Showing papers by "Richard M. Murray published in 1990"

Nonlinear controllers for non-integrable systems: the Acrobot example

Abstract: Recent developments in the theory of geometric nonlinear control provide powerful methods for controller design for a large class of nonlinear systems. Many systems, however, do not satisfy the restrictive conditions necessary for either full state linearization [6, 5] or input-output linearization with internal stability [2]. In this paper, we present an approach to controller design based on finding a linearizable nonlinear system that well approximates the true system over a desirable region. We outline an engineering procedure for constructing the approximating nonlinear system given the true system. We demonstrate this approach by designing a nonlinear controller for a simple mechanical system patterned after a gymnast performing on a single parallel bar.

Steering nonholonomic systems using sinusoids

Abstract: Methods for steering systems with nonholonomic constraints between arbitrary configurations are investigated. R.W. Brockett (1981) derived the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields and their (first-order) Lie brackets. Using Brockett's result as motivation, the authors derive suboptimal trajectories for systems which are not in canonical form and consider systems in which it takes more than one level of bracketing to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. Examples and simulation results are presented. >

Control primitives for robot systems

Abstract: A methodology is developed for describing of hierarchical control of robot systems in a manner which is faithful to the underlying mechanics, structured enough to be used as an interpreted language, and sufficiently flexible to encompass a wide variety of systems. A consistent set of primitive operations which form the core of a robot system description and control language is presented. This language, motivated by the hierarchical organization of neuromuscular systems, is capable of describing a large class of robot systems under a variety of single-level and distributed control schemes. >

Grasping and Manipulation Using

Abstract: In these notes we give the reader a feel for the mathematical problems involved in describing grasping and fine motion manipulation of objects with multifingered robot hands. Multifingered robot hands can be thought of as several robots (fingers) on a common base (palm) cooperatively manipulating all object. It is clear that positioning an object in space, namely specifying its position and orientation needs 6 degrees of freedom. However, dextrously manipulating objects requires far more degrees of freedom especially in the execution of tasks involving picking up an object, regrasping it and using the object. It is here that the study of multifingered hands is important. The study of multifingered hands has a long history not just in the context of robotics but also in the context of prosthesis. In Chapter 2, we set down a brief discussion of the kinematics of a single rigid body, followed by study of contacts and the kinematics of rolling. Rolling Is an especially important way in which finger tips move over the surface of an object in order both to reposition and regrasp the object. In Section 2.4 we study the kinematics of a multifingered hand in terms of the kinematics of the individual fingers. Finally, we define grasp stability and the manipulability of grasps. The appendix contains a derivation of the contact equations in terms of the metric tensor and connection form of the surfaces in contact at the finger tip and object. In Chapter 3, we develop the dynamics of multifingered hands by aggregating the dynamics of individual fingers with the dynamics of the grasped object and the kinematic equations of contact. In Section 3.3 we describe a few different control techniques to follow a specified trajectory for the body and the grasp forces exerted on it. In Chapter 4, we axiomatize the process of regrasping an object by rolling the finger tips on the surface of the object. We show how the problem of finding geodesics for singular or Carnot-Caratheodory metrics is useful in steering the finger tips from one grasp to another. We conclude with some open problems. The discussion of this paper is a summary of our own work and that of others, notably those at Harvard, in the last few years in this area. Detailed references to these appear in the body of the notes.

Primitives for Robot Control

Abstract: Inspired by the control system of the mammalian neuro-muscular system, we were motivated to develop a methodology for description of hierarchical control in a manner which is faithful to the underlying mechanics, structured enough to be used as an interpreted language, and sufficiently flexible to allow the description of a wide variety of systems. We present a consistent set of primitive operations which form the core of a robot system description and control language. This language is capable of describing a large class of robot systems under a variety of single level and distributed control schemes. We review a few pertinent results of classical mechanics, describe the functionality of our primitive operations, and present several different hierarchical strategies for the description and control of a two fingered hand holding a box.