Optimal sliding mode controllers for attitude tracking of spacecraft

This paper studies two optimal sliding mode control laws using integral sliding mode control (ISM) for some spacecraft attitude tracking problems. Integral sliding mode control combining the first order sliding mode and optimal control is applied to quaternion-based spacecraft attitude tracking manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state dependent Riccati equation (SDRE) and Control Lyapunov function (CLF) approaches are used to solve the infinite-time nonlinear optimal problem. The second method of Lyapunov is used to show that tracking is achieved globally. An example of multiaxial attitude tracking manoeuvres is presented and simulation results are included to verify the usefulness of these controllers

Adaptive backstepping control for optimal descent with embedded autonomy

Using Lyapunov stability theory, an adaptive backstepping controller is presented in this paper for optimal descent tracking. Unlike the traditional approach, the proposed control law can cope with input saturation and failure which enables the embedded autonomy of lander system. In addition, this control law can also restrain the unknown bounded terms (i.e., disturbance). To show the controller’s performance in the presence of input saturation, input failure and bounded external disturbance, simulation was carried out under a lunar landing scenario

Integrated Optimal and Robust Control of Spacecraft in Proximity Operations

With the rapid growth of space activities and advancement of aerospace science and technology, many autonomous space missions have been proliferating in recent decades. Control of spacecraft in proximity operations is of great importance to accomplish these missions. The research in this dissertation aims to provide a precise, efficient, optimal, and robust controller to ensure successful spacecraft proximity operations. This is a challenging control task since the problem involves highly nonlinear dynamics including translational motion, rotational motion, and flexible structure deformation and vibration. In addition, uncertainties in the system modeling parameters and disturbances make the precise control more difficult. Four control design approaches are integrated to solve this challenging problem. The first approach is to consider the spacecraft rigid body translational and rotational dynamics together with the flexible motion in one unified optimal control framework so that the overall system performance and constraints can be addressed in one optimization process. The second approach is to formulate the robust control objectives into the optimal control cost function and prove the equivalency between the robust stabilization problem and the transformed optimal control problem. The third approach is to employ the è-D technique, a novel optimal control method that is based on a perturbation solution to the Hamilton-Jacobi-Bellman equation, to solve the nonlinear optimal control problem obtained from the indirect robust control formulation. The resultant optimal control law can be obtained in closedorm, and thus facilitates the onboard implementation. The integration of these three approaches is called the integrated indirect robust control scheme. The fourth approach is to use the inverse optimal adaptive control method combined with the indirect robust control scheme to alleviate the conservativeness of the indirect robust control scheme by using online parameter estimation such that adaptive, robust, and optimal properties can all be achieved. To show the effectiveness of the proposed control approaches, six degree-offreedom spacecraft proximity operation simulation is conducted and demonstrates satisfying performance under various uncertainties and disturbances

Large angle reorientation manoeuvre of spacecraft using robust backstepping control

The nonlinear control design problem for large angle reorientation manoeuvre of spacecraft has a proper structure for the direct application of backstepping design as its dynamics and kinematics are naturally in a cascade form. In this paper, the robustness of the backstepping control against the uncertainties in the moment of inertia matrix is investigated and a sufficient condition for the robust stability is derived. Numerical simulations show the validity of the condition

Autonomous attitude using potential function method under control input saturation

The potential function method has been used extensively in nonlinear control for the development of feedback laws which result in global asymptotic stability for a certain prescribed operating point of the closed-loop system. It is a variation of the Lyapunov direct method in the sense that here the Lyapunov function, also called potential function, is constructed in such a way that the undesired points of the system state space are avoided. The method has been considered for the space applications where the systems involved are usually composed of the cascaded subsystems of kinematics and dynamics and the kinematic states are mapped onto an appropriate potential function which is augmented for the overall system by the use of the method of integrator backstepping. The conventional backstepping controls, however, may result in an excessive control effort that may be beyond the saturation bound of the actuators. The present paper, while remaining within the framework of conventional backstepping control design, proposes analytical formulation for the control torque bound being a function of the tracking error and the control gains. The said formulation can be used to tune to the control gains to bound the control torque to a prescribed saturation bound of the control actuators

Nonlinear Attitude Control of Spacecraft with a captured asteroid

One of the main control challenges of National Aeronautics and Space Administration’s proposed Asteroid Redirect Mission (ARM) is to stabilize and control the attitude of the spacecraft-asteroid combination in the presence of large uncertainty in the physical model of a captured asteroid. We present a new robust nonlinear tracking control law that guarantees global exponential convergence of the system’s attitude trajectory to the desired attitude trajectory. In the presence of modeling errors and disturbances, this control law is finite-gain L_p stable and input-to-state stable. We also present a few extensions of this control law, such as exponential tracking control on SO(3) and integral control, and show its relation to the well-known tracking control law for Euler-Lagrangian systems. We show that the resultant disturbance torques for control laws that use feed-forward cancellation is comparable to the maximum control torque of the conceptual ARM spacecraft and such control laws are therefore not suitable. We then numerically compare the performance of multiple viable attitude control laws, including the robust nonlinear tracking control law, nonlinear adaptive control, and derivative plus proportional-derivative linear control. We conclude that under very small modeling uncertainties, which can be achieved using online system identification, the robust nonlinear tracking control law that guarantees globally exponential convergence to the fuel-optimal reference trajectory is the best strategy as it consumes the least amount of fuel. On the other hand, in the presence of large modeling uncertainties and actuator saturations, a simple derivative plus proportional-derivative (D+PD) control law is effective, and the performance can be further improved by using the proposed nonlinear tracking control law that tracks a (D+PD)-control-based desired attitude trajectory. We conclude this paper with specific design guidelines for the ARM spacecraft for efficiently stabilizing a tumbling asteroid and spacecraft combination

Attitude Control and Stabilization of Spacecraft with a Captured Asteroid

National Aeronautics and Space Administration's Asteroid Redirect Mission (ARM) aims to capture a Near Earth Orbit (NEO) asteroid or a piece of a large asteroid and transport it to the Earth{Moon system. In this paper, we provide a detailed analysis of one of the main control challenges for the first ARM mission concept, namely despinning and three-axis stabilizing the asteroid and spacecraft combination after the ARM spacecraft captures the tumbling NEO asteroid. We first show that control laws, which explicitly use the dynamics of the system in their control law equation, encounter a fundamental limitation due to modeling uncertainties. We show that in the presence of large modeling uncertainties, the resultant disturbance torque for such control laws may well exceed the maximum control torque of the conceptual ARM spacecraft. We then numerically compare the performance of three viable control laws: the robust nonlinear tracking control law, the adaptive nonlinear tracking control law, and the simple derivative plus proportional-derivative linear control strategy. We conclude that under very small mod- eling uncertainties, which can be achieved using online system identification, the robust nonlinear tracking control law guarantees exponential convergence to the fuel-optimal reference trajectory and hence consumes the least fuel. On the other hand, in the presence of large modeling uncertainties, measurement errors, and actuator saturations, the best strategy for stabilizing the asteroid and spacecraft combination is to first despin the system using a derivative (rate damping) linear control law and then stabilize the system in the desired orientation using the simple proportional-derivative linear control law. More-over, the fuel consumed by the conceptual ARM spacecraft using these control strategies is upper bounded by 300 kg for the nominal range of NEO asteroid parameters. We conclude this paper with specific design guidelines for the ARM spacecraft for efficiently stabilizing the tumbling NEO asteroid and spacecraft combination

Spacecraft nonlinear attitude control with bounded control input

The research in this thesis deals with nonlinear control of spacecraft attitude stabilization and tracking manoeuvres and addresses the issue of control toque saturation on a priori basis. The cascaded structure of spacecraft attitude kinematics and dynamics makes the method of integrator backstepping preferred scheme for the spacecraft nonlinear attitude control. However, the conventional backstepping control design method may result in excessive control torque beyond the saturation bound of the actuators. While remaining within the framework of conventional backstepping control design, the present work proposes the formulation of analytical bounds for the control torque components as functions of the initial attitude and angular velocity errors and the gains involved in the control design procedure. The said analytical bounds have been shown to be useful for tuning the gains in a way that the guaranteed maximum torque upper bound lies within the capability of the actuator and, hence, addressing the issue of control input saturation. Conditions have also been developed as well as the generalization of the said analytical bounds which allow for the tuning of the control gains to guarantee prescribed stability with the additional aim that the control action avoids reaching saturation while anticipating the presence of bounded external disturbance torque and uncertainties in the spacecraft moments of inertia. Moreover, the work has also been extended blending it with the artificial potential function method for achieving autonomous capability of avoiding pointing constraints for the case of spacecraft large angle slew manoeuvres. The idea of undergoing such manoeuvres using control moment gyros to track commanded angular momentum rather than a torque command has also been studied. In this context, a gimbal position command generation algorithm has been proposed for a pyramid-type cluster of four single gimbal control moment gyros. The proposed algorithm not only avoids the saturation of the angular momentum input from the control moment gyro cluster but also exploits its maximum value deliverable by the cluster along the direction of the commanded angular momentum for the major part of the manoeuvre. In this way, it results in rapid spacecraft slew manoeuvres. The ideas proposed in the thesis have also been validated using numerical simulations and compared with results already existing in the literature