Analysis and Performance Evaluation of the ZEM/ZEV Guidance and its Sliding Robustification for Autonomous Rendezvous in Relative Motion

Devising closed-loop guidance algorithms for autonomous relative motion is an important problem within the field of orbital dynamics. In this paper, we study the guided relative motion of two spacecraft for which one of them is executing an autonomous rendezvous via the ZEM/ZEV feedback guidance and its robustified Optimal Sliding Guidance (OSG) counterpart. Starting from the classical Clohessy-Wiltshire (CW) model, we systematically analyze the ability of the ZEM/ZEV feedback guidance to generate closed loop trajectories that drive the deputy spacecraft to the chief satellite and evaluate its performance in terms of target accuracy and propellant consumption. It is shown that the guidance gains and the time of flight predicted by the theoretical solution generates a class of feedback trajectories that are accurate but suboptimal with respect to the open-loop fuel-optimal solution. Indeed, a parametric study shows that a different set of gains may generate relative guided trajectories that yields fuel consumption closer to the ideal optimal. The guidance algorithms are also demonstrated to be accurate in guiding the relative motion of the deputy toward a chief spacecraft in highly elliptical orbit where the Linearized Equations of Relative Motions (LERM) are employed to compute the Zero-Effort-Miss (ZEM) and Zero-Effort-Velocity (ZEV) necessary to compute the acceleration command as prescribed by the theory

Fixed-time rendezvous control of spacecraft with a tumbling target under loss of actuator effectiveness

This paper investigates the fixed-time fault-tolerant control problem of spacecraft rendezvous and docking with a freely tumbling target in the presence of external disturbance and thruster faults. More specifically, based on the attitude of the target spacecraft, a line-of-sight coordinate frame is defined first, and the dynamical equations relative to the tumbling target are derived to describe the relative position (not six degrees of freedom). Then two fixed-time position controllers are proposed to guarantee that the closed-loop system is stable in finite time in the sense of a fixed-time concept, even in the presence of simultaneous external disturbance and thruster faults. Numerical simulations illustrate that the chaser spacecraft can successfully perform the rendezvous using the proposed controllers

Dual-Quaternion-Based Fault-Tolerant Control for Spacecraft Tracking With Finite-Time Convergence

Results are presented for a study of dual-quaternion-based fault-tolerant control for spacecraft tracking. First, a six-degrees-of-freedom dynamic model under a dual-quaternion-based description is employed to describe the relative coupled motion of a target-pursuer spacecraft tracking system. Then, a novel fault-tolerant control method is proposed to enable the pursuer to track the attitude and the position of the target even though its actuators have multiple faults. Furthermore, based on a novel time-varying sliding manifold, finite-time stability of the closed-loop system is theoretically guaranteed, and the convergence time of the system can be given explicitly. Multiple-task capability of the proposed control law is further demonstrated in the presence of disturbances and parametric uncertainties. Finally, numerical simulations are presented to demonstrate the effectiveness and advantages of the proposed control method

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

State-of-the-art in Comprehensive Cascade Control Approach through Monte-Carlo Based Representation

The research relies on the comprehensive cascade control approach to be developed in the area of spacecraft, as long as Monte-Carlo based representation is taken into real consideration with respect to state-of-the-art. It is obvious that the conventional methods do not have sufficient merit to be able to deal with such a process under control, constantly, provided that a number of system parameters variations are to be used in providing real situations. It is to note that the new insights in the area of the research’s topic are valuable to outperform a class of spacecrafts performance as the realizations of the acquired results are to be addressed in both real and academic environments. In a word, there are a combination of double closed loop based upon quaternion based control approach in connection with Euler based control approach to handle the three-axis rotational angles and its rates, synchronously, in association with pulse modulation analysis and control allocation, where the dynamics and kinematics of the present system under control are analyzed. A series of experiments are carried out to consider the approach performance in which the aforementioned Monte-Carlo based representation is to be realized in verifying the investigated outcomes

Docking Manoeuvre Control for CubeSats

Rendezvous and Docking missions of small satellites are opening new scenarios to accomplish unprecedented in-obit operations. These missions impose to win the new technical challenges that enable the possibility to successfully perform complex and safety-critical manoeuvres. The disturbance forces and torques due to the hostile space environment, the uncertainties introduced by the onboard technologies and the safety constraints and reliability requirements lead to select advanced control systems. The paper proposes a control strategy based on Model Predictive Control for trajectory control and Sliding Mode Control for attitude control of the chaser in last meters before the docking. The control performances are verified in a dedicated simulation environment in which a non-linear six Degrees of Freedom and coupled dynamics, uncertainties on sensors and actuators responses are included. A set of 300 Monte Carlo Simulation with this Non-Linear system are carried out, demonstrating the capabilities of the proposed control system to achieve the final docking point with the required accuracy

Autonomous Satellite Rendezvous and Proximity Operations with Time-Constrained Sub-Optimal Model Predictive Control

This paper presents a time-constrained model predictive control strategy for the 6 degree-of-freedom (6DOF) autonomous rendezvous and docking problem between a controllable "deputy" spacecraft and an uncontrollable "chief" spacecraft. The control strategy accounts for computational time constraints due to limited onboard processing speed. The translational dynamics model is derived from the Clohessy-Wiltshire equations and the angular dynamics are modeled on gas jet actuation about the deputy's center of mass. Simulation results are shown to achieve the docking configuration under computational time constraints by limiting the number of allowed algorithm iterations when computing each input. Specifically, we show that upwards of 90% of computations can be eliminated from a model predictive control implementation without significantly harming control performance

Modeling, Stability Analysis, and Testing of a Hybrid Docking Simulator

A hybrid docking simulator is a hardware-in-the-loop (HIL) simulator that includes a hardware element within a numerical simulation loop. One of the goals of performing a HIL simulation at the European Proximity Operation Simulator (EPOS) is the verification and validation of the docking phase in an on-orbit servicing mission.....Comment: 30 papge