This paper is concerned with the stabilization of discrete-time linear systems with quantization of the input and output spaces, i.e., when available values of inputs and outputs are discrete. Unlike most of the existing literature, we assume that how the input and output spaces are quantized is a datum of the problem, rather than a degree of freedom in design. Our focus is hence on the existence and synthesis of symbolic feedback controllers, mapping output words into the input alphabet, to steer a quantized I/O system to within small invariant neighborhoods of the equilibrium starting from large attraction basins. We provide a detailed analysis of the practical stabilizability of systems in terms of the size of hypercubes bounding the initial conditions, the state transient and the steady state evolution. We also provide an explicit construction of a practically stabilizing controller for the quantized I/O case.
We investigated whether the visual hMT+ cortex plays a role in supramodal representation of sensory flow, not mediated by visual mental imagery. We used functional magnetic resonance imaging to measure neural activity in sighted and congenitally blind individuals during passive perception of optic and tactile flows. Visual motion-responsive cortex, including hMT+, was identified in the lateral occipital and inferior temporal cortices of the sighted subjects by response to optic flow. Tactile flow perception in sighted subjects activated the more anterior part of these cortical regions but deactivated the more posterior part. By contrast, perception of tactile flow in blind subjects activated the full extent, including the more posterior part. These results demonstrate that activation of hMT+ and surrounding cortex by tactile flow is not mediated by visual mental imagery and that the functional organization of hMT+ can develop to subserve tactile flow perception in the absence of any visual experience. Moreover, visual experience leads to a segregation of the motion-responsive occipitotemporal cortex into an anterior subregion involved in the representation of both optic and tactile flows and a posterior subregion that processes optic flow only.
This paper deals with design and implementation of innovative haptic interfaces based on Magnetorheological fluids (MRFs). This pioneering research work consists in developing 2D and quasi-3D MRF-based devices capable of suitably energizing the fluid with a magnetic field in order to build figures which can be directly squeezed by hands. These devices are able to properly create a distribution of magnetic field over time and space inducing the fluid to assume desired shape and compliance. We implemented different prototypes whose synthesis and design phase, here described in detail, was prepared by preliminary simulations obtained by means of software based on a 3D Finite Element code. In this way, both magnetic field and shear stress profiles inside the fluid can be carefully predicted. Finally, performance of these devices was evaluated and assessed.
A broad spectrum of issues have to be addressed in order to tackle the problem of a safe and dependable physical Human-Robot Interaction (pHRI). In the immediate future, metrics related to safety and dependability have to be found in order to successfully introduce robots in everyday enviornments. While there are certainly also ``cognitive
The problem of efficiently steering dynamical systems by generating finite input plans is considered. Finite plans are finite–length words constructed on a finite alphabet of input symbols, which could be e.g. transmitted through a limited capacity channel to a remote system, where they can be decoded in suitable control actions. Efficiency is considered in terms of the computational complexity of plans, and in terms of their description length (in number of bits). We show that, by suitable choice of the control encoding, finite plans can be efficiently built for a wide class of dynamical systems, computing arbitrarily close approximations of a desired equilibrium in polynomial time. The paper also investigates how the efficiency of planning is affected by the choice of inputs, and provides some results as to optimal performance in terms of accuracy and range.
It is well established that for a cascade of two uniformly globally asymptotically stable (UGAS) systems, the origin remains UGAS provided that the solutions of the cascade are uniformly globally bounded. While this result has met considerable popularity in specific applications it remains restrictive since, in practice, it is often the case that the decoupled subsystems are only uniformly \emph{semiglobally} \emph{practically} asymptotically stable (USPAS). Recently, we established that the cascade of USPAS systems is USPAS under a local boundedness assumption and the hypothesis that one knows a Lyapunov function for the driven subsystem. The contribution of this paper is twofold: 1) we establish USPAS of cascaded systems without the requirement of a Lyapunov function and 2) we present a converse theorem for USPAS. While other converse theorems in the literature cover the case of USPAS ours has the advantage of providing a bound on the gradient of the Lyapunov function, which is fundamental to establish theorems for cascades.
It is due to the modularity they provide that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on ``adding integrators''. Nevertheless, the standing assumptions in most of the present literature on cascaded systems is that, when \emph{decoupled}, the subsystems constituting the cascade are uniformly globally asymptotically stable (UGAS). Hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable (USPAS). This situation is often encountered in control practice, ıt e.g.}, in control of physical systems with external perturbations, measurement noise, unmodelled dynamics, ıt etc}. After giving a rigorous framework for the analysis of such stability properties, this paper generalizes previous results for cascades by establishing that, under a uniform boundedness condition on its solutions, the cascade of two USPAS systems remains USPAS. An analogous result is derived for uniformly semiglobally asymptotically stable (USAS) systems in cascade. Furthermore, we show the utility of our results in the PID control of mechanical systems affected by unknown non-dissipative forces and considering the dynamics of the DC motors.
This paper aims to give sufficient conditions for a cascade composed of nonlinear time-varying systems that are uniformly globally practically asymptotically stable (UGPAS) to be UGPAS. These conditions are expressed as relations between the Lyapunov function of the driven subsystem and the interconnection term. Our results generalise previous theorems that establish the uniform global asymptotic stability of cascades.
In this paper, we consider the problem of stabilizing the kinematic model of a car to a path in the plane under rather general conditions. The path is subject to very mild restrictions, while the car model, although rather simplified, contains the most relevant limitations inherent in wheeled robots kinematics. Namely, the car can only move forward, its steering radius is lower bounded and a limited sensory information only provides a partial knowledge of some state parameters. In particular, we consider the case that the current distance and the heading angle error with respect to the closest point on the reference path can be measured but only the sign of the path curvature is detected. These constraints are such to make classical control techniques inefficient. As the feedback information is both continuous and discrete, the hybrid systems formalism turns out to be well appropriate to model the problem. The proposed approach is based on optimal control techniques successfully applied in a previous work for following rectilinear path. We propose here an extension to the tracking of more general paths with moderate curvature. The stability of the closed-loop system is proved by means of the hybrid system formalism and hybrid formal verification techniques. Finally, the practicality of the proposed approach, in spite of non–idealities in real-world applications, is discussed by reporting experimental results.
In this paper we describe work being done at our department to make the Robotics Laboratory accessible to student and colleagues, to execute and watch real-time experiments at any time and from anywhere. We describe few different installations, and highlight the underlying philosophy, wich is aimed at enlarging the lab in all the dimensions of space, time, and available resources, through the use of Internet technologies.
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Special Issue on Internet & Online Robots for Telemanipulation
In this paper the synthesis and design of a new device for the energization and characterization of Magneto-Rheological Fluids (MRF) for haptic interfaces are presented. Due to the core structure and feeding conditions, only a 3D numerical analysis provides an accurate prediction of the electromagnetic quantities and the rheological behavior of an excited specimen. The design constraints are shown in details and the results in terms of magnetic field inside the fluid and its spatial resolution are discussed.
We address the problem of synthesising real-time embedded controllers taking into account constraints deriving from the implementation platform. Assuming a time-triggered model of computation for tasks controlling a set of independent systems and a real-time preemptive scheduling policy managing a single CPU processor board, we deal with two problems: 1- deciding whether a performance specification can be met on a given platform, 2- optimising performance on a platform. Decision variables of the design problems are the activation periods of the tasks , while the considered performance metric is the minimum stability radius attained over the different feedback loops, which is related to the technological feasibility of the controller and to the robustness of the controlled systems. The analytical formulation of the design problems enables efficient numerical solutions. The resulting control policies are directly implementable without performance degradation that may otherwise arise due to scheduling and execution delays.
In this work we face the stability problem for quantized control systems (QCS). A discrete–time single–input linear model is considered and, motivated by technological applications, we assume that a uniform quantization of the control set is a priori fixed. As it is well known, for QCS only practical stability properties can be achieved, therefore we focus on the existence and construction of quantized controllers capable of steering a system to within invariant neighborhoods of the equilibrium. The main contribution of the paper consists in a theorem which provides a condition for the practical stabilization in a fixed number of steps: not only the result is interesting in itself, but also it enables to construct a family of stabilizing controllers by means of Model Predictive Control (MPC) techniques. In the last part of the paper some results on the characterization of controlled–invariant sets are reviewed and a lower bound on the size of invariant sets is provided.
Rolling a ball on a plane is a standard example of nonholonomy reported in many textbooks, and the problem is also well understood for any smooth deformation of the surfaces. For non-smoothly deformed surfaces, however, much less is known. Although it may seem intuitive that nonholonomy is conserved (think e.g. to polyhedral approximations of smooth surfaces), current definitions of ``nonholonomy'' are inherently referred to systems described by ordinary differential equations, and are thus inapplicable to such systems. \İn this paper we study the set of positions and orientations that a polyhedral part can reach by rolling on a plane through sequences of adjacent faces. We provide a description of such reachable set, discuss conditions under which the set is dense, or discrete, or has a compound structure, and provide a method for steering the system to a desired reachable configuration, robustly with respect to model uncertainties. \\Based on ideas and concepts encountered in this case study, and in some other examples we provide, we turn back to the most general aspects of the problem and investigate the possible generalization of the notion of (kinematic) nonholonomy to non-smooth, discrete, and hybrid dynamical systems. To capture the essence of phenomena commonly regarded as ``nonholonomic'', at least two irreducible concepts are to be defined, of ``internal'' and ``external'' nonholonomy, which may coexist in the same system. These definitions are instantiated by examples.
In this paper we discuss the problem of achieving good performance in accuracy and promptness by a robot manipulator under the condition that safety is guaranteed throughout task execution. The particular but basic problem of single-joint actuation is considered in detail. Intuitively, while a rigid and powerful structure of the arm would favour its performance, lightweight compliant structures are more suitable to safe operation. The quantitative analysis of the resulting design trade-off between safety and performance is one of the objectives of our work. Such analysis has a strong impact on how robot mechanisms and controllers should be designed for human-interactive applications. We discuss few different possible concepts for safely actuating joints, and focus our attention on one, the Variable-Stiffness Transmission (VST) approach. Some aspects related to the implementation of the mechanics and control of VST joints are reported.
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PUBLISHER'S NOTE: In this paper, there are three errors introduced during production. First, the correct title of the article is Fast and Soft Arm Tactics. Also, on formulae for GSI and HIC in page 23, the acceleration is measured in multiples of the acceleration of gravity (g) [not grams], while time is measured in seconds. Finally, within Figure 1, one should read Compliant Covering, and Mrob = Mrotor + Mlink [instead of Krob = Krotor + Klink]. Please visit http://www.ncsu.edu/IEEE-RAS/RAM/BicchiFigure1.pdf to see the original figure.
