Discontinuous feedback stabilization of the angular velocity of a rigid body with two control torques

There has been much interest over the past decade in the problem of asymptotic stabilization of the angular velocity of a rigid body with only two torque inputs. The smooth feedback laws proposed in the literature provide asymptotic stability with nonexponential convergence rates. This paper proposes discontinuous feedback laws to achieve asymptotic stability with exponential convergence rate

On the stabilization of a class of nonholonomic systems using invariant manifold technique

This paper presents an asymptotically stabilizing discontinuous feedback controller for a class of nonholonomic systems. The controller consists of two parts: the first part yields an invariant manifold on which all trajectories of the closed-loop system tend to the origin, and the latter part renders the invariant manifold attractive, while avoiding a discontinuity surface. The controller yields exponential stability so that the convergence can be chosen arbitrarily fas

Modelling and Control of Space Vehicles with Fuel Slosh Dynamics

Ever since the launch of the early high-efficiency rockets, controlling liquid fuel slosh within a launch vehicle has been a major design concern. Moreover, with today\u27s large and complex spacecraft, a substantial mass of fuel is necessary to place them into orbit and to perform orbital maneuvers. --from the book\u27s introductio

Nonlinear Attitude Control of Planar Structures in Space Using Only Internal Controls

An attitude control strategy for maneuvers of an interconnection of planar bodies in space is developed. It is assumed that there are no exogeneous torques and that torques generated by joint motors are used as means of control so that the total angular momentum of the multibody system is a constant, assumed to be zero. The control strategy utilizes the nonintegrability of the expression for the angular momentum. Large angle maneuvers can be designed to achieve an arbitrary reorientation of the multibody system with respect to an inertial frame. The theoretical background for carrying out the required maneuvers is summarized

Attitude stabilization of a rigid spacecraft using gas jet actuators operating in a failure mode

The attitude stabilization of a rigid spacecraft using control torques supplied by gas jet actuators about only two of its principal axes is considered. First, the case where the uncontrolled principal axis of the spacecraft is not an axis of symmetry is considered. In this case, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft cannot be asymptotically stabilized to an equilibrium attitude using time-invariant continuous feedback. A discontinuous stabilizing feedback control strategy is constructed which stabilizes the spacecraft to an equilibrium attitude. Next, the case where the uncontrolled principal axis of the spacecraft is an axis of symmetry is considered. In this case, the complete spacecraft dynamics are not even accessible. However, the spacecraft dynamics are strongly accessible and small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized to an equilibrium attitude using time-invariant continuous feedback, but again a discontinuous stabilizing feedback control strategy is constructed. In both cases, the discontinuous feedback controllers are constructed by switching between one of several feedback functions

Nonlinear control of a class of underactuated systems

A theoretical framework is established for the dynamics and control of underactuated systems, defined as systems which have fewer inputs than degrees of freedom. Control system formulation of underactuated systems is addressed and the class of second-order nonholonomic systems is identified. Controllability and stabilizability results are derived for this class of underactuated systems. Examples are included to illustrate the result

Nonlinear Dynamics and Control of Aerial Robots

Aerial robotics is one of the fastest growing industry and has a number of evolving applications. Higher agility make aerial robots ideal candidate for applications like rescue missions especially in difficult to access areas. This chapter first derives the complete nonlinear dynamics of an aerial robot consisting of a quadcopter with a two-link robot manipulator. Precise control of such an aerial robot is a challenging task due to the fact that the translational and rotational dynamics of the quadcopter are strongly coupled with the dynamics of the manipulator. We extend our previous results on the control of quadrotor UAVs to the control of aerial robots. In particular, we design a backstepping and Lyapunov-based nonlinear feedback control law that achieves point-to-point control of the areal robot. The effectiveness of this feedback control law is illustrated through a simulation example