Our approach tackles scenarios in which the swarm must reach multiple spatially distributed targets, and enforce the constraint that the robot network cannot be split. The basic idea behind our work is to construct a logical tree topology over the physical network formed by the robots. The logical tree acts as a backbone used by robots to enforce connectivity constraints. We study and compare two algorithms to form the logical tree: outwards and inwards. These algorithms differ in the order in which the robots join the tree: the outwards algorithm starts at the tree root and grows towards the targets, while the inwards algorithm proceeds in the opposite manner. Both algorithms perform periodic reconfiguration, to prevent suboptimal topologies from halting the growth of the tree. Our contributions are (i) The formulation of the two algorithms; (ii) A comparison of the algorithms in extensive physics-based simulations; (iii) A validation of our findings through real-robot experiments.Comment: 8 pages, 8 figures, submitted to IROS 201

Modeling Perceptual Aliasing in SLAM via Discrete-Continuous Graphical Models

Perceptual aliasing is one of the main causes of failure for Simultaneous Localization and Mapping (SLAM) systems operating in the wild. Perceptual aliasing is the phenomenon where different places generate a similar visual (or, in general, perceptual) footprint. This causes spurious measurements to be fed to the SLAM estimator, which typically results in incorrect localization and mapping results. The problem is exacerbated by the fact that those outliers are highly correlated, in the sense that perceptual aliasing creates a large number of mutually-consistent outliers. Another issue stems from the fact that most state-of-the-art techniques rely on a given trajectory guess (e.g., from odometry) to discern between inliers and outliers and this makes the resulting pipeline brittle, since the accumulation of error may result in incorrect choices and recovery from failures is far from trivial. This work provides a unified framework to model perceptual aliasing in SLAM and provides practical algorithms that can cope with outliers without relying on any initial guess. We present two main contributions. The first is a Discrete-Continuous Graphical Model (DC-GM) for SLAM: the continuous portion of the DC-GM captures the standard SLAM problem, while the discrete portion describes the selection of the outliers and models their correlation. The second contribution is a semidefinite relaxation to perform inference in the DC-GM that returns estimates with provable sub-optimality guarantees. Experimental results on standard benchmarking datasets show that the proposed technique compares favorably with state-of-the-art methods while not relying on an initial guess for optimization.Comment: 13 pages, 14 figures, 1 tabl

Accurate position tracking with a single UWB anchor

Accurate localization and tracking are a fundamental requirement for robotic applications. Localization systems like GPS, optical tracking, simultaneous localization and mapping (SLAM) are used for daily life activities, research, and commercial applications. Ultra-wideband (UWB) technology provides another venue to accurately locate devices both indoors and outdoors. In this paper, we study a localization solution with a single UWB anchor, instead of the traditional multi-anchor setup. Besides the challenge of a single UWB ranging source, the only other sensor we require is a low-cost 9 DoF inertial measurement unit (IMU). Under such a configuration, we propose continuous monitoring of UWB range changes to estimate the robot speed when moving on a line. Combining speed estimation with orientation estimation from the IMU sensor, the system becomes temporally observable. We use an Extended Kalman Filter (EKF) to estimate the pose of a robot. With our solution, we can effectively correct the accumulated error and maintain accurate tracking of a moving robot.Comment: Accepted by ICRA202