Alessandro Macchelli

Modeling and Control of Complex Physical Systems

Energy exchange is a major foundation of the dynamics of physical systems, and, hence, in the study of complex multi-domain systems, methodologies that explicitly describe the topology of energy exchanges are instrumental in structuring the modeling and the computation of the systems dynamics and its control. This book is the outcome of the European Project Geoplex (FP5 IST-2001-34166) that studied and extended such system modeling and control methodologies. This unique book starts from the basic concept of port-based modeling, and extends it to port-Hamiltonian systems. This generic paradigm is applied to various physical domains, showing its power and unifying flexibility for real multi-domain systems.

Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency

In this paper, a two-layer approach is presented to guarantee the stable behavior of bilateral telemanipulation systems in the presence of time-varying destabilizing factors such as hard contacts, relaxed user grasps, stiff control settings, and/or communication delays. The approach splits the control architecture into two separate layers. The hierarchical top layer is used to implement a strategy that addresses the desired transparency, and the lower layer ensures that no “virtual” energy is generated. This means that any bilateral controller can be implemented in a passive manner. Separate communication channels connect the layers at the slave and master sides so that information related to exchanged energy is completely separated from information about the desired behavior. Furthermore, the proposed implementation does not depend on any type of assumption about the time delay in the communication channel. By complete separation of the properties of passivity and transparency, each layer can accommodate any number of different implementations that allow for almost independent optimization. Experimental results are presented, which highlight the benefit of the proposed framework.

Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach

The purpose of this paper is to show how the Timoshenko beam can be fruitfully described within the framework of distributed port Hamiltonian (dpH) systems so that rather simple and elegant considerations can be drawn regarding both the modeling and control of this mechanical system. After the dpH model of the beam is introduced, the control problem is discussed. In particular, it is shown how control approaches already presented in the literature can be unified, and a new control methodology is presented and discussed. This control methodology relies on the generalization to infinite dimensions of the concept of structural invariant (Casimir function) and on the extension to distributed systems of the so-called control by interconnection methodology. In this way, finite dimensional passive controllers can stabilize distributed parameter systems by shaping their total energy, i.e., by assigning a new minimum in the desired equilibrium configuration that can be reached if a dissipative effect is introduced.

Modeling and control of a flying robot for contact inspection

This paper focuses on the modeling and control of a flying robot. The complete system, composed of a quadrotor unmanned aerial vehicle and a custom-made manipulator, has been designed for remote inspection by contact of industrial plants. The goal of this paper is to show the dynamical characteristics of the flying robot during tasks that require physical interaction, and to determine a control strategy that allows to safely interact with unknown environments. The methodology has been implemented on a real prototype and tested in an indoor area. Experimental results validate the proposed controller and show its effectiveness.

Control by interconnection of mixed port Hamiltonian systems

In this note, the regulation problem for mixed finite and infinite dimensional port Hamiltonian systems (m-pH systems) is discussed. A m-pH system results from the power conserving interconnection of finite and infinite dimensional systems in port Hamiltonian form. In particular, the system given by the interconnection of two finite dimensional systems, one of which is the controller, by means of an infinite dimensional connection is studied. The proposed control methodology is a generalization to the infinite dimensional case of a well-established passivity-based control technique for finite-dimensional port Hamiltonian systems, the control by interconnection and energy shaping, according to which the open-loop energy function is shaped so that a minimum in the desired configuration is introduced. This procedure is possible once the state variable of the controller is related to the state variable of the plant by constraining the state of the closed-loop system on a structural invariant (defined by a set of Casimir functions). In this way, the energy function of the controller, which is freely assignable, becomes a function of the configuration of the plant and, then, it can be easily shaped in order to solve the regulation problem.

Developing an aerial manipulator prototype: physical interaction with the environment

This article focuses on the design, modeling, and control of an aerial manipulator prototype, i.e., an innovative configuration consisting of a miniature quadrotor helicopter endowed with a robotic manipulator. The overall system is designed to accomplish operations that require physical interaction with the surrounding environment while remaining airborne. To investigate the dynamical model of the aerial manipulator, a simple planar benchmark is used to analyze the interactions between the quadrotor, the robotic manipulator, and the environment. A control strategy for the planar system is designed to guarantee robustness in the presence or absence of contacts. Experiments on a real setup validate the control in the two different scenarios in which the aerial manipulator is either freely flying or physically interacting with the environment.

Impedance control of an aerial manipulator

This work focuses on the modeling and control of an innovative configuration of aerial robot arising from the combination of a vertical take-off and landing aircraft and a robotic arm. The overall system, denoted as aerial manipulator, is able to accomplish operations requiring the physical interaction with the surrounding environment while remaining airborne. After introducing a detailed dynamical model, a control law, based on the impedance control paradigm, able to govern all the degrees of freedom of the system is proposed. The effectiveness of the proposed control algorithm are investigated also considering the case in which contacts with the surrounding environment are achieved.

Exponential Stabilization of Boundary Controlled Port-Hamiltonian Systems With Dynamic Feedback

It is shown that a strictly-input passive linear finite dimensional controller exponentially stabilizes a large class of partial differential equations actuated at the boundary of a one dimensional spatial domain. This follows since the controller imposes exponential dissipation of the total energy. The result can by use for control synthesis and for the stability analysis of complex systems modeled by sets of coupled PDEs and ODEs. The result is specialized to port-Hamiltonian control systems and a simplified DNA-manipulation process is used to illustrate the result.

Port Hamiltonian formulation of infinite dimensional systems I. Modeling

In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multivariable case. The resulting class of infinite dimensional systems is quite general, thus allowing the description of several physical phenomena, such as heat conduction, piezoelectricity and elasticity. Furthermore, classical PDEs can be rewritten within this framework. The key point is the generalization of the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables.

Energy shaping of distributed parameter port-Hamiltonian systems based on finite element approximation

The main contribution of this paper is a procedure for the control by energy shaping via Casimir generation of infinite dimensional port-Hamiltonian systems based on a particular finite element approximation. The proposed approach is justified by the fact that the adopted spatial discretization technique is able to preserve Casimir functions in the closed-loop system when going from the distributed to the (approximated) lumped parameter system. Besides the intrinsic difficulties related to the large number of state variables, the finite element model is generally given in terms of a Dirac structure and is completely a-causal, which implies that the plant dynamics is not given in standard input-state-output form, but as a set of DAEs. Consequently, the classical energy Casimir method has to be extended in order to deal with dynamical systems with constraints, usually appearing in the form of Lagrangian multipliers. The general methodology is illustrated with the help of an example in which the distributed parameter system is a lossless transmission line.