arXiv subjects

A. Pedro Aguiar

Publications and source records attributed to A. Pedro Aguiar.

At least 55 records · Page 3Linked to original sources

arXiv2022

Decomposition of admissible functions in weighted coupled cell networks

This work makes explicit the degrees of freedom involved in modeling the dynamics of a network, or some other first-order property of a network, such as a measurement function. In previous work, an admissible function in a network was constructed through the evaluation of what we called oracle components. These oracle components are defined through some minimal properties that they are expected to obey. This is a high-level description in the sense that it is not clear how one could design such an object. The goal is to obtain a low-level representation of these objects by unwrapping them into their degrees of freedom. To achieve this, we introduce two decompositions. The first one is the more intuitive one and allows us to define the important concept of coupling order. The second decomposition is built on top of the first one and is valid for the class of coupling components that have finite coupling order. Despite this requirement, we show that this is still a very useful tool for designing coupling components with infinite coupling orders, through a limit approach.

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arXiv2021

Distributed design of deterministic discrete-time privacy preserving average consensus for multi-agent systems through network augmentation

Average consensus protocols emerge with a central role in distributed systems and decision-making such as distributed information fusion, distributed optimization, distributed estimation, and control. A key advantage of these protocols is that agents exchange and reveal their state information only to their neighbors. Yet, it can raise privacy concerns in situations where the agents' states contain sensitive information. In this paper, we propose a novel (noiseless) privacy preserving distributed algorithms for multi-agent systems to reach an average consensus. The main idea of the algorithms is that each agent runs a (small) network with a crafted structure and dynamics to form a network of networks (i.e., the connection between the newly created networks and their interconnections respecting the initial network connections). Together with a re-weighting of the dynamic parameters dictating the inter-agent dynamics and the initial states, we show that it is possible to ensure that the value of each node converges to the consensus value of the original network. Furthermore, we show that, under mild assumptions, it is possible to craft the dynamics such that the design can be achieved in a distributed fashion. Finally, we illustrate the proposed algorithm with examples.

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arXiv2021

Minimum jointly structural input and output selection for strongly connected networks

In this paper, given a linear time-invariant strongly connected network, we study the problem of determining the minimum number of state variables that need to be simultaneously actuated and measured to ensure structural controllability and observability, respectively. This problem is fundamental in the design of multi-agent systems, where there are economic constraints in the decision of which agents to equip with a more costly on-board system that will allow the agent to have both actuation and sensing capabilities. Despite the combinatorial nature of this problem, we present a solution that couples the design of both structural controllability and structural observability counterparts to address it with polynomial-time complexity.

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arXiv2021

Discrete-Time Fractional-Order Dynamical Networks Minimum-Energy State Estimation

Fractional-order dynamical networks are increasingly being used to model and describe processes demonstrating long-term memory or complex interlaced dependencies amongst the spatial and temporal components of a wide variety of dynamical networks. Notable examples include networked control systems or neurophysiological networks which are created using electroencephalographic (EEG) or blood-oxygen-level-dependent (BOLD) data. As a result, the estimation of the states of fractional-order dynamical networks poses an important problem. To this effect, this paper addresses the problem of minimum-energy state estimation for discrete-time fractional-order dynamical networks (DT-FODN), where the state and output equations are affected by an additive noise that is considered to be deterministic, bounded, and unknown. Specifically, we derive the corresponding estimator and show that the resulting estimation error is exponentially input-to-state stable with respect to the disturbances and to a signal that is decreasing with the increase of the accuracy of the adopted approximation model. An illustrative example shows the effectiveness of the proposed method on real-world neurophysiological networks.

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arXiv2021

On Incremental Structure-from-Motion using Lines

Humans tend to build environments with structure, which consists of mainly planar surfaces. From the intersection of planar surfaces arise straight lines. Lines have more degrees-of-freedom than points. Thus, line-based Structure-from-Motion (SfM) provides more information about the environment. In this paper, we present solutions for SfM using lines, namely, incremental SfM. These approaches consist of designing state observers for a camera's dynamical visual system looking at a 3D line. We start by presenting a model that uses spherical coordinates for representing the line's moment vector. We show that this parameterization has singularities, and therefore we introduce a more suitable model that considers the line's moment and shortest viewing ray. Concerning the observers, we present two different methodologies. The first uses a memory-less state-of-the-art framework for dynamic visual systems. Since the previous states of the robotic agent are accessible -- while performing the 3D mapping of the environment -- the second approach aims at exploiting the use of memory to improve the estimation accuracy and convergence speed. The two models and the two observers are evaluated in simulation and real data, where mobile and manipulator robots are used.

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arXiv2020

Three Dimensional Moving Path Following Control for Robotic Vehicles with Minimum Positive Forward Speed

This paper addresses the problem of steering a robotic vehicle along a geometric path specified with respect to a reference frame moving in three dimensions, termed the Moving Path Following (MPF) motion control problem. The MPF motion control problem is solved for a large class of robotic vehicles that require a minimum positive forward speed to operate, which poses additional constraints, and is developed using geometric concepts, wherein the attitude control problem is formulated on Special Orthogonal group SO(3). Furthermore, the proposed control law is derived from a novel MPF error model formulation that allows to exclude the conservative constraints on the initial position of the vehicle with respect to the reference path by enabling the explicit control of the progression of a virtual point moving along the reference path. The task of the MPF control law is then to steer the vehicle towards the moving path and converge to the virtual point. Formal stability and convergence guarantees are provided using the Input-to-State Stability concept. In particular, we show that the proposed controller is robust to imperfect tracking errors by the autopilot and wind gusts. Simulation results are presented to illustrate the efficacy of the proposed MPF control law.

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arXiv2020

Structural Systems Theory: an overview of the last 15 years

In this paper, we provide an overview of the research conducted in the context of structural systems since the latest survey by Dion et al. in 2003. We systematically consider all the papers that cite this survey as well as the seminal work in this field that took place on and after the publication of the later survey, are published in peer-reviewed venues and in English. Structural systems theory deals with parametric systems where parameters might be unknown and, therefore, addresses the study of systems properties that depend only on the system's structure (or topology) described by the inter-dependencies between state variables. Remarkably, structural systems properties hold generically (i.e., almost always) under the assumption that parameters are independent. Therefore, it constitutes an approach to assess necessary conditions that systems should satisfy. In recent years, structural systems theory was applied to design systems that attain such properties, as well as to endure resilient/security and privacy properties. Furthermore, structural systems theory enables the formulation of such topics as combinatorial optimization problems, which allow us to understand their computational complexity and find algorithms that are efficiently deployed in the context of large-scale systems. In particular, we present an overview of how structural systems theory has been used in the context of linear time-invariant systems, as well as other dynamical models, for which a brief description of the different problem statements and solutions approaches are presented. Next, we describe recent variants of structural systems theory, as well as different applications of the classical and new approaches. Finally, we provide an overview of recent and future directions in this field.

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arXiv2020

Control Barrier Function based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria

Control Lyapunov functions (CLFs) and control barrier functions (CBFs) have been used to develop provably safe controllers by means of quadratic programs (QPs), guaranteeing safety in the form of trajectory invariance with respect to a given set. In this manuscript, we show that this framework can introduce equilibrium points (particularly at the boundary of the unsafe set) other than the minimum of the Lyapunov function into the closed-loop system. We derive explicit conditions under which these undesired equilibria (which can even appear in the simple case of linear systems with just one convex unsafe set) are asymptotically stable. To address this issue, we propose an extension to the QP-based controller unifying CLFs and CBFs that explicitly avoids undesirable equilibria on the boundary of the safe set. The solution is illustrated in the design of a collision-free controller.

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arXiv2020

Active Depth Estimation: Stability Analysis and its Applications

Recovering the 3D structure of the surrounding environment is an essential task in any vision-controlled Structure-from-Motion (SfM) scheme. This paper focuses on the theoretical properties of the SfM, known as the incremental active depth estimation. The term incremental stands for estimating the 3D structure of the scene over a chronological sequence of image frames. Active means that the camera actuation is such that it improves estimation performance. Starting from a known depth estimation filter, this paper presents the stability analysis of the filter in terms of the control inputs of the camera. By analyzing the convergence of the estimator using the Lyapunov theory, we relax the constraints on the projection of the 3D point in the image plane when compared to previous results. Nonetheless, our method is capable of dealing with the cameras' limited field-of-view constraints. The main results are validated through experiments with simulated data.

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arXiv2019

A Framework for Depth Estimation and Relative Localization of Ground Robots using Computer Vision

The 3D depth estimation and relative pose estimation problem within a decentralized architecture is a challenging problem that arises in missions that require coordination among multiple vision-controlled robots. The depth estimation problem aims at recovering the 3D information of the environment. The relative localization problem consists of estimating the relative pose between two robots, by sensing each other's pose or sharing information about the perceived environment. Most solutions for these problems use a set of discrete data without taking into account the chronological order of the events. This paper builds on recent results on continuous estimation to propose a framework that estimates the depth and relative pose between two non-holonomic vehicles. The basic idea consists in estimating the depth of the points by explicitly considering the dynamics of the camera mounted on a ground robot, and feeding the estimates of 3D points observed by both cameras in a filter that computes the relative pose between the robots. We evaluate the convergence for a set of simulated scenarios and show experimental results validating the proposed framework.

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arXiv2019

An optimization-based cooperative path-following framework for multiple robotic vehicles

This paper addresses the design of an optimization-based cooperative path-following control law for multiple robotic vehicles that optimally balances the transient trade-off between coordination and path-following errors. To this end, we formulate a more general multi-agent framework where each agent is associated with (i) a continuous-time dynamical model, which governs the evolution of its state, and (ii) an output equation that is a function of both the state of the agent and a coordination vector. According to a given network topology, each agent can access its state and coordination vector, as well as the coordination vectors of the neighboring agents. In this setup, the goal is to design a distributed control law that steers the output signals to the origin, while simultaneously driving the coordination vectors of the agents of the network to consensus. To solve this, we propose a model predictive control scheme that builds on a pre-existing auxiliary consensus control law to design a performance index that combines the output regulation objective with the consensus objective. Convergence guarantees under which one can solve this coordinated output regulation problem are provided. Numerical simulations display the effectiveness of the proposed scheme applied to a cooperative path following control problem of a network of 3D nonholonomic robotic vehicles.

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arXiv2019

Finite-dimensional control of linear discrete-time fractional-order systems

This paper addresses the design of finite-dimensional feedback control laws for linear discrete-time fractional-order systems with additive state disturbance. A set of sufficient conditions are provided to guarantee convergence of the state trajectories to an ultimate bound around the origin with size increasing with the magnitude of the disturbances. Performing a suitable change of coordinates, the latter result can be used to design a controller that is able to track reference trajectories that are solutions of the unperturbed fractional-order system. To overcome the challenges associated with the generation of such solutions, we address the practical case where the references to be tracked are generated as a solution of a specific finite-dimensional approximation of the original fractional-order system. In this case, the tracking error trajectory is driven to an asymptotic bound that is increasing with the magnitude of the disturbances and decreases with the increment in the accuracy of the approximation. The proposed controllers are finite-dimensional, in the sense that the computation of the control input only requires a finite number of previous state and input vectors of the system. Numerical simulations illustrate the proposed design methods in different scenarios.

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arXiv2019

Selective Strong Structural Minimum Cost Resilient Co-Design for Regular Descriptor Linear Systems

This paper addresses the problem of minimum cost resilient actuation-sensing-communication co-design for regular descriptor systems while ensuring selective strong structural system's properties. More specifically, the problem consists of determining the minimum cost deployment of actuation and sensing technology, as well as communication between the these, such that decentralized control approaches are viable for an arbitrary realization of regular descriptor systems satisfying a pre-specified selective structure, i.e., some entries can be zero, nonzero, or either zero/nonzero. Towards this goal, we rely on strong structural systems theory and extend it to cope with the selective structure that casts resiliency/robustness properties and uncertainty properties of system's model. Upon such framework, we introduce the notion of selective strong structural fixed modes as a characterization of the feasibility of decentralized control laws. Also, we provide necessary and sufficient conditions for this property to hold, and show how these conditions can be leveraged to determine the minimum cost resilient placement of actuation-sensing-communication technology ensuring feasible solutions. In particular, we study the minimum cost resilient actuation and sensing placement, upon which we construct the solution to our problem. Finally, we illustrate the applicability the main results of this paper on an electric power grid example.

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arXiv2018

Low-level Active Visual Navigation: Increasing robustness of vision-based localization using potential fields

This paper proposes a low-level visual navigation algorithm to improve visual localization of a mobile robot. The algorithm, based on artificial potential fields, associates each feature in the current image frame with an attractive or neutral potential energy, with the objective of generating a control action that drives the vehicle towards the goal, while still favoring feature rich areas within a local scope, thus improving the localization performance. One key property of the proposed method is that it does not rely on mapping, and therefore it is a lightweight solution that can be deployed on miniaturized aerial robots, in which memory and computational power are major constraints. Simulations and real experimental results using a mini quadrotor equipped with a downward looking camera demonstrate that the proposed method can effectively drive the vehicle to a designated goal through a path that prevents localization failure.

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arXiv2017

Feature Based Potential Field for Low-level Active Visual Navigation

This paper proposes a novel solution for improving visual localization in an active fashion. The solution, based on artificial potential field, associates each feature in the current image frame with an attractive or neutral potential energy. The resultant action drives the vehicle towards the goal, while still favoring feature rich areas. Experimental results with a mini quadrotor equipped with a downward looking camera assess the performance of the proposed method.

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arXiv2017

Structurally Observable Distributed Networks of Agents under Cost and Robustness Constraints

In many problems, agents cooperate locally so that a leader or fusion center can infer the state of every agent from probing the state of only a small number of agents. Versions of this problem arise when a fusion center reconstructs an extended physical field by accessing the state of just a few of the sensors measuring the field, or a leader monitors the formation of a team of robots. Given a link cost, the paper presents a polynomial time algorithm to design a minimum cost coordinated network dynamics followed by the agents, under an observability constraint. The problem is placed in the context of structural observability and solved even when up to k agents in the coordinated network dynamics fail.

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arXiv2016

Minimum Sensor Placement for Robust Observability of Structured Complex Networks

This paper addresses problems on the robust structural design of complex networks. More precisely, we address the problem of deploying the minimum number of dedicated sensors, i.e., those measuring a single state variable, that ensure the network to be structurally observable under disruptive scenarios. The disruptive scenarios considered are as follows: (i) the malfunction/loss of one arbitrary sensor, and (ii) the failure of connection (either unidirectional or bidirectional communication) between a pair of agents. First, we show these problems to be NP-hard, which implies that efficient algorithms to determine a solution are unlikely to exist. Secondly, we propose an intuitive two step approach: (1) we achieve an arbitrary minimum sensor placement ensuring structural observability; (2) we develop a sequential process to find minimum number of additional sensors required for robust observability. This step can be solved by recasting it as a weighted set covering problem. Although this is known to be an NP-hard problem, feasible approximations can be determined in polynomial-time that can be used to obtain feasible approximations to the robust structural design problems with optimality guarantees.

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arXiv2016

The Robust Minimal Controllability Problem

In this paper, we address two minimal controllability problems, where the goal is to determine a minimal subset of state variables in a linear time-invariant system to be actuated to ensure controllability under additional constraints. First, we study the problem of characterizing the sparsest input matrices that assure controllability when the autonomous dynamics' matrix is simple. Secondly, we build upon these results to describe the solutions to the robust minimal controllability problem, where the goal is to determine the sparsest input matrix ensuring controllability when specified number of inputs fail. Both problems are NP-hard, but under the assumption that the dynamics' matrix is simple, we show that it is possible to reduce these two problems to set multi-covering problems. Consequently, these problems share the same computational complexity, i.e., they are NP-complete, but polynomial algorithms to approximate the solutions of a set multi-covering problem can be leveraged to obtain close-to-optimal solutions to either of the minimal controllability problems.

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