Andrea Carron

An Asynchronous Consensus-Based Algorithm for Estimation From Noisy Relative Measurements

In this paper, we address the problem of optimal estimating the position of each agent in a network from relative noisy vectorial distances with its neighbors by means of only local communication and bounded complexity, independent of network size and topology. We propose a consensus-based algorithm with the use of local memory variables which allows asynchronous implementation, has guaranteed exponential convergence to the optimal solution under simple deterministic and randomized communication protocols, and requires minimal packet transmission. In the randomized scenario, we then study the rate of convergence in expectation of the estimation error and we argue that it can be used to obtain upper and lower bound for the rate of converge in mean square. In particular, we show that for regular graphs, such as Cayley, Ramanujan, and complete graphs, the convergence rate in expectation has the same asymptotic degradation of memoryless asynchronous consensus algorithms in terms of network size. In addition, we show that the asynchronous implementation is also robust to delays and communication failures. We finally complement the analytical results with some numerical simulations, comparing the proposed strategy with other algorithms which have been recently proposed in the literature.

Distributed multi-hop reactive power compensation in smart micro-grids subject to saturation constraints

In this paper we address the problem of exploiting the distributed energy resources (DER) available in a smart micro-grid to minimize the power distribution losses via optimal reactive power compensation. Due to their typically small size, the amount of reactive power provided by each micro-generator is subject to tight saturation constraints. As a consequence, it might be impossible to achieve convergence to the global optimum based on algorithms that rely on short-range, gossip-type communication. We therefore propose a randomized multi-hop protocol that guarantees convergence of the distributed optimization algorithm also when only short-range communications are possible, at the expense of some additional communication overhead.

The Hitting Time of Multiple Random Walks

This work provides generalized notions and analysis methods for the hitting time of random walks on graphs. The hitting time, also known as the Kemeny constant or the mean first passage time, of a random walk is widely studied; however, only limited work is available for the multiple random walker scenario. In this work we provide a novel method for calculating the hitting time for a single random walker as well as the first analytic expression for calculating the hitting time for multiple random walkers, which we denote as the group hitting time. We also provide a closed form solution for calculating the hitting time between specified nodes for both the single and multiple random walker cases. Our results allow for the multiple random walks to be different and, moreover, for the random walks to operate on different subgraphs. Finally, using sequential quadratic programming, we show that the combination of transition matrices that generate the minimal group hitting time for various graph topologies is oft...

Multi-agents adaptive estimation and coverage control using Gaussian regression

We consider a scenario where the aim of a group of agents is to perform the optimal coverage of a region according to a sensory function. In particular, centroidal Voronoi partitions have to be computed. The difficulty of the task is that the sensory function is unknown and has to be reconstructed on line from noisy measurements. Hence, estimation and coverage needs to be performed at the same time. We cast the problem in a Bayesian regression framework, where the sensory function is seen as a Gaussian random field. Then, we design a set of control inputs which try to find a good balance between coverage and estimation, also discussing convergence properties of the algorithm. Numerical experiments show the effectiveness of the new approach.

Multi-robot localization via GPS and relative measurements in the presence of asynchronous and lossy communication

This work addresses the problem of distributed multi-agent localization in presence of heterogeneous measurements and wireless communication. The proposed algorithm integrates low precision global sensors, like GPS and compasses, with more precise relative position (i.e., range plus bearing) sensors. Global sensors are used to reconstruct the absolute position and orientation, while relative sensors are used to retrieve the shape of the formation. A fast distributed and asynchronous linear least-squares algorithm is proposed to solve an approximated version of the non-linear Maximum Likelihood problem. The algorithm is provably shown to be robust to communication losses and random delays. The use of ACK-less broadcast-based communication protocols ensures an efficient and easy implementation in real world scenarios. If the relative measurement errors are sufficiently small, we show that the algorithm attains a solution which is very close to the maximum likelihood solution. The theoretical findings and the algorithm performances are extensively tested by means of Monte-Carlo simulations.

Distributed localization from relative noisy measurements: A robust gradient based approach

In this work we address the problem of optimal estimating the position of each agent in a network from relative noisy vectorial distances with its neighbors. Although the problem can be cast as a standard least-squares problem, the main challenge is to devise scalable algorithms that allow each agent to estimate its own position by means of only local communication and bounded complexity, independently of the network size and topology. We propose a gradient based algorithm that is guaranteed to have exponentially convergence rate to the optimal centralized least-square solution. Moreover we show the convergence also in presence of bounded delays and packet losses. We finally provide numerical results to support our work.

Kinematics and control of redundant robotic arm based on dielectric elastomer actuators

Soft robotics is a promising field and its application to space mechanisms could represent a breakthrough in space technologies by enabling new operative scenarios (e.g. soft manipulators, capture systems). Dielectric Elastomers Actuators have been under deep study for a number of years and have shown several advantages that could be of key importance for space applications. Among such advantages the most notable are high conversion efficiency, distributed actuation, self-sensing capability, multi-degree-of-freedom design, light weight and low cost. The big potentialities of double cone actuators have been proven in terms of good performances (i.e. stroke and force/torque), ease of manufacturing and durability. In this work the kinematic, dynamic and control design of a two-joint redundant robotic arm is presented. Two double cone actuators are assembled in series to form a two-link design. Each joint has two degrees of freedom (one rotational and one translational) for a total of four. The arm is designed to move in a 2-D environment (i.e. the horizontal plane) with 4 DoF, consequently having two degrees of redundancy. The redundancy is exploited in order to minimize the joint loads. The kinematic design with redundant Jacobian inversion is presented. The selected control algorithm is described along with the results of a number of dynamic simulations that have been executed for performance verification. Finally, an experimental setup is presented based on a flexible structure that counteracts gravity during testing in order to better emulate future zero-gravity applications.

Machine learning meets Kalman Filtering

In this work we study the problem of efficient non-parametric estimation for non-linear time-space dynamic Gaussian processes (GP). We propose a systematic and explicit procedure to address this problem by pairing GP regression with Kalman Filtering. Under a specific separability assumption of the modeling kernel and periodic sampling on a (possibly non-uniform) space-grid, we show how to build an exact finite dimensional discrete-time state-space representation for the modeled process. The major finding is that the state at instant k of the associated Kalman Filter represents a sufficient statistic to compute the minimum variance prediction of the process at instant k over any arbitrary finite subset of the space. Finally, we compare the proposed strategy with standard approaches.

Multi-robots Gaussian estimation and coverage control: From client–server to peer-to-peer architectures☆

Abstract In this work we study the problem of multi-robot coverage of a planar region when the sensory field used to approximate the density of event appearance is not known in advance. We address the problem by considering two different communication architectures: client–server and peer-to-peer . In the first architecture the robots are allowed to communicate with a central server/base station. In the second the robots communicate among neighboring peers by means of a gossip protocol in a distributed fashion. For both the architectures, we resort to nonparametric Gaussian regression approach to estimate the unknown sensory field of interest from a collection of noisy samples. We propose a probabilistic control strategy based on the posterior of the estimation error variance, which lets the robots to estimate the true sensory field with any arbitrary accuracy while simultaneously computing and exploiting the corresponding centroidal Voronoi partitions. We also present a numerically efficient approximation based on a spatial discretization to trade-off the accuracy of the estimated map against the required computational complexity. This trade-off can be tuned based on explicit estimation error bounds which depend on the spatial resolution and the Gaussian kernel parameters. Finally, we test the proposed solutions via extensive numerical simulations.

Hitting time for doubly-weighted graphs with application to robotic surveillance

This article provides analysis results for the weighted hitting time and the pairwise weighted hitting time of a Markov chain. This concepts are useful in many applications from robotics to patrolling, environment monitoring and resources optimization. The aforementioned quantities are a performance indexes which measure the expected time taken by a random walker to travel from an arbitrary node of a graph to a second randomly selected node and the expected time to travel between two chosen nodes. These metrics can be used as objective function in optimization problems. In fact we propose a numerical example applied to robotic surveillance where the weighted hitting time is our cost to minimize with respect to the transition matrix of the agent.