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 well balance coverage and estimation, also discussing convergence properties of the algorithm. Numerical experiments show the effectivness of the new approach

Zero-Order Optimization for Gaussian Process-based Model Predictive Control

By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based control community. Yet, solving the resulting optimal control problem in real-time generally remains a major challenge, due to i) the increased number of augmented states in the optimization problem, as well as ii) computationally expensive evaluations of the posterior mean and covariance and their respective derivatives. To tackle these challenges, we employ i) a tailored Jacobian approximation in a sequential quadratic programming (SQP) approach, and combine it with ii) a parallelizable GP inference and automatic differentiation framework. Reducing the numerical complexity with respect to the state dimension $n_x$ for each SQP iteration from $\mathcal{O}(n_x^6)$ to $\mathcal{O}(n_x^3)$, and accelerating GP evaluations on a graphical processing unit, the proposed algorithm computes suboptimal, yet feasible solutions at drastically reduced computation times and exhibits favorable local convergence properties. Numerical experiments verify the scaling properties and investigate the runtime distribution across different parts of the algorithm.Comment: accepted for European Journal of Control (EJC), ECC 2023 Special Issu

EFFICIENT PARAMETRIC AND NON-PARAMETRICLOCALIZATION AND MAPPING IN ROBOTIC NETWORKS

Since the eighties localization and mapping problems have attracted the efforts of robotics researchers. However in the last decade, thanks to the increasing capabilities of the new electronic devices, many new related challenges have been posed, such as swarm robotics, aerial vehicles, autonomous cars and robotics networks. Efficiency, robustness and scalability play a key role in these scenarios. Efficiency is intended as an ability for an application to minimize the resources usage, in particular CPU time and memory space. In the aforementioned applications an underlying communication network is required so, for robustness we mean asynchronous algorithms resilient to delays and packet-losses. Finally scalability is the ability of an application to continue functioning without any dramatic performance degradation even if the number of devices involved keep increasing. In this thesis the interest is focused on parametric and non-parametric estimation algorithms ap- plied to localization and mapping in robotics. The main contribution can be summarized in the following four arguments: (i) Consensus-based localization 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. In particular 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. (ii) Aerial Vehicles distributed localization: We study 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. (iii) Estimation and Coverage: We address the problem of optimal coverage of a region via multiple robots when the sensory field used to approximate the density of event appearance is not known in advance. We address this problem in the context of a client-server architecture in which the mobile robots can communicate with a base station via a possibly unreliable wireless network subject to packet losses. Based on Gaussian regression which allows to estimate the true sensory field with any arbitrary accuracy, we propose a randomised strategy in which the robots and the base station simultaneously estimate the true sensory distribution by collecting measurements and compute the corresponding optimal Voronoi partitions. This strategy is designed to promote exploration at the beginning and then smoothly transition to station the robots at the centroid of the estimated optimal Voronoi partitions. Under mild assumptions on the transmission failure probability, we prove that the proposed strategy guarantees the convergence of the estimated sensory field to the true field and that the corresponding Voronoi partitions asymptotically becomes arbitrarily close to an optimal Voronoi partition. Additionally, we also provide numerically efficient approximation that trade-off accuracy of the estimated map for reduced memory and CPU complexity. Finally, we provide a set of extensive simulations which confirm the effectiveness of the proposed approach. (iv) Non-parametric estimation of spatio-temporal fields: We address the problem of efficiently and optimally estimating an unknown time-varying function through the collection of noisy measurements. We cast our problem in the framework of non-parametric estimation and we assume that the unknown function is generated by a Gaussian process with a known covariance. Under mild assumptions on the kernel function, we propose a solution which links the standard Gaussian regression to the Kalman filtering thanks to the exploitation of a grid where measurements collection and estimation take place. This work show an efficient in time and space method to estimate time-varying function, which combine the advantages of the Gaussian regression, e.g. model-less, and of the Kalman filter, e.g. efficiency

Meta Learning MPC using Finite-Dimensional Gaussian Process Approximations

Data availability has dramatically increased in recent years, driving model-based control methods to exploit learning techniques for improving the system description, and thus control performance. Two key factors that hinder the practical applicability of learning methods in control are their high computational complexity and limited generalization capabilities to unseen conditions. Meta-learning is a powerful tool that enables efficient learning across a finite set of related tasks, easing adaptation to new unseen tasks. This paper makes use of a meta-learning approach for adaptive model predictive control, by learning a system model that leverages data from previous related tasks, while enabling fast fine-tuning to the current task during closed-loop operation. The dynamics is modeled via Gaussian process regression and, building on the Karhunen-Lo{\`e}ve expansion, can be approximately reformulated as a finite linear combination of kernel eigenfunctions. Using data collected over a set of tasks, the eigenfunction hyperparameters are optimized in a meta-training phase by maximizing a variational bound for the log-marginal likelihood. During meta-testing, the eigenfunctions are fixed, so that only the linear parameters are adapted to the new unseen task in an online adaptive fashion via Bayesian linear regression, providing a simple and efficient inference scheme. Simulation results are provided for autonomous racing with miniature race cars adapting to unseen road conditions

A predictive safety filter for learning-based racing control

The growing need for high-performance controllers in safety-critical applications like autonomous driving has been motivating the development of formal safety verification techniques. In this paper, we design and implement a predictive safety filter that is able to maintain vehicle safety with respect to track boundaries when paired alongside any potentially unsafe control signal, such as those found in learning-based methods. A model predictive control (MPC) framework is used to create a minimally invasive algorithm that certifies whether a desired control input is safe and can be applied to the vehicle, or that provides an alternate input to keep the vehicle in bounds. To this end, we provide a principled procedure to compute a safe and invariant set for nonlinear dynamic bicycle models using efficient convex approximation techniques. To fully support an aggressive racing performance without conservative safety interventions, the safe set is extended in real-time through predictive control backup trajectories. Applications for assisted manual driving and deep imitation learning on a miniature remote-controlled vehicle demonstrate the safety filter's ability to ensure vehicle safety during aggressive maneuvers

Modelling Immunological Systems using PEPA: a preliminary report

We present preliminary work on modelling aspects of the immune system using process algebra. The problem addressed is how T-helper cell populations respond to co-infections with parasites making conflicting immunological demands. Our goal is to build PEPA models of alternative hypotheses around T-helper cell behaviour and to evaluate those with respect to experimental data