Right-invertibility for a class of nonlinear control systems: A geometric approach

In recent years it has become evident that various synthesis problems known from linear system theory can also be solved for nonlinear control systems by using differential geometric methods. The purpose of this paper is to use this mathematical framework for giving a preliminary account on the notion of right-invertibility of a nonlinear system. This concept, which is of importance in several tracking problems, requires a Taylor-series expansion of the output function. We will also show that there is an appealing geometric interpretation of the lower-order terms in this series expansion. In this way a function that can occur as output function of a nonlinear system is partly described by specifying its k-jet

Feedback decomposition of nonlinear control systems

By using the recently developed (differential) geometric approach to nonlinear systems, a feedback decomposion for nonlinear control systems is derived

On dynamic decoupling and dynamic path controllability in economic systems

In this paper the dynamic decouplability and dynamic path controllability of nonlinear discrete-time economic systems in state space form are discussed. Based on the observation that both properties are equivalent, a (theoretical) efficient way of target path controllability is proposed. This is illustrated for a fairly general example of a closed economy

Global regulation of robots using only position measurements

In this note we propose a simple solution to the regulation problem of rigid robots based on the availability of only joint position measurements. The controller consists of two parts: (1) a gravitation compensation, (2) a linear dynamic first-order compensator. The gravitation compensation part can be chosen to be a function of either the actual joint position or the desired joint position. Both possibilities are aproved to yield global asymptotic stability. Performance issues of the controller are illustrated in a simulation study of a two degrees-of-freedom robot manipulator

On the stabilization of bilinear systems via constant feedback

We study the problem of stabilization of a bilinear system via a constant feedback. The question reduces to an eigenvalue problem on the pencil A+α0B of two matrices. Using the idea of simultaneous triangularization of the matrices involved, some easily checkable conditions for the solvability of this question are obtained. Algorithms for checking these conditions are given and illustrated by a few examples

Robust control of robots via linear estimated state feedback

In this note we propose a robust tracking controller for robots that requires only position measurements. The controller consists of two parts: a linear observer part that generates an estimated error state from the error on the joint position and a linear feedback part that utilizes this estimated state. It is shown that this computationally efficient controller yields semi-global uniform ultimate boundedness of the tracking error. An interesting feature of the controller is that it straightforwardly extends results on robust control of robots by linear state feedback to linear estimated-state feedbac

Adaptive tracking control of nonholonomic systems: an example

We study an example of an adaptive (state) tracking control problem for a four-wheel mobile robot, as it is an illustrative example of the general adaptive state-feedback tracking control problem. It turns out that formulating the adaptive state-feedback tracking control problem is not straightforward, since specifying the reference state-trajectory can be in conflict with not knowing certain parameters. Our example illustrates this difficulty and we propose a problem formulation for the adaptive state-feedback tracking problem that meets the natural prerequisite that it reduces to the state-feedback tracking problem if the parameters are known. A general methodology for solving the problem is derive

Experimental comparison of parameter estimation methods in adaptive robot control

In the literature on adaptive robot control a large variety of parameter estimation methods have been proposed, ranging from tracking-error-driven gradient methods to combined tracking- and prediction-error-driven least-squares type adaptation methods. This paper presents experimental data from a comparative study between these adaptation methods, performed on a two-degrees-of-freedom robot manipulator. Our results show that the prediction error concept is sensitive to unavoidable model uncertainties. We also demonstrate empirically the fast convergence properties of least-squares adaptation relative to gradient approaches. However, in view of the noise sensitivity of the least-squares method, the marginal performance benefits, and the computational burden, we (cautiously) conclude that the tracking-error driven gradient method is preferred for parameter adaptation in robotic applications

An addendum on "Robust control of robots by the computed torque method"

We reinterprete and improve recent results on robust control of robots by the computed method. The methods and ideas used are inspired by `passivity based¿ control methods for robot manipulators and lead to a significant increase in freedom of controller implementation, thereby providing more flexibility to the designer of robot control systems