N.H. McClamroch

Bio: N.H. McClamroch is an academic researcher from University of Michigan. The author has contributed to research in topics: Nonlinear system & Control system. The author has an hindex of 30, co-authored 118 publications receiving 6317 citations. Previous affiliations of N.H. McClamroch include Worcester Polytechnic Institute & University of Texas at Austin.

Attitude maneuvers of a rigid spacecraft in a circular orbit

Abstract: A global model is presented that can be used to study attitude maneuvers of a rigid spacecraft in a circular orbit about a large central body. The model includes gravity gradient effects that arise from the non-uniform gravity field and characterizes the spacecraft attitude with respect to the uniformly rotating local vertical local horizontal coordinate frame. An accurate computational approach for solving a nonlinear boundary value problem is proposed, assuming that control torque impulses can be applied at initiation and at termination of the maneuver. If the terminal attitude condition is relaxed, then an accurate computational approach for solving the minimal impulse optimal control problem is presented. Since the attitude is represented by a rotation matrix, this approach avoids any singularity or ambiguity arising from other attitude representations such as Euler angles or quaternions.

The drilling problem: A stochastic modeling and control example in manufacturing

Abstract: A machining economics problem is considered where feed rate selection and tool replacement policies are to be determined. A new stochastic model for tool wear, called a diffusion-threshold model, is proposed. This tool wear model allows the machining economics problem to be formulated as a stochastic optimal control problem incorporating measurement feedback of tool wear. Two types of control policies are described. One is a traditional machining economics policy and the other utilizes tool wear feedback and allows on-line decision making. The optimal policy is described for both types. An example problem based on actual data is worked out that compares the two approaches and demonstrates the utility of information feedback and on-line control.

Stabilization and asymptotic path tracking of a rolling disk

Abstract: In this paper, the dynamics and control of a uniform disk (a thin wheel) rolling without slipping on a horizontal plane are considered. A model of the rolling disk is derived using the Lagrangian formulation, assuming that rolling, steering and leaning torques are available as control inputs. A dynamic extension is used to achieve a well defined vector relative degree. On the basis of the dynamic extension, a feedback control law is designed to stabilize the disk from falling over, while simultaneously allowing the disk to asymptotically track a ground reference trajectory. For this class of stabilization and tracking problems, the nonholonomic rolling without slipping constraint does not preclude the existence of smooth feedback that accomplishes the control objectives.

A new approach to position and contact force regulation in constrained robot systems

Abstract: A feedback control problem for regulation of contact force and position in constrained robot systems is considered. The nonlinear differential-algebraic equations which describe the dynamics of a constrained robot system are linearized about a constrained equilibrium. A method of obtaining an equivalent state realization for the resulting linear differential-algebraic equations is developed. This method is numerically efficient since it is based on a singular value decomposition. A linear quadratic optimal control problem associated with the linearized differential-algebraic equations is solved. The resulting linear feedback control law guarantees good regulation of both contact force and position of the constrained robot. Since the method is based on the linearization of the nonlinear differential-algebraic equations, it is valid only in a neighborhood about the point of linearization. Two robot examples are considered in order to illustrate the proposed method. >

Development of air spindle and triaxial air bearing testbeds for spacecraft dynamics and control experiments

Abstract: The dynamics and control of spacecraft have been widely studied because of their technological significance. In the classical case the spacecraft is assumed to consist of a single rigid body with three-axis torque inputs and with attitude and rate sensing. In practice, however, the situation may be far more complex. For example, any component of the spacecraft that deforms relative to other components will entail a change in the spacecraft mass distribution; in effect, the spacecraft becomes a multibody system. Similarly, structural flexibility and fuel slosh give rise to vibrational degrees of freedom. Spacecraft control is also exacerbated by sensor and actuator nonlinearities. Traditional actuation devices such as thrusters, reaction wheels, momentum wheels, and control moment gyros entail amplitude and rate saturation constraints, gyroscopic coupling, and coupling between translational and attitude dynamics. Additional difficulties arise when accounting for gravitational effects and external disturbances. All of these issues have technological implications. A fundamental difficulty associated with spacecraft technology is the fact that ground-based testing must occur in a 1-g environment whereas the hardware will operate under zero-g conditions. Consequently, spacecraft control engineering must depend on first-principles analysis as well as extrapolation from 1-g testing. The purpose of this paper is to describe a laboratory-based testbed that will be used to explore various issues and concepts in spacecraft dynamics and control. This testbed is based on a triaxial air bearing to allow experiments involving large-angle, three-axis motion. As a precursor to this testbed, we have also developed an air spindle testbed which allows single-axis rotation.

A Mathematical Introduction to Robotic Manipulation

Abstract: INTRODUCTION: Brief History. Multifingered Hands and Dextrous Manipulation. Outline of the Book. Bibliography. RIGID BODY MOTION: Rigid Body Transformations. Rotational Motion in R3. Rigid Motion in R3. Velocity of a Rigid Body. Wrenches and Reciprocal Screws. MANIPULATOR KINEMATICS: Introduction. Forward Kinematics. Inverse Kinematics. The Manipulator Jacobian. Redundant and Parallel Manipulators. ROBOT DYNAMICS AND CONTROL: Introduction. Lagrange's Equations. Dynamics of Open-Chain Manipulators. Lyapunov Stability Theory. Position Control and Trajectory Tracking. Control of Constrained Manipulators. MULTIFINGERED HAND KINEMATICS: Introduction to Grasping. Grasp Statics. Force-Closure. Grasp Planning. Grasp Constraints. Rolling Contact Kinematics. HAND DYNAMICS AND CONTROL: Lagrange's Equations with Constraints. Robot Hand Dynamics. Redundant and Nonmanipulable Robot Systems. Kinematics and Statics of Tendon Actuation. Control of Robot Hands. NONHOLONOMIC BEHAVIOR IN ROBOTIC SYSTEMS: Introduction. Controllability and Frobenius' Theorem. Examples of Nonholonomic Systems. Structure of Nonholonomic Systems. NONHOLONOMIC MOTION PLANNING: Introduction. Steering Model Control Systems Using Sinusoids. General Methods for Steering. Dynamic Finger Repositioning. FUTURE PROSPECTS: Robots in Hazardous Environments. Medical Applications for Multifingered Hands. Robots on a Small Scale: Microrobotics. APPENDICES: Lie Groups and Robot Kinematics. A Mathematica Package for Screw Calculus. Bibliography. Index Each chapter also includes a Summary, Bibliography, and Exercises

Basic problems in stability and design of switched systems

Abstract: By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.

Adaptive Control

Abstract: This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Perspectives and results on the stability and stabilizability of hybrid systems

Abstract: This paper introduces the concept of a hybrid system and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems. In this endeavour, this paper surveys the major results in the (Lyapunov) stability of finite-dimensional hybrid systems and then discusses the stronger, more specialized results of switched linear (stable and unstable) systems. A section detailing how some of the results can be formulated as linear matrix inequalities is given. Stability analyses on the regulation of the angle of attack of an aircraft and on the PI control of a vehicle with an automatic transmission are given. Other examples are included to illustrate various results in this paper.

Developments in nonholonomic control problems

Abstract: Provides a summary of recent developments in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole. The paper is organized as follows: introduction to nonholonomic control systems and where they arise in applications, classification of models of nonholonomic control systems, control problem formulations, motion planning results, stabilization results, and current and future research topics.