N. McClamroch | University of Michigan (original) (raw)

Papers by N. McClamroch

arXiv (Cornell University), Jan 18, 2006

An efficient and accurate computational approach is proposed for optimal attitude control of a ri... more An efficient and accurate computational approach is proposed for optimal attitude control of a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete necessary conditions for optimality are derived, and an efficient computational approach is proposed to solve the resulting two point boundary value problem. The use of geometrically exact computations on SO(3) guarantees that this optimal control approach has excellent convergence properties even for highly nonlinear large angle attitude maneuvers. Numerical results are presented for attitude maneuvers of a 3D pendulum and a spacecraft in a circular orbit.

International Journal of Non-linear Mechanics, Jul 1, 2003

Proceedings of the ... American Control Conference, Jul 1, 2007

A 3D pendulum implemented using a triaxial air bearing system is proposed for Earth-based testing... more A 3D pendulum implemented using a triaxial air bearing system is proposed for Earth-based testing of orbiting spacecraft attitude dynamics and closed loop systems. This proposal is based on prior research on attitude dynamics and control of orbiting spacecraft, attitude dynamics and control of the 3D pendulum, and an experimental implementation of the 3D pendulum in our laboratory, referred to as the Triaxial Attitude Control Testbed (TACT). These research themes are integrated to assess the strengths and weaknesses of such an Earth-based testbed for spacecraft attitude dynamics and control hardware and software components. Several different cases, based on the importance of orbital effects and gravitational effects, are analyzed.

arXiv (Cornell University), Feb 24, 2007

Motivated by attitude control and attitude estimation problems for a rigid body, computational me... more Motivated by attitude control and attitude estimation problems for a rigid body, computational methods are proposed to propagate uncertainties in the angular velocity and the attitude. The nonlinear attitude flow is determined by Euler-Poincaré equations that describe the rotational dynamics of the rigid body acting under the influence of an attitude dependent potential and by a reconstruction equation that describes the kinematics expressed in terms of an orthogonal matrix representing the rigid body attitude. Uncertainties in the angular velocity and attitude are described in terms of ellipsoidal sets that are propagated through this highly nonlinear attitude flow. Computational methods are proposed, one method based on a local linearization of the attitude flow and two methods based on propagation of a small (unscented) sample selected from the initial uncertainty ellipsoid. Each of these computational methods is constructed using the Lie group variational integrator algorithm, viewed as a discretization of the attitude flow dynamics. Computational results are obtained that indicate (1) the strongly nonlinear attitude flow characteristics and (2) the limitations of each of these methods, and indeed any method, in providing effective global bounds on the nonlinear attitude flow.

arXiv (Cornell University), Jul 9, 2007

A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees... more A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the spherical 2D pendulum models as special cases. The case where the rigid body is asymmetric and the center of mass is distinct from the pivot location leads to the 3D pendulum. Full and reduced 3D pendulum models are introduced and used to study important features of the nonlinear dynamics: conserved quantities, equilibria, invariant manifolds, local dynamics near equilibria and invariant manifolds, and the presence of chaotic motions. These results demonstrate the rich and complex dynamics of the 3D pendulum.

Mathematical and Computer Modelling of Dynamical Systems, Jun 1, 2003

The Triaxial Attitude Control Testbed has been developed as part of a research program at the Uni... more The Triaxial Attitude Control Testbed has been developed as part of a research program at the University of Michigan on multibody rotational dynamics and control. In this paper, equations of motion are derived and presented in various forms. Actuation mechanisms are incorporated into the models; these include fan actuators, reaction wheel actuators and proof mass actuators that are £xed to the triaxial base body. The models also allow incorporation of unactuated auxiliary bodies that are constrained to move relative to the triaxial base body. The models expose the dynamic coupling between the rotational motion of the triaxial base body, the relative or shape motion of the unactuated auxiliary degrees of freedom, and dynamics associated with actuation mechanisms. Many different model simpli£cations and approximations are developed. Control models for the triaxial attitude control testbed are formulated that re¤ect speci£c assumptions.

Journal of Nonlinear Science, Sep 25, 2010

A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees... more A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. 3D pendulum dynamics have been much studied in integrable cases that arise when certain physical symmetry assumptions are made. This paper treats the nonintegrable case of the 3D pendulum dynamics when the rigid body is asymmetric and the center of mass is distinct from the pivot location. 3D pendulum full and reduced models are introduced and used to study important features of the nonlinear dynam-Communicated by R. Sepulchre.

Proceedings of the 28th IEEE Conference on Decision and Control

ABSTRACT

International Journal of Control, 1967

ABSTRACT

Journal of Nonlinear Science, 2011

A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees... more A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. 3D pendulum dynamics have been much studied in integrable cases that arise when certain physical symmetry assumptions are made. This paper treats the nonintegrable case of the 3D pendulum dynamics when the rigid body is asymmetric and the center of mass is distinct from the pivot location. 3D pendulum full and reduced models are introduced and used to study important features of the nonlinear dynam-4 J Nonlinear Sci (2011) 21: 3-32 ics: conserved quantities, equilibria, relative equilibria, invariant manifolds, local dynamics, and presence of chaotic motions. The paper provides a unified treatment of the 3D pendulum dynamics that includes prior results and new results expressed in the framework of geometric mechanics. These results demonstrate the rich and complex dynamics of the 3D pendulum.

Journal of Guidance, Control, and Dynamics, 1989

... He received a B.Sc (Eng.) degree in Aeronautical Engineering from Punjab Engineering College,... more ... He received a B.Sc (Eng.) degree in Aeronautical Engineering from Punjab Engineering College, Chandigarh, India, in 1982, and an MSE degree in Aerospace Engineering from the University of Michigan, Ann Arbor, in 1984, where he is currently at the Department of ...

Journal of Guidance, Control, and Dynamics, 1990

Journal of Dynamical and Control Systems, 1995

ABSTRACT

Journal of Dynamical and Control Systems, 2008

Abstract. An efficient and accurate computational approach is pro-posed for a nonconvex optimal a... more Abstract. An efficient and accurate computational approach is pro-posed for a nonconvex optimal attitude control for a rigid body. The problem is formulated directly as a discrete time optimization prob-lem using a Lie group variational integrator. Discrete time necessary conditions for ...

International Journal of Robust and Nonlinear Control, 2000

We study a control problem for a special class of underactuated mechanical systems, namely for me... more We study a control problem for a special class of underactuated mechanical systems, namely for mechanical systems with several directly actuated degrees of freedom and a single unactuated degree of freedom that must be controlled through the system coupling. Speci"c assumptions are introduced that de"ne this class, which includes many important models of mechanical system examples. The main result of the paper is the construction of a discontinuous nonlinear feedback controller for which the closed loop equilibrium at the origin is made &globally attractive'. The control construction approach is introduced in detail, and a proof of attractiveness is presented. The results are applied to control of the planar motion of a rigid body with a single unactuated internal degree of freedom.

The International Journal of Robotics Research, 2002

We study the simultaneous control of three dimensional translation and rotation of an underactuat... more We study the simultaneous control of three dimensional translation and rotation of an underactuated multibody space robot using sliding masses that are configured as ideal prismatic actuators. A crucial assumption is that the total linear and angular momenta of the space robot are zero. The prismatic actuators may be intentional actuation devices or they may be dual-use devices such as retractable booms, tethers, or antennas that can also serve as space robot actuation devices. The paper focuses on the underactuation case, i.e., the space robot has three independent prismatic actuators, which are used to control the six base body degrees of freedom. Controllability results are developed, revealing controllability properties for the base body translation, base body attitude, and actuator displacement. Based on the controllability results, an algorithm for rest-to-rest base body maneuvers is constructed using a Lie bracket expansion. An example of a three dimensional space robot maneuver is presented. The results in the paper demonstrate the importance of "nonholonomy" and related nonlinear control approaches for space robots that satisfy the prismatic actuation assumptions. KEY WORDS—space robots, translational and rotational maneuvers, nonlinear control, underactuated systems, pris- matic actuators, nonholonomy

International Journal of Control, 1967

ABSTRACT

International Journal of Control, 1992

Control systems described in terms of a class of linear differential-algebraic equations are intr... more Control systems described in terms of a class of linear differential-algebraic equations are introduced. Under appropriate relative degree assumptions, a computational procedure for obtaining an equivalent state realization is developed using a singular value decomposition. Properties such as stability, controllability, observability, etc, for the differential-algebraic system may be studied directly from the state realization. For linear constrained hamiltonian systems, it

arXiv (Cornell University), Jan 18, 2006

An efficient and accurate computational approach is proposed for optimal attitude control of a ri... more An efficient and accurate computational approach is proposed for optimal attitude control of a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete necessary conditions for optimality are derived, and an efficient computational approach is proposed to solve the resulting two point boundary value problem. The use of geometrically exact computations on SO(3) guarantees that this optimal control approach has excellent convergence properties even for highly nonlinear large angle attitude maneuvers. Numerical results are presented for attitude maneuvers of a 3D pendulum and a spacecraft in a circular orbit.

International Journal of Non-linear Mechanics, Jul 1, 2003

Proceedings of the ... American Control Conference, Jul 1, 2007

A 3D pendulum implemented using a triaxial air bearing system is proposed for Earth-based testing... more A 3D pendulum implemented using a triaxial air bearing system is proposed for Earth-based testing of orbiting spacecraft attitude dynamics and closed loop systems. This proposal is based on prior research on attitude dynamics and control of orbiting spacecraft, attitude dynamics and control of the 3D pendulum, and an experimental implementation of the 3D pendulum in our laboratory, referred to as the Triaxial Attitude Control Testbed (TACT). These research themes are integrated to assess the strengths and weaknesses of such an Earth-based testbed for spacecraft attitude dynamics and control hardware and software components. Several different cases, based on the importance of orbital effects and gravitational effects, are analyzed.

arXiv (Cornell University), Feb 24, 2007

Motivated by attitude control and attitude estimation problems for a rigid body, computational me... more Motivated by attitude control and attitude estimation problems for a rigid body, computational methods are proposed to propagate uncertainties in the angular velocity and the attitude. The nonlinear attitude flow is determined by Euler-Poincaré equations that describe the rotational dynamics of the rigid body acting under the influence of an attitude dependent potential and by a reconstruction equation that describes the kinematics expressed in terms of an orthogonal matrix representing the rigid body attitude. Uncertainties in the angular velocity and attitude are described in terms of ellipsoidal sets that are propagated through this highly nonlinear attitude flow. Computational methods are proposed, one method based on a local linearization of the attitude flow and two methods based on propagation of a small (unscented) sample selected from the initial uncertainty ellipsoid. Each of these computational methods is constructed using the Lie group variational integrator algorithm, viewed as a discretization of the attitude flow dynamics. Computational results are obtained that indicate (1) the strongly nonlinear attitude flow characteristics and (2) the limitations of each of these methods, and indeed any method, in providing effective global bounds on the nonlinear attitude flow.

arXiv (Cornell University), Jul 9, 2007

A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees... more A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the spherical 2D pendulum models as special cases. The case where the rigid body is asymmetric and the center of mass is distinct from the pivot location leads to the 3D pendulum. Full and reduced 3D pendulum models are introduced and used to study important features of the nonlinear dynamics: conserved quantities, equilibria, invariant manifolds, local dynamics near equilibria and invariant manifolds, and the presence of chaotic motions. These results demonstrate the rich and complex dynamics of the 3D pendulum.

Mathematical and Computer Modelling of Dynamical Systems, Jun 1, 2003

The Triaxial Attitude Control Testbed has been developed as part of a research program at the Uni... more The Triaxial Attitude Control Testbed has been developed as part of a research program at the University of Michigan on multibody rotational dynamics and control. In this paper, equations of motion are derived and presented in various forms. Actuation mechanisms are incorporated into the models; these include fan actuators, reaction wheel actuators and proof mass actuators that are £xed to the triaxial base body. The models also allow incorporation of unactuated auxiliary bodies that are constrained to move relative to the triaxial base body. The models expose the dynamic coupling between the rotational motion of the triaxial base body, the relative or shape motion of the unactuated auxiliary degrees of freedom, and dynamics associated with actuation mechanisms. Many different model simpli£cations and approximations are developed. Control models for the triaxial attitude control testbed are formulated that re¤ect speci£c assumptions.

Journal of Nonlinear Science, Sep 25, 2010

A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees... more A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. 3D pendulum dynamics have been much studied in integrable cases that arise when certain physical symmetry assumptions are made. This paper treats the nonintegrable case of the 3D pendulum dynamics when the rigid body is asymmetric and the center of mass is distinct from the pivot location. 3D pendulum full and reduced models are introduced and used to study important features of the nonlinear dynam-Communicated by R. Sepulchre.

Proceedings of the 28th IEEE Conference on Decision and Control

ABSTRACT

International Journal of Control, 1967

ABSTRACT

Journal of Nonlinear Science, 2011

A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees... more A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. 3D pendulum dynamics have been much studied in integrable cases that arise when certain physical symmetry assumptions are made. This paper treats the nonintegrable case of the 3D pendulum dynamics when the rigid body is asymmetric and the center of mass is distinct from the pivot location. 3D pendulum full and reduced models are introduced and used to study important features of the nonlinear dynam-4 J Nonlinear Sci (2011) 21: 3-32 ics: conserved quantities, equilibria, relative equilibria, invariant manifolds, local dynamics, and presence of chaotic motions. The paper provides a unified treatment of the 3D pendulum dynamics that includes prior results and new results expressed in the framework of geometric mechanics. These results demonstrate the rich and complex dynamics of the 3D pendulum.

Journal of Guidance, Control, and Dynamics, 1989

... He received a B.Sc (Eng.) degree in Aeronautical Engineering from Punjab Engineering College,... more ... He received a B.Sc (Eng.) degree in Aeronautical Engineering from Punjab Engineering College, Chandigarh, India, in 1982, and an MSE degree in Aerospace Engineering from the University of Michigan, Ann Arbor, in 1984, where he is currently at the Department of ...

Journal of Guidance, Control, and Dynamics, 1990

Journal of Dynamical and Control Systems, 1995

ABSTRACT

Journal of Dynamical and Control Systems, 2008

Abstract. An efficient and accurate computational approach is pro-posed for a nonconvex optimal a... more Abstract. An efficient and accurate computational approach is pro-posed for a nonconvex optimal attitude control for a rigid body. The problem is formulated directly as a discrete time optimization prob-lem using a Lie group variational integrator. Discrete time necessary conditions for ...

International Journal of Robust and Nonlinear Control, 2000

We study a control problem for a special class of underactuated mechanical systems, namely for me... more We study a control problem for a special class of underactuated mechanical systems, namely for mechanical systems with several directly actuated degrees of freedom and a single unactuated degree of freedom that must be controlled through the system coupling. Speci"c assumptions are introduced that de"ne this class, which includes many important models of mechanical system examples. The main result of the paper is the construction of a discontinuous nonlinear feedback controller for which the closed loop equilibrium at the origin is made &globally attractive'. The control construction approach is introduced in detail, and a proof of attractiveness is presented. The results are applied to control of the planar motion of a rigid body with a single unactuated internal degree of freedom.

The International Journal of Robotics Research, 2002

We study the simultaneous control of three dimensional translation and rotation of an underactuat... more We study the simultaneous control of three dimensional translation and rotation of an underactuated multibody space robot using sliding masses that are configured as ideal prismatic actuators. A crucial assumption is that the total linear and angular momenta of the space robot are zero. The prismatic actuators may be intentional actuation devices or they may be dual-use devices such as retractable booms, tethers, or antennas that can also serve as space robot actuation devices. The paper focuses on the underactuation case, i.e., the space robot has three independent prismatic actuators, which are used to control the six base body degrees of freedom. Controllability results are developed, revealing controllability properties for the base body translation, base body attitude, and actuator displacement. Based on the controllability results, an algorithm for rest-to-rest base body maneuvers is constructed using a Lie bracket expansion. An example of a three dimensional space robot maneuver is presented. The results in the paper demonstrate the importance of "nonholonomy" and related nonlinear control approaches for space robots that satisfy the prismatic actuation assumptions. KEY WORDS—space robots, translational and rotational maneuvers, nonlinear control, underactuated systems, pris- matic actuators, nonholonomy

International Journal of Control, 1967

ABSTRACT

International Journal of Control, 1992

Control systems described in terms of a class of linear differential-algebraic equations are intr... more Control systems described in terms of a class of linear differential-algebraic equations are introduced. Under appropriate relative degree assumptions, a computational procedure for obtaining an equivalent state realization is developed using a singular value decomposition. Properties such as stability, controllability, observability, etc, for the differential-algebraic system may be studied directly from the state realization. For linear constrained hamiltonian systems, it