B. Brogliato

On the control of finite-dimensional mechanical systems with unilateral constraints

This paper focuses on the problem of the control of a class of mechanical systems with a finite number of degrees-of-freedom, subject to unilateral constraints on the position. Roughly speaking, those systems are described by a set of ordinary differential equations that represent smooth dynamics, together with an algebraic inequality condition F(q)/spl ges/0 (where q is the vector of generalized coordinates) and an impact rule relating the interaction impulse and the velocity. Nonsmooth dynamics is at the core of the study of such systems. This implies that one can suitably define solutions and stability concepts that fit with the considered model. We then discuss the closed-loop control problem, and analyze various switching control strategies.

Global tracking controllers for flexible-joint manipulators: a comparative study

Abstract Several new controller design techniques for global stabilization of nonlinear systems have recently been reported. Typically, these methodologies provide the designer with various degrees of freedom; consequently, their application in specific examples leads to the definition of various control schemes. One question of interest is the relationship between these schemes, or whether one contains the other. Further, since these schemes will, in general, exhibit different transients and possess different robustness properties, another challenging research problem is to establish some common framework to compare their robustness and performance properties. In this paper we investigate these questions for three different controller design techniques as applied to the problem of global tracking of robots with flexible joints. The connection between the various controllers are investigated. Further, they are compared using the following performance indicators: continuity properties vis-a-vis the joint stiffness, availability of adaptive implementations when the robot parameters are unknown, and robustness to ‘energy-preserving’ (i.e. passive) unmodelled effects. Complete stability proofs of all the resulting controllers are given.

Passivity and global stabilization of cascaded nonlinear systems

An alternative stability analysis is presented for recent results on global stabilization of a nonlinear system in cascade with a linear system. The analysis is carried out using passivity arguments. The relationship between passivity and an important class of Lyapunov function is also presented. >

An exponentially stable adaptive control for force and position tracking of robot manipulators

The problem of controlling a robot manipulator while the end effector is in contact with an environment of finite but unknown stiffness is considered. An exponentially stable control law is derived starting from a passivity-based position control algorithm. The original position trajectory is scaled along the interaction direction so as to achieve force tracking as well as position tracking along the unconstrained directions. A passivity-based adaptive algorithm is designed to avoid the explicit computation of the scaling factor, which depends on the unknown stiffness of the environment, leading to time-varying PID control actions on the force error.

Practical stabilization of a class of nonlinear systems with partially known uncertainties

Abstract In this paper we deal with robust control of a class of nonlinear systems which contain uncertainties. It can be viewed as an extension of the work in Corless and Leitmann [IEEE Trans, Autom. Control, AC-26, 1139–1144 (1981)] for the cases where the vector of uncertainties is only partially known. To cope with the uncertainties, an adaptive controller using a dead-zone and a hysteresis function is proposed and both the uniform boundedness of all the closed-loop signals and uniform ultimate boundedness of the system state are guaranteed. In contrast with some previous attempts to relax the a priori knowledge on the uncertainties bounds by using a discontinuous control law, we propose continuous control laws in this paper. Hence, chattering problems (which have practical importance) can be avoided.

Adaptive control of first-order nonlinear systems with reduced knowledge of the plant parameters

This paper presents an adaptive control strategy for a class of first-order nonlinear systems of the form x/spl dot/=/spl theta//sub 1/*/sup T/f(x)+/spl theta//sub 2/*/sup T/g(x), where g(x) is a smooth function, whereas f(x) satisfies sectoricity conditions. /spl theta//sub 1/* and /spl theta//sub 2/* are constant parameter vectors. It is assumed that the system remains controllable for all values of x, but the sign of /spl theta//sub 2/*/sup T/g(x)(x) is unknown. The proposed adaptive scheme extends ideas previously presented the authors (1992) where the term premultiplying the input was supposed to be constant. The standard least-squares estimates of /spl theta//sub 2/* are modified using a hysteresis type switching algorithm that enables us to conclude on existence, uniqueness, boundedness and convergence of the solutions of the adaptive closed-loop system. >

Direct adaptive impedance control including transition phases

This paper presents a new direct adaptive impedance controller for force/position task that includes transition phases from free to constrained motions. This scheme ensures global asymptotic stability without the need for a priori knowledge of environment stiffness. One of the major consequence of this study is that a generalization of the time-varying impedance leads to integral force feedback. Experimental results on a two-degree-of-freedom planar manipulator are reported.

On the transition phase in robotics: impact models, dynamics and control

The aim of this note is threefold: i) to introduce a rigorous mathematical model of impulsive collisions dynamics through the use of Schwartzs distributions; ii) to study the relationships between impulsive and continuous dynamics models of impacts (i.e. models composed of mass, spring, damper); and iii) to analyze the difficulties associated with the transition phase control. The authors start a tentative comparison on two models of impacts through a simple example of a mass colliding with a wall. Numerical simulations illustrating the examples are presented.<<ETX>>

Direct adaptive impedance control

Abstract This note presents a new direct adaptive impedance controller for force /position task. We assume that the environment stiffness is unknown and we consider the one-degree of freedom (dof) case. One of the major consequence of this study is that a generalization of the time-varying impedance leads to integral force feedback. Experimental results on a 2-dof planar manipulator are reported.

Correction to "Adaptive control of robot manipulators with flexible joint"

The above paper by the authors (Lozano and Brogliato, ibid., vol.37, p.174-81, 1992) contains two flaws that were brought to their attention. The first mistake concerns the definition of a signal which then effects the initial conditions on the state and on the desired trajectory. The second mistake is in the regressor matrix. Consequently the stability analysis given in one of the appendices is not complete. The authors provide corrections to the above mistakes.