Analytical solution of the optimal steering law for non-ideal solar sail

Solar sails have many advantages over traditional chemical propulsion spacecraft, such as needlessness of fuel, high payload ratio, long service life, and great application potential in deep space exploration, interstellar voyage, and other aerospace application fields However, the period of solar sail transfer from the initial orbit to the desired orbit is relatively long Thus, it is necessary to optimize the transfer trajectory of solar sail according to specific tasks The hp-adaptive pseudospectral method combines the global pseudospectral method with the finite element method, which adopts double layer optimization strategy to solve the optimal control problem and has higher computational efficiency and accuracy than the traditional global pseudospectral method In this paper, the pressure of solar light acting on the solar sail is analyzed, and the kinematic equation of the solar sail is established in polar coordinate system first; then the basic principle of the hp-adaptive pseudospectral method is introduced, and the steps of solving the transfer trajectory optimization problem by hp-adaptive pseudospectral method are proposed; finally, the trajectory optimization of the solar sail from Earth orbit to Sun-centered Mars orbit is simulated as an example to demonstrate the effectiveness of hp-adaptive pseudospectral method in the orbit transfer optimization problem of solar sail The simulation results show that the adopted method is not sensitive to the initial values and has more reasonable distribution and less computational cost than the Gauss pseudospectral method

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The Earth-Mars Transfer Trajectory Optimization of Solar Sail Based on hp-Adaptive Pseudospectral Method

The success of a space mission where the satellite must perform rapid attitude maneuvers with great angles is extremely dependent of a careful investigation of the nonlinear dynamics of the satellite. Since these big maneuvers imply in the dynamic coupling between the satellites angular motion and the actuators such as reaction wheels and/or gas jets. As a result, this coupling must be taking into account in the Attitude Control System (ACS) design. This paper presents the nonlinear model derivation of a rigid satellite and the performance comparison of two controllers designed by Lyapunov and LQR methods. The dynamics of the satellite is initially derived in the non-linear Euler equations form and the kinematics is based on the quaternion parametrization which represent the rotation and attitude motion, respectively. In the sequel, the linear model is obtained where linearization is about an operating point of the arbitrary angular velocity and the reaction wheel angular momentum. From this model, several simulations are performed in order to investigate the influence of the nonlinear dynamics in the in the SCA performance which is designed by trial and error and by the Linear Quadratic Regulator approaches. The ACS performance is evaluated considering the capacity of the reaction wheels to maintain the stability and to control the angular velocity and the attitude of the satellite. The stability is investigated comparing the location of the poles and zeros of the open and closed loops. The ACS performance is evaluated comparing the amount of energy spend by each control law. Keywords: Satellite Control, nonlinear dynamics, LQR and Lyapunov theory

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Satellite attitude control system design with nonlinear dynamics and kinemtics of quaternion using reaction wheels

This paper presents the Attitude Control System (ACS) design for a rigid-flexible satellite with two vibrations mode, using the H infinity method considering the parametric uncertainty over the mass matrix. Usually the mathematic model obtained from the linearization and/or reduction of the rigid flexible model loses information about the flexible dynamical behavior and introduces some uncertainty. As a result, the ACS performance can be degraded when controlling large angle maneuvers. One way to recovery the dynamics information is to include in the ACS design the parametric and not parametric uncertainties of the system. The rigid flexible satellite dynamics can be represented by an ordinary differential equation (EDO), which coefficients are the matrices mass, damping and rigidly. In this paper one investigates the influence of the uncertainty in the mass matrix in the control law performance designed by the H infinity control methodology. The results of the simulations have shown that the control law designed using the H-infinity control method considering the parametric uncertainty is robust since the ACS performance has been improved in controlling the rigid flexible satellite attitude and suppressing vibrations. Keywords: ACS, Satellite rigid-flexible, Uncertain, H infinity

Attitude control system design for a rigid-flexible satellite using the h-infinity method with parametric uncertainty

A simple mathematical model for a constrained robotic manipulator is investigated. Besides the fact that this model is relatively simple, all the features present in more complex problems are similar to the ones analyzed here. The fully plastic impact is considered in this paper. Expressions for the velocities of the colliding bodies after impact are developed. These expressions are important in the numerical integration of the governing equations of motion when one must exchange the set of unconstrained equations for the set of constrained equation. The theory presented in this work can be applied to problems in which robots have to follow some prescribed patterns or trajectories when in contact with the environment. It can also de applied to problems in which robotic manipulators must handle payloads.

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The Determination of the Velocities after Impact for the Constrained Bar Problem

A comparative study between control strategies for a solar sailcraft in an Earth–Mars transfer

Contact dynamics problems arises in numerous applications in space and industry, as robotic welding, parts assembly, the operation of capturing a satellite in orbit or the general problem of a robotic manipulator grabbing and handling any object with its own dynamics. The theory developed here can also be applied to problems in which robots have to follow some prescribed patterns or trajectories when in contact with the environment (like in painting activities, for instance, or the ROKVISS experiment investigated at DLR). In this paper, the governing equations of motion of a system representative of a robotic manipulator in contact with a dynamic environment are derived. These equations are obtained through the Lagrangian formalism. The constraints are introduced into the governing equations for the case in which the bodies are in contact via the Lagrange multipliers. Some preliminary results (including profiles for the contact force) and recommendations are discussed.

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A mathematical model to investigate contact dynamics in constrained robots

This paper describes the dynamical behavior of a nonlinear flexible beam (cubic nonlinearities considered) connected to a dc motor (responsible for the slewing motion) when the angular displacement of the slewing axis and its derivatives are considered to be of a harmonic type and the system is excited near a resonance (present due to the nonlinear contribution).

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L. C. Gadelha de Souza

Papers

A comparative study between control strategies for a solar sailcraft in an Earth–Mars transfer

A mathematical model to investigate contact dynamics in constrained robots

A brief comment on the dynamical behavior of a forced nonlinear slewing beam: 1. Superharmonic resonance