Graph-based algorithms for the efficient solution of a class of optimization problems

In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and to the linear subcase. With numerical experiments, we show that the proposed algorithms outperform generic commercial solvers.Comment: 27 pages, 9 figures, 1 tabl

Algoritmi di ottimizzazione basati su grafi con applicazioni alla pianificazione di traiettoria

In this work, we address a class of specially structured optimization problems. We introduce relevant applications in control engineering and telecommunication which fall in this class. We develop new graph-based procedures for efficiently solving problems belonging to this class, provide correctness and speed of convergence proofs and present some numerical experiments. We also address one of these problems in the continuous time domain

A Consensus Approach to Dynamic Programming

Motivated by the finite element formulation of the Hamilton-Jacobi-Bellman (HJB) equation, we introduce a consensus algorithm to compute the solution of a class of optimization problems that can be solved with a fixed point iteration. The proposed algorithm reduces the computational cost in terms of elementary operations with respect to a complete fixed point iteration. We provide theoretical results on maximum error rate and on the convergence of the algorithm. As an application, we compute the minimum-time solution for a parking maneuver of a car-like vehicle, comparing the fixed point iteration with the consensus iteration

A Jacobi-like acceleration for dynamic programming

The Hamilton-Jacobi-Bellman (HJB) equation provides a general method to solve optimal control problems. Since the HJB equation is a nonlinear partial differential equation, a closed form solution does not exist for the general case and various numerical procedures have been developed for its solution. Some recent approaches, after some simplifications, convert the problem into a fixed-point iteration. One problem related to the iteration is that its convergence speed is rather poor. We propose a Jacobi-like acceleration that allows to improve the convergence speed. As an application, we compute the minimum-time solution of a parking maneuver for a car-like vehicle with bounded velocity and steering angle

A LoRaWAN Multi-Technological Architecture for Construction Site Monitoring

It is necessary to ensure safety in terms of health and accidents through the real-time monitoring of the construction site environment and workers. This problem has become of great importance due to the economic and social implications. Therefore, a sensor-based approach has been found to be beneficial in Building Information Modeling (BIM). Wireless Sensor Network (WSN) technologies are well-suited for the deployment of monitoring systems. A suitable technical solution for node communication in a WSN is Long Range (LoRa) modulation technology. In this study, an autonomous LoRa-based system for the monitoring of a construction site in Lungro, Calabria, Italy, is presented. The spatial monitoring of working personnel is achieved by employing a tracker device with an Inertial Measurement Unit (IMU) and a Global Positioning System (GPS) device. Accesses of personnel and gear to the site are registered using Radio Frequency Identification (RFID) tags equipped with protective gear. Fixed-position solar-powered sensor nodes are also employed for structural monitoring, i.e., movement sensors are used to monitor the variation of scaffolding, building structures, and under-work housing inclinations. Long Range Wide Area Network (LoRaWAN) gateways interface with the nodes and the internet for data exchange, enabling an Internet of Things (IoT) paradigm for the monitoring solution. A comprehensive overview of the workers and structural nodes, along with the RFID access management system and LoRaWAN gateway features, is provided in this article. A description of the web interface is also reported