Catálogo de publicaciones - libros

This chapter illustrates various finite-time analysis and design problems for linear systems. Most of this work deals with continuous-time systems. First, some conditions for finite-time stability and boundedness are presented; then we turn to the design problem. In this context, we consider both the state feedback and the output feedback synthesis. For both cases, we end up with some sufficient conditions involving linear matrix inequalities (both algebraic and differential). The last section of the chapter extends the previous results to discrete-time systems.

The plant model appropriate for designing the control strongly depends on the requirements. Simple models are enough to compute nondemanding controls. The parameters of well-defined structural models of flexible robot manipulators are difficult to determine because their effect is only visible if the manipulator is under strong actions or with high-frequency excitation. Thus, in this chapter, an iterative approach is suggested. This approach is applied to a one-degree-of-freedom flexible robot manipulator, first using some well-known models and then controlling a lab prototype. This approach can be used with a variety of control design and/or identification techniques.

Several tasks of the most recent robotics applications require high control performances, which cannot be achieved by the classical joint independent control schemes widely used in the industrial field. The necessity to directly take into account parasitic phenomena affecting motion control, such as friction, often leads to the development of model-based control schemes. The actual effectiveness of such schemes is strongly dependent on the accuracy with which the robot dynamics and the friction effects are compensated by the identified models, and it must be assessed by suitable experimental tests. In this chapter, different solutions are investigated for the development of a model-based control scheme, including joint friction compensation, for a two-links, planar, direct-drive manipulator. In particular, the use of available nominal robot inertial parameters for the identification of a nonlinear friction function, based on the well-known LuGre model, is compared with a complete dynamic calibration of the manipulator, including the estimation of both the robot dynamics and the parameters of a polynomial friction function. The identification results are discussed in the two cases, and inverse dynamics control schemes, based on the identified models, are experimentally applied to the manipulator for the execution of different trajectories, which allow the evaluation of the control performances in different conditions.

The problem of controlling the interaction of a flexible link arm with a compliant environment is considered. The arm’s tip is required to keep contact with a surface by applying a constant force and maintaining a prescribed position or following a desired path on the surface. Using singular perturbation theory, the system is decomposed into a slow subsystem associated with rigid motion and a fast subsystem associated with link flexible dynamics. A parallel force and position control developed for rigid robots is adopted for the slow subsystem, while a fast control action is employed to stabilize the link deflections. Simulation results are presented for a two-link planar arm under gravity in contact with an elastically compliant surface.

In this paper an implicit fault tolerant control scheme is specialized for an n -degrees-of-freedom fully actuated mechanical manipulator subject to sinusoidal torque disturbances acting on joints. We show in detail how a standard tracking controller can be “augmented” with an internal model unit designed to compensate the unknown spurious torque harmonics. In this way the controller is proved to be global implicitly fault tolerant to all the faults belonging to the model embedded in the regulator. Moreover, by simply testing the state of the internal model we will show how to perform fault detection and isolation.

Autonomous navigation of mobile robots requires the continuous estimation of the vehicle position and orientation in a given reference frame (localization problem). When moving in unknown environments, the more challenging problem of building a map, while at the same time localizing within it, must be faced (simultaneous localization and map building, SLAM). By adopting a landmark-based description of the environment, both tasks can be cast as a state estimation problem for an uncertain dynamic system, based on noisy measurements. Under the assumption that both process disturbances and measurement errors are unknown but bounded, the estimation process can be carried out in terms of feasible sets. This chapter reviews efficient set membership localization and mapping techniques for different kinds of available measurements and different classes of approximating regions. An extension of the SLAM algorithm to the case of a team of cooperating robots is also presented. The proposed techniques are validated through extensive numerical simulations and experimental tests performed in a laboratory setup.

In this chapter we present an epipolar-based visual servoing for holonomic mobile robots equipped with panoramic camera. The proposed visual servoing is based on epipolar geometry and exploits the auto-epipolar property , a special configuration for the epipoles that occurs when the desired and the current panoramic views undergo a pure translation. This occurrence is detectable directly in the image plane simply controlling when the so-called biosculating conics all co-intersect at only two points. Our visual servoing control law exploits the auto-epipolar property in order to retrieve the equal orientation between target and current camera. Translation is performed by exploiting the epipoles. Simulation results and Lyapunov-based stability analysis demonstrate the parametric robustness of the proposed method. We also provide a short introduction to the Epipolar Geometry Toolbox (EGT), a free MATLAB software package developed at the University of Siena, with which all simulation results have been obtained. EGT can be downloaded from the EGT web site together with a detailed manual and code examples.

The chapter focuses on concepts and methodologies of coordinating and motion control aimed at maintaining complex spatial behaviour of nonlinear dynamical systems. The main approach is discussed in connection with problems of control of mechanical systems (rigid bodies, robotic manipulators, and mobile robots) and is naturally extended to coordinating the motions of redundant robots, underactuated mechanisms, and walking machines.

In this chapter, we present two main contributions: (1) a leader-follower formation controller based on dynamic feedback linearization, and (2) a framework for coordinating teams of mobile robots (i.e., swarms). We derive coordination algorithms that allow robot swarms having independent goals but sharing a common environment to reach their target destinations. Derived from simple potential fields and the hierarchical composition of potential fields, our framework leads to a decentralized approach to coordinate complex group interactions. Because the framework is decentralized, it can potentially scale to teams of tens and hundreds of robots. Simulation results verify the scalability and feasibility of the proposed coordination scheme.

In this chapter we provide a solution to the long-standing problem of transient stabilization of multimachine power systems with nonnegligible transfer conductances. More specifically, we consider the full 3 n -dimensional model of the n -generator system with lossy transmission lines and loads and prove the existence of a nonlinear static state feedback law for the generator excitation field that ensures asymptotic stability of the operating point with a well-defined estimate of the domain of attraction provided by a bona fide Lyapunov function. To design the control law we apply the recently introduced interconnection and damping assignment passivity-based control methodology that endows the closed-loop system with a port-controlled Hamiltonian structure with desired total energy function. The latter consists of terms akin to kinetic and potential energies, thus has a clear physical interpretation. Our derivations underscore the deleterious effects of resistive elements that, as is well known, hamper the assignment of simple “gradient” energy functions and compel us to include nonstandard cross terms. A key step in the construction is the modification of the energy transfer between the electrical and the mechanical parts of the system, which is obtained via the introduction of state-modulated interconnections.