Spacecraft Attitude Stabilization with Piecewise-constant Magnetic Dipole Moment

In actual implementations of magnetic control laws for spacecraft attitude stabilization, the time in which Earth magnetic field is measured must be separated from the time in which magnetic dipole moment is generated. The latter separation translates into the constraint of being able to genere only piecewise-constant magnetic dipole moment. In this work we present attitude stabilization laws using only magnetic actuators that take into account of the latter aspect. Both a state feedback and an output feedback are presented, and it is shown that the proposed design allows for a systematic selection of the sampling period.Comment: arXiv admin note: text overlap with arXiv:1411.275

A Luenberger-style Observer for Robot Manipulators with Position Measurements

This paper presents a novel Luenberger-style observer for robot manipulators with position measurements. Under the assumption that the state evolutions that are to be observed have bounded velocities, it is shown that the origin of the observation error dynamics is globally exponentially stable and that the corresponding convergence rate can be made arbitrarily high by increasing a gain of the observer. Comparisons and relations between the proposed observer and existing observers are discussed. The effectiveness of the result here presented is illustrated by a simulation of the observer for the Pendubot, an underactuated two-joint manipulator.Comment: 6 pages, 2 figure

Global and robust attitude control of a launch vehicle in exoatmospheric flight

The goal of this research is to design global and robust attitude control systems for launch vehicles in exoatmospheric flight. An attitude control system is global when it guarantees that the vehicle converges to the desired attitude regardless of its initial condition. Global controllers are important because when large angle maneuvers must be performed, it is simpler to use a single global controller than several local controllers patched together. In addition, the designed autopilots must be robust with respect to uncertainties in the parameters of the vehicle, which means that global convergence must be achieved despite of those uncertainties. Two designs are carried out. In the first one possible delays introduced by the actuator are neglected. The design is performed by using a Lyapunov approach, and the obtained autopilot is a standard proportional-derivative controller. In the second one, the effects of the actuator are considered. Then the design is based on robust backstepping which leads to a memory-less nonlinear feedback of attitude, attitude-rate, and of the engine deflection angle. Both autopilots are validated in a case study

Lunar Ascent and Orbit Injection via Neighboring Optimal Guidance and Constrained Attitude Control

Future human or robotic missions to the Moon will require efficient ascent path and accurate orbit injection maneuvers, because the dynamical conditions at injection affect the subsequent phases of spaceflight. This research focuses on the original combination of two techniques applied to lunar ascent modules, i.e., (1) the recently introduced variable-time-domain neighboring optimal guidance (VTD-NOG), and (2) a constrained proportional-derivative (CPD) attitude control algorithm. VTD-NOG belongs to the class of feedback implicit guidance approaches aimed at finding the corrective control actions capable of maintaining the spacecraft sufficiently close to the reference trajectory. CPD pursues the desired attitude using thrust vector control while constraining the rate of the thrust deflection angle. The numerical results unequivocally demonstrate that the joint use of VTD-NOG and CPD represents an accurate and effective methodology for guidance and control of lunar ascent path and orbit injection in the presence of nonnominal flight conditions

A robust optimization approach for magnetic spacecraft attitude stabilization

Attitude stabilization of spacecraft using magnetorquers can be achieved by a proportional–derivative-like control algorithm. The gains of this algorithm are usually determined by using a trial-and-error approach within the large search space of the possible values of the gains. However, when finding the gains in this manner, only a small portion of the search space is actually explored. We propose here an innovative and systematic approach for finding the gains: they should be those that minimize the settling time of the attitude error. However, the settling time depends also on initial conditions. Consequently, gains that minimize the settling time for specific initial conditions cannot guarantee the minimum settling time under different initial conditions. Initial conditions are not known in advance. We overcome this obstacle by formulating a min–max problem whose solution provides robust gains, which are gains that minimize the settling time under the worst initial conditions, thus producing good average behavior. An additional difficulty is that the settling time cannot be expressed in analytical form as a function of gains and initial conditions. Hence, our approach uses some derivative-free optimization algorithms as building blocks. These algorithms work without the need to write the objective function analytically: they only need to compute it at a number of points. Results obtained in a case study are very promising

Determining optimal parameters in magnetic spacecraft stabilization via attitude feedback

The attitude control of a spacecraft using magnetorquers can be achieved by a feedback control law which has four design parameters. However, the practical determination of appropriate values for these parameters is a critical open issue. We propose here an innovative systematic approach for finding these values: they should be those that minimize the convergence time to the desired attitude. This a particularly diffcult optimization problem, for several reasons: 1) such time cannot be expressed in analytical form as a function of parameters and initial conditions; 2) design parameters may range over very wide intervals; 3) convergence time depends also on the initial conditions of the spacecraft, which are not known in advance. To overcome these diffculties, we present a solution approach based on derivative-free optimization. These algorithms do not need to write analytically the objective function: they only need to compute it in a number of points. We also propose a fast probing technique to identify which regions of the search space have to be explored densely. Finally, we formulate a min-max model to find robust parameters, namely design parameters that minimize convergence time under the worst initial conditions. Results are very promising

Gain Selection for Attitude Stabilization of Earth-Pointing Spacecraft Using Magnetorquers

AbstractThis paper considers a feedback control law that achieves attitude stabilization for Earth-pointing spacecraft using only magnetorquers as torque actuators. The control law is proportional derivative (PD)-like with matrix gains, and it guarantees asymptotic stability. The PD matrix gains are determined through the numerical solution of a periodic linear quadric regulator problem. A case study shows the effectiveness of the considered control law, and specifically of the gain selection method, in a simplified simulation scenario

Robust Three-axis Attitude Stabilization for Inertial Pointing Spacecraft Using Magnetorquers

In this work feedback control laws are designed for achieving three-axis attitude stabilization of inertial pointing spacecraft using only magnetic torquers. The designs are based on an almost periodic model of geomagnetic field along the spacecraft's orbit. Both attitude plus attitude rate feedback, and attitude only feedback are proposed. Both feedback laws achieve local exponential stability robustly with respect to large uncertainties in the spacecraft's inertia matrix. The latter properties are proved using general averaging and Lyapunov stability. Simulations are included to validate the effectiveness of the proposed control algorithms

Neighboring optimal guidance and proportional-derivative attitude control applied to low-thrust orbit transfers

This work presents a unified guidance and control architecture, termed VTD-NOG & PD-RM, and describes its application to low-thrust orbit transfer from a low Earth orbit to a geostationary orbit. The variable time-domain neighboring optimal guidance (VTD-NOG) is a feedback guidance technique based upon minimizing the second differential of the objective function along the perturbed trajectory, and was proven to avoid the numerical difficulties encountered with alternative neighboring optimal algorithms. VTD-NOG identifies the trajectory corrections assuming the thrust direction as the control input. A proportional-derivative attitude control based on rotation matrices (PD-RM) is used to drive the actual thrust direction toward the desired one, determined by VTD-NOG. Reaction wheels are employed to perform the attitude control action. In the dynamical simulations, thrust oscillations, errors on the initial conditions, and gravitational perturbations are considered. Extensive Monte Carlo simulations point out that orbit injection occurs with very satisfactory accuracy, even in the presence of nonnominal flight conditions

Parameter Optimization for Spacecraft Attitude Stabilization Using Magnetorquers

The attitude stabilization of a spacecraft that uses magnetorquers as torque actuators is a very important task. Depending on the availability of angular rate sensors on the spacecraft, control laws can be designed either by using measurements of both attitude and attitude rate or by using measurements of attitude only. The parameters of both types of control laws are usually determined by means of a simple trial-and-error approach. Evidently, such an approach has several drawbacks. This chapter describes recently developed systematic approaches for determining the parameters using derivative-free optimization techniques. These approaches allow to find the parameter values that minimize the settling time of the attitude error or an indirect measure of this error. However, such cost indices depend also on initial conditions of the spacecraft, which are not known in advance. Thus, a min-max optimization problem is formulated, whose solution provides values of the parameters minimizing the chosen cost index under the worst initial conditions. The chapter also provides numerical results showing the effectiveness of the described approaches