Handling Constrained Optimization in Factor Graphs for Autonomous Navigation

Factor graphs are graphical models used to represent a wide variety of problems across robotics, such as Structure from Motion (SfM), Simultaneous Localization and Mapping (SLAM) and calibration. Typically, at their core, they have an optimization problem whose terms only depend on a small subset of variables. Factor graph solvers exploit the locality of problems to drastically reduce the computational time of the Iterative Least-Squares (ILS) methodology. Although extremely powerful, their application is usually limited to unconstrained problems. In this letter, we model constraints over variables within factor graphs by introducing a factor graph version of the Augmented Lagrangian (AL) method. We show the potential of our method by presenting a full navigation stack based on factor graphs. Differently from standard navigation stacks, we can model both optimal control for local planning and localization with factor graphs, and solve the two problems using the standard ILS methodology.We validate our approach in real-world autonomous navigation scenarios, comparing it with the de facto standard navigation stack implemented in ROS. Comparative experiments show that for the application at hand our system outperforms the standard nonlinear programming solver Interior-Point Optimizer (IPOPT) in runtime, while achieving similar solutions

An Experimentally Validated Model of the Propeller Force Accounting for Cross Influences on Multi-Rotor Aerial Systems

In this paper, we propose a model for the thrust coefficient of propellers that can take into account cross-influence between adjacent propellers. The aerodynamic interaction between propellers in multirotor aerial vehicles reduces the thrust they can produce. The influence between propellers depends on their relative positioning and orientation, which are taken into account by the proposed model. It is validated on measurements collected by a force sensor mounted on a propeller for different configurations of the adjacent propellers in a support structure. In this work, we focus on configurations with small relative orientations. Results show that the proposed model outperforms the traditional constant model in terms of thrust prediction on the data we collected, and it performs better than other models with fewer parameters, being the only one with less than 10% maximum percentage error

Invisible Servoing:a Visual Servoing Approach with Return-Conditioned Latent Diffusion

In this paper, we present a novel visual servoing (VS) approach based on latent Denoising Diffusion Probabilistic Models (DDPMs). Opposite to classical VS methods, the proposed approach allows reaching the desired target view, even when the target is initially not visible. This is possible thanks to the learning of a latent representation that the DDPM uses for planning and a dataset of trajectories encompassing target-invisible initial views. The latent representation is learned using a Cross-Modal Variational Autoencoder, and used to estimate the return for conditioning the trajectory generation of the DDPM. Given the current image, the DDPM generates trajectories in the latent space driving the robotic platform to the desired visual target. The approach is applicable to any velocity-based controlled platform. We test our method with simulated and real-world experiments using generic multi-rotor Uncrewed Aerial Vehicles (UAVs). A video of our experiments can be found at https://youtu.be/yu-aTxqceOA

How-to Augmented Lagrangian on Factor Graphs

Robotics is progressively pervading our daily-lives. Robots can be divided in two large categories: manipulators and mobile robotics. In this thesis, we focus on the latter. An autonomous robotics navigation system needs to address many tasks. Simultaneous Localization and Mapping (SLAM) is the task of simultaneously build a map of the environment and localizing in it, control is the task of computing the platform inputs, which can be acceleration, velocity, jerk, that allow the robot to reach a given goal, high-level planning is the more abstract task of selecting a sequence of goals that allow the robot to perform the high-level task, e.g. mapping an area, driving to a final position, rescue survivors to an accident, and many others. In a divide-and-conquer approach, each task is delegated to a sub-module. These components have been investigated separately by different research communities, that has developed sophisticated tools to address the sub-problems of interest. In particular, the SLAM community consolidated the Maximum-A-Posteriori approach, and the usage of factor graphs as an effective tool to model and solve large mapping problems. Whatever the problem is, real-world, long-term and broad diffusion of robotic systems require the tools to be efficient, robust and resource-aware. Factor graphs are graphical models used to represent unconstrained optimization problems that combine many objectives, each of which only depends on a subset of variables. Extending factor graphs to constrained optimization allows to enlarge their application domain. Under the factor graph formulation, control systems can benefit from the efficiency of existing factor graph-solvers, the ease of modeling and of combining objectives. Moreover, some estimation problems inherently involve constraints in their formulation, that can be straightforwardly embedded in the graph. Potentially, mapping and control sub-modules can be unified under one common language, which implies that they can share consistently information about the environment. In this thesis, we investigate how to embed constraints in the factor graph-formalism. We introduce a generalized version based on the Augmented Lagrangian (AL) method, where edges can be objective terms or constraints. We support our methodology by presenting many applications, ranging from group synchronization, which arises for example as sub-problem of Structure from Motion (SfM), to optimal control. The contributions presented in this thesis are available as open-source software packages to foster the development of this research area

An optimal control approach to public investments for unemployment reduction

The paper deals with the modelling and the control of a job market dynamics which considers unemployed individuals and two classes of jobs: a temporary one, characterised by a lower quality of economical treatment and/or long duration assurance for the workers, and a regular one, more stable and economically more satisfactory. For each of the two classes, the active workers as well as the vacancies are considered. Control actions are introduced, representing different government efforts devoted to the quantity and the quality improvements of the work. Choices in the model are discussed and compared with literature. The numerical results of some simulations are reported to better put in evidence the results obtained

Two months of radiation oncology in the heart of Italian “red zone” during COVID-19 pandemic: paving a safe path over thin ice

Abstract Background Coronavirus Disease 2019 (COVID-19) pandemic had an overwhelming impact on healthcare worldwide. Outstandingly, the aftermath on neoplastic patients is still largely unknown, and only isolated cases of COVID-19 during radiotherapy have been published. We will report the two-months experience of our Department, set in Lombardy “red-zone”. Methods Data of 402 cancer patients undergoing active treatment from February 24 to April 24, 2020 were retrospectively reviewed; several indicators of the Department functioning were also analyzed. Results Dedicated measures allowed an overall limited reduction of the workload. Decrease of radiotherapy treatment number reached 17%, while the number of administration of systemic treatment and follow up evaluations kept constant. Conversely, new treatment planning faced substantial decline. Considering the patients, infection rate was 3.23% (13/402) and mortality 1.24% (5/402). Median age of COVID-19 patients was 69.7 years, the large majority were male and smokers (84.6%); lung cancer was the most common tumor type (61.5%), 84.6% of subjects were stage III-IV and 92.3% had comorbidities. Remarkably, 92.3% of the cases were detected before March 24. Globally, only 2.5% of ongoing treatments were suspended due to suspect or confirmed COVID-19 and 46.2% of positive patients carried on radiotherapy without interruption. Considering only the last month, infection rate among patients undergoing treatment precipitated to 0.43% (1/232) and no new contagions were reported within our staff. Conclusions Although mortality rate in COVID-19 cancer patients is elevated, our results support the feasibility and safety of continuing anticancer treatment during SARS-Cov-2 pandemic by endorsing consistent preventive measures. </jats:sec