Showing papers by "N.H. McClamroch published in 1997"

Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system

Abstract: This paper studies a specific mechanical example that is representative of a class of underactuated, weakly coupled, unstable mechanical systems that are exceptionally difficult to stabilize. In particular, systems in this class are not stabilizable using static smooth feedback but are stabilizable using nonsmooth feedback. Although similar purely theoretical developments have been previously presented, we emphasize the physical basis and physical implications of the theoretical conclusions in the context of a specific example. The development in this paper is limited to a specific physical example, but the approach is applicable to a wide class of underactuated, weakly coupled, unstable mechanical systems.

Hybrid control for stabilization of a class of cascade nonlinear systems

Abstract: Presents a hybrid feedback control approach for stabilizing a class of cascade nonlinear systems to an equilibrium. The control architecture is a combination of nonlinear analog feedback and switched (sampled data) feedback, that, in a certain sense, feedback linearizes the closed loop at the analog time scale and at the time scale induced by the switching. Conditions for local asymptotic stability and global asymptotic stability of the equilibrium of the closed loop hybrid system are developed. The results are applied to the construction of hybrid controllers that stabilize a class of underactuated mechanical systems and a class of nonlinear nonminimum phase systems. In particular, a hybrid controller is developed and studied for the model of a rotational and translational actuator.

An articulated-body model for a free-flying robot and its use for adaptive motion control

Abstract: We synthesize an adaptive motion control law for a free-flying robot with no external forces or moments. The basic idea is to make use of the articulated part of the space robot to control the position and orientation of the end-effector in an inertial frame. The inertia parameters for the robot end-effector and load are assumed to be a priori unknown. The articulated-body model is linear in the unknown parameters, so that an adaptive control law is developed. A novel feature of our approach is that the parameter estimates are obtained using momentum integrals only. In addition, we use unit quaternions to represent orientation errors. The stability properties of the adaptive control law is shown using Lyapunov stability theory. Computer simulations of an example 12 degrees of freedom space robot system are presented.

Hybrid closed loop systems: a nonlinear control perspective

Abstract: A survey of hybrid closed loop control problems that arise from the use of hybrid controllers to control smooth nonlinear systems is presented. This is a special class of hybrid closed loop systems, but they are of substantial interest in identifying the value of hybrid control as a generalization of classical control approaches for nonlinear systems.

Control problems for a multibody spacecraft via shape changes: constant nonzero angular momentum

Abstract: In this paper, a three dimensional reorientation problem for an underactuated multibody spacecraft in the case of constant nonzero angular momentum is studied. The spacecraft is underactuated because it is in a free floating mode where no external forces or torques are applied. The only means of actuation are provided by the joint actuators. The control construction is based on a formula for approximating the orientation changes induced by small amplitude periodic shape changes and nonzero angular momentum. On the basis of the formula, an explicit algorithm is provided for synthesizing periodic open loop shape changes for reorientation of the spacecraft from a given initial orientation to a desired final orientation within a specified finite time interval while the initial and final shapes of the spacecraft are the same. In particular, the algorithm can be applied to transfer the spacecraft to one of its relative equilibria. An example of reorientation of a four link multibody spacecraft illustrates the general results.

Three dimensional reorientation of a spacecraft containing a single reaction wheel and a single movable appendage

Abstract: In this paper, we consider a three dimensional reorientation problem for a multibody spacecraft containing a single reaction wheel, whose axis is fixed in the spacecraft, and a single movable appendage. If the appendage is fixed relative to the spacecraft, the spacecraft can only be rotated about the axis of the reaction wheel and it is impossible to achieve arbitrary reorientation manoeuvres. However, it is shown that when the appendage is movable, the spacecraft can be reoriented from an arbitrary initial orientation to an arbitrary final orientation with prescribed accuracy. The reorientation manoeuvre is accomplished by the reaction wheel in coordination with the periodic motions of the movable appendage. An algorithm is provided for synthesizing open loop controls that accomplish a specified reorientation manoeuvre. The algorithm can be applied to reorientation of a spacecraft in case of thruster or reaction wheel failures. Simulation results are reported.