Model Based Control of Soft Robots: A Survey of the State of the Art and Open Challenges

Continuum soft robots are mechanical systems entirely made of continuously deformable elements. This design solution aims to bring robots closer to invertebrate animals and soft appendices of vertebrate animals (e.g., an elephant's trunk, a monkey's tail). This work aims to introduce the control theorist perspective to this novel development in robotics. We aim to remove the barriers to entry into this field by presenting existing results and future challenges using a unified language and within a coherent framework. Indeed, the main difficulty in entering this field is the wide variability of terminology and scientific backgrounds, making it quite hard to acquire a comprehensive view on the topic. Another limiting factor is that it is not obvious where to draw a clear line between the limitations imposed by the technology not being mature yet and the challenges intrinsic to this class of robots. In this work, we argue that the intrinsic effects are the continuum or multi-body dynamics, the presence of a non-negligible elastic potential field, and the variability in sensing and actuation strategies.Comment: 69 pages, 13 figure

Formulation of Model-Based Optimal Control for Practical Applications

Ph.DDOCTOR OF PHILOSOPH

Stochastic Hybrid Model Predictive Control using Gaussian Processes for Systems with Piecewise Residual Dynamics

Data-driven control methods have been used to provide performance and safety benefits for systems where lower fidelity nominal dynamics models are insufficient when operating systems at their limits. These methods typically make the implicit assumption that the underlying model is unimodal and does not vary at different points in the workspace. However, when dealing with systems operating under the effect of piecewise unmodelled dynamics, approximating these by unimodal learnt models leads to inaccuracies in prediction over a horizon affecting performance and safety. In contrast, this thesis proposes the learning of hybrid models for use in a hybrid Model Predictive Control (MPC) framework to address these issues. An algorithm to help with improving the computational tractability of such a controller is also developed. Finally, a methodology is demonstrated that allows for efficiently identifying the active mode (component of unmodelled dynamics) in effect at different points of the workspace by leveraging the information contained in the hybrid model

Model Predictive Control Strategies for Advanced Battery Management Systems

Consumer electronics, wearable and personal health devices, power networks, microgrids, and hybrid electric vehicles (HEVs) are some of the many applications where Lithium-ion (Li-ion) batteries are employed. From a manufacturer point of view, the optimal design and management of such electrochemical accumulators are important aspects for ensuring safe and profitable operations. The adoption of mathematical models can support the achievement of the best performance, while saving time and money. In the literature, all the models used to describe the behavior of a Li-ion battery belong to one of the two following families: (i) Equivalent Circuit Models (ECMs), and (ii) Electrochemical Models (EMs). While the former family represents the battery dynamics by means of electrical circuits, the latter resorts to first principles laws of modeling. As a first contribution, this Thesis provides a thorough investigation of the pseudo-two-dimensional (P2D) Li-ion battery EM. In particular, the objectives are to provide: (i) a detailed description of the model formulation, (ii) the Li-ION SIMulation BAttery (LIONSIMBA) toolbox as a finite volume Matlab implementation of the P2D model, for design, simulation, and control of Li-ion cells or battery packs, (iii) a validation of the proposed tool with respect to the COMSOL MultiPhysics commercial software and the Newman's DUALFOIL code, and (iv) some demonstrative simulations involving thermal dynamics, a hybrid charge-discharge cycle emulating the throttle of an HEV, and a battery pack of series connected cells. The second contribution is related to the development of several charging strategies for Advanced Battery Management Systems (ABMSs), where predictive approaches are employed to attain optimal control. Model Predictive Control (MPC) refers to a particular family of control algorithms that, according to a mathematical model, predicts the future behavior of a plant, while considering inputs and outputs constraints. According to this paradigm, in this Thesis different ABMSs strategies have been developed, and their effectiveness shown through simulations. Due to the complexity of the P2D model, its inclusion within an MPC context could prevent the online application of the control algorithm. For this reason, different approximations of the P2D dynamics are proposed and their MPC formulations carefully explained. In particular, finite step response, autoregressive exogenous, piecewise affine, and linear time varying approximations are presented. For all the aforementioned reformulations, the closed-loop performance are evaluated considering the P2D implementation of LIONSIMBA as the real plant. The closed-loop simulations highlight the suitability of the MPC paradigm to be employed for the development of the future ABMSs. In fact, its ability to predict the future behavior of the cell while considering operating constraints can help in preventing possible safety issues and improving the charging performance. Finally, the reliability and efficiency of the proposed Matlab toolbox in simulating the P2D dynamics, support the idea that LIONSIMBA can significantly contribute in the advance of the battery field.Consumer electronics, wearable and personal health devices, power networks, microgrids, and hybrid electric vehicles (HEVs) are some of the many applications where Lithium-ion (Li-ion) batteries are employed. From a manufacturer point of view, the optimal design and management of such electrochemical accumulators are important aspects for ensuring safe and profitable operations. The adoption of mathematical models can support the achievement of the best performance, while saving time and money. In the literature, all the models used to describe the behavior of a Li-ion battery belong to one of the two following families: (i) Equivalent Circuit Models (ECMs), and (ii) Electrochemical Models (EMs). While the former family represents the battery dynamics by means of electrical circuits, the latter resorts to first principles laws of modeling. As a first contribution, this Thesis provides a thorough investigation of the pseudo-two-dimensional (P2D) Li-ion battery EM. In particular, the objectives are to provide: (i) a detailed description of the model formulation, (ii) the Li-ION SIMulation BAttery (LIONSIMBA) toolbox as a finite volume Matlab implementation of the P2D model, for design, simulation, and control of Li-ion cells or battery packs, (iii) a validation of the proposed tool with respect to the COMSOL MultiPhysics commercial software and the Newman's DUALFOIL code, and (iv) some demonstrative simulations involving thermal dynamics, a hybrid charge-discharge cycle emulating the throttle of an HEV, and a battery pack of series connected cells. The second contribution is related to the development of several charging strategies for Advanced Battery Management Systems (ABMSs), where predictive approaches are employed to attain optimal control. Model Predictive Control (MPC) refers to a particular family of control algorithms that, according to a mathematical model, predicts the future behavior of a plant, while considering inputs and outputs constraints. According to this paradigm, in this Thesis different ABMSs strategies have been developed, and their effectiveness shown through simulations. Due to the complexity of the P2D model, its inclusion within an MPC context could prevent the online application of the control algorithm. For this reason, different approximations of the P2D dynamics are proposed and their MPC formulations carefully explained. In particular, finite step response, autoregressive exogenous, piecewise affine, and linear time varying approximations are presented. For all the aforementioned reformulations, the closed-loop performance are evaluated considering the P2D implementation of LIONSIMBA as the real plant. The closed-loop simulations highlight the suitability of the MPC paradigm to be employed for the development of the future ABMSs. In fact, its ability to predict the future behavior of the cell while considering operating constraints can help in preventing possible safety issues and improving the charging performance. Finally, the reliability and efficiency of the proposed Matlab toolbox in simulating the P2D dynamics, support the idea that LIONSIMBA can significantly contribute in the advance of the battery field

Invariant Set-based Methods for the Computation of Input and Disturbance Sets

This dissertation presents new methods to synthesize disturbance sets and input constraints set for constrained linear time-invariant systems. Broadly, we formulate and solve optimization problems that (a) compute disturbance sets such that the reachable set of outputs approximates an assigned set, and (b) compute input constraint sets guaranteeing the stabilizability of a given set of initial conditions. The proposed methods find application in the synthesis and analysis of several control schemes such as decentralized control, reduced-order control, etc., as well as in practical system design problems such as actuator selection, etc. The key tools supporting the develpment of the aforementioned methods are Robust Positive Invariant (RPI) sets. In particular, the problems that we formulate are such that they co-synthesize disturbance/input constraint sets along with the associated RPI sets. This requires embedding existing techniques to compute RPI sets within an optimization problem framework, that we facilitate by developing new results related to properties of RPI sets, polytope representations, inclusion encoding techniques, etc. In order to solve the resulting optimization problems, we develop specialized structure-exploiting solvers that we numerically demonstrate to outperform conventional solution methods. We also demonstrate several applications of the methods we propose for control design. Finally, we extend the methods to tackle data-driven control synthesis problems in an identification-for-control framework

Approximation methodologies for explicit model predictive control of complex systems

This thesis concerns the development of complexity reduction methodologies for the application of multi-parametric/explicit model predictive (mp-MPC) control to complex high fidelity models. The main advantage of mp-MPC is the offline relocation of the optimization task and the associated computational expense through the use of multi-parametric programming. This allows for the application of MPC to fast sampling systems or systems for which it is not possible to perform online optimization due to cycle time requirements. The application of mp-MPC to complex nonlinear systems is of critical importance and is the subject of the thesis. The first part is concerned with the adaptation and development of model order reduction (MOR) techniques for application in combination to mp-MPC algorithms. This first part includes the mp-MPC oriented use of existing MOR techniques as well as the development of new ones. The use of MOR for multi-parametric moving horizon estimation is also investigated. The second part of the thesis introduces a framework for the ‘equation free’ surrogate-model based design of explicit controllers as a possible alternative to multi-parametric based methods. The methodology relies upon the use of advanced data-classification approaches and surrogate modelling techniques, and is illustrated with different numerical examples.Open Acces