Distance-Based Formation Control of Multi-Agent Systems

This Ph.D. dissertation studies the distance-based formation control of multi-agent systems. A new approach to the distance-based formation control problem is proposed in this thesis. We formulated distance-based formation in a nonlinear optimal control framework and used the state-dependent Riccati equation (SDRE) technique as the primary tool for solving the optimal control problem. In general, a distance-based formation can be undirected, where distance constraints between pairs of agents are actively controlled by both adjacent agents, or directed, where just one of the neighboring agents is responsible for maintaining the desired distance. This thesis presents both, undirected and directed formations, and provides extensive simulations to verify the theoretical results. For undirected topologies, we studied the formation control problem where we showed that the proposed control law results in the global asymptotic stability of the closed-loop system under certain conditions. The formation tracking problem was studied, and the uniform ultimate boundedness of the solutions is rigorously proven. The proposed method guarantees collision avoidance among neighboring agents and prevents depletion of the agents' energy. In the directed distance-based formation control case, we developed a distributed, hierarchical control scheme for a particular class of directed graphs, namely directed triangulated and trilateral Laman graphs. The proposed controller ensures the global asymptotic stability of the desired formation. Rigorous stability analyses are carried out in all cases. Moreover, we addressed the flip-ambiguity issue by using the signed area and signed volume constraints. Additionally, we introduced a performance index for a formation mission that can indicate the controller's overall performance. We also studied the distance-based formation control of nonlinear agents. We proposed a method that can guarantee asymptotic stability of the distance-based formation for a broad category of nonlinear systems. Furthermore, we studied a distance-based formation control of uncertain nonlinear agents. Based on the combination of integral sliding mode control (ISMC) theory with the SDRE method, we developed a robust optimal formation control scheme that guarantees asymptotic stability of the desired distance-based formation in the presence of bounded uncertainties. We have shown that the proposed controller can compensate for the effect of uncertainties in individual agents on the overall formation

Resilient visual perception for multiagent systems

There has been an increasing interest in visual sensors and vision-based solutions for single and multi-robot systems. Vision-based sensors, e.g., traditional RGB cameras, grant rich semantic information and accurate directional measurements at a relatively low cost; however, such sensors have two major drawbacks. They do not generally provide reliable depth estimates, and typically have a limited field of view. These limitations considerably increase the complexity of controlling multiagent systems. This thesis studies some of the underlying problems in vision-based multiagent control and mapping. The first contribution of this thesis is a method for restoring bearing rigidity in non-rigid networks of robots. We introduce means to determine which bearing measurements can improve bearing rigidity in non-rigid graphs and provide a greedy algorithm that restores rigidity in 2D with a minimum number of added edges. The focus of the second part is on the formation control problem using only bearing measurements. We address the control problem for consensus and formation control through non-smooth Lyapunov functions and differential inclusion. We provide a stability analysis for undirected graphs and investigate the derived controllers for directed graphs. We also introduce a newer notion of bearing persistence for pure bearing-based control in directed graphs. The third part is concerned with the bearing-only visual homing problem with a limited field of view sensor. In essence, this problem is a special case of the formation control problem where there is a single moving agent with fixed neighbors. We introduce a navigational vector field composed of two orthogonal vector fields that converges to the goal position and does not violate the field of view constraints. Our method does not require the landmarks' locations and is robust to the landmarks' tracking loss. The last part of this dissertation considers outlier detection in pose graphs for Structure from Motion (SfM) and Simultaneous Localization and Mapping (SLAM) problems. We propose a method for detecting incorrect orientation measurements before pose graph optimization by checking their geometric consistency in cycles. We use Expectation-Maximization to fine-tune the noise's distribution parameters and propose a new approximate graph inference procedure specifically designed to take advantage of evidence on cycles with better performance than standard approaches. These works will help enable multi-robot systems to overcome visual sensors' limitations in collaborative tasks such as navigation and mapping

Robust Observation and Control of Complex Networks

The problem of understanding when individual actions of interacting agents display to a coordinated collective behavior has receiving a considerable attention in many research fields. Especially in control engineering, distributed applications in cooperative environments are achieving resounding success, due to the large number of relevant applications, such as formation control, attitude synchronization tasks and cooperative applications in large-scale systems. Although those problems have been extensively studied in Literature, themost of classic approaches use to consider the unrealistic scenario in which networks always consist of identical, linear, time-invariant entities. It’s clear that this assumption strongly approximates the effective behavior of a network. In fact agents can be subjected to parameter uncertainties, unmodeled dynamics or simply characterized by proper nonlinear dynamics. Therefore, motivated by those practical problems, the present Thesis proposes various approaches for dealing with the problem of observation and control in both the framework of multi-agents and complex interconnected systems. The main contributions of this Thesis consist on the development of several algorithms based on concepts of discontinuous slidingmode control. This techniques can be employed for solving in finite-time problems of robust state estimation and consensus-based synchronization in network of heterogenous nonlinear systems subjected to unknown but bounded disturbances and sudden topological changes. Both directed and undirected topologies have been taken into account. It is worth to mention also the extension of the consensus problem to networks of agents governed by a class parabolic partial differential equation, for which, for the first time, a boundary-based robust local interaction protocol has been presented

Robust Observation and Control of Complex Networks

The problem of understanding when individual actions of interacting agents display to a coordinated collective behavior has receiving a considerable attention in many research fields. Especially in control engineering, distributed applications in cooperative environments are achieving resounding success, due to the large number of relevant applications, such as formation control, attitude synchronization tasks and cooperative applications in large-scale systems. Although those problems have been extensively studied in Literature, themost of classic approaches use to consider the unrealistic scenario in which networks always consist of identical, linear, time-invariant entities. It’s clear that this assumption strongly approximates the effective behavior of a network. In fact agents can be subjected to parameter uncertainties, unmodeled dynamics or simply characterized by proper nonlinear dynamics. Therefore, motivated by those practical problems, the present Thesis proposes various approaches for dealing with the problem of observation and control in both the framework of multi-agents and complex interconnected systems. The main contributions of this Thesis consist on the development of several algorithms based on concepts of discontinuous slidingmode control. This techniques can be employed for solving in finite-time problems of robust state estimation and consensus-based synchronization in network of heterogenous nonlinear systems subjected to unknown but bounded disturbances and sudden topological changes. Both directed and undirected topologies have been taken into account. It is worth to mention also the extension of the consensus problem to networks of agents governed by a class parabolic partial differential equation, for which, for the first time, a boundary-based robust local interaction protocol has been presented

Mathematical Theory and Modelling in Atmosphere-Ocean-Science

Participants from around the world gathered to review application and development of mathematics in relation to problems in the atmospheric, oceanic and climate sciences

Contributions of synaptic filters to models of synaptically stored memory

The question of how neural systems encode memories in one-shot without immediately disrupting previously stored information has puzzled theoretical neuroscientists for years and it is the central topic of this thesis. Previous attempts on this topic, have proposed that synapses probabilistically update in response to plasticity inducing stimuli to effectively delay the degradation of old memories in the face of ongoing memory storage. Indeed, experiments have shown that synapses do not immediately respond to plasticity inducing stimuli, since these must be presented many times before synaptic plasticity is expressed. Such a delay could be due to the stochastic nature of synaptic plasticity or perhaps because induction signals are integrated before overt strength changes occur.The later approach has been previously applied to control fluctuations in neural development by low-pass filtering induction signals before plasticity is expressed. In this thesis we consider memory dynamics in a mathematical model with synapses that integrate plasticity induction signals to a threshold before expressing plasticity. We report novel recall dynamics and considerable improvements in memory lifetimes against a prominent model of synaptically stored memory. With integrating synapses the memory trace initially rises before reaching a maximum and then falls. The memory signal dissociates into separate oblivescence and reminiscence components, with reminiscence initially dominating recall. Furthermore, we find that integrating synapses possess natural timescales that can be used to consider the transition to late-phase plasticity under spaced repetition patterns known to lead to optimal storage conditions. We find that threshold crossing statistics differentiate between massed and spaced memory repetition patterns. However, isolated integrative synapses obtain an insufficient statistical sample to detect the stimulation pattern within a few memory repetitions. We extend the modelto consider the cooperation of well-known intracellular signalling pathways in detecting storage conditions by utilizing the profile of postsynaptic depolarization. We find that neuron wide signalling and local synaptic signals can be combined to detect optimal storage conditions that lead to stable forms of plasticity in a synapse specific manner.These models can be further extended to consider heterosynaptic and neuromodulatory interactions for late-phase plasticity.<br/

Analysis, modelling and prediction of deterministic and stochastic complex systems

The analysis of complex systems at nano- and micro-scales often requires their numerical simulation. Atomistic simulations, that rely on solving Newton's equation for each component of the system, despite being exact, are often too computationally expensive. In this work, firstly we analyse the properties of confined systems by extracting mesoscopic information directly from particles coordinate. Then, taking advantage of Mori-Zwanzig projector operator techniques and advanced data-analysis tools, we present a novel approach to parametrize non-Markovian coarse-graining models of molecular system. We focus on the parametrization of the memory terms in the stochastic Generalized Langevin Equation through a deep-learning approach. Moreover, in the framework of Dynamical Density Functional Theory (DDFT) we derive a continuum non-Markovian formulation, able to describe, given the proper free-energy, the physical properties of an atomistic system. Comparisons between molecular dynamics, fluctuating dynamical density functional theory and fluctuating hydrodynamics simulations validate our approach. Finally, we propose some numerical schemes for the simulation of DDFT with additional complexities, i.e. with stochastic terms and non-homogeneous non-constant diffusion.Open Acces

Complex oscillations with multiple timescales - Application to neuronal dynamics

The results gathered in this thesis deal with multiple time scale dynamical systems near non-hyperbolic points, giving rise to canard-type solutions, in systems of dimension 2, 3 and 4. Bifurcation theory and numerical continuation methods adapted for such systems are used to analyse canard cycles as well as canard-induced complex oscillations in three-dimensional systems. Two families of such complex oscillations are considered: mixed-mode oscillations (MMOs) in systems with two slow variables, and bursting oscillations in systems with two fast variables. In the last chapter, we present recent results on systems with two slow and two fast variables, where both MMO-type dynamics and bursting-type dynamics can arise and where complex oscillations are also organised by canard solutions. The main application area that we consider here is that of neuroscience, more precisely low-dimensional point models of neurons displaying both sub-threshold and spiking behaviour. We focus on analysing how canard objects allow to control the oscillatory patterns observed in these neuron models, in particular the crossings of excitability thresholds