On the constraints violation in forward dynamics of multibody systems

It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian and the coordinate partitioning method.The first author expresses his gratitude to the Portuguese Foundation for Science and Technology through the PhD grant (PD/BD/114154/2016). This work has been supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.info:eu-repo/semantics/publishedVersio

Slew Maneuver of a Flexible Spacecraft Using On-Off Thrusters

The article of record as published may be found at http://dx.doi.org/10.2514/6.1993-3724A closed loop switching function for single-axis slew maneuvers of spacecraft using on-off thrusters is investigated by analytical simulations and experimental demonstrations. The proposed switching function provides flexibility of controlling multiple firing and pointing errors in the presence of modelling errors and structural flexibility. The proposed switching functions for three-axis maneuver of a rigid body are also investigated by analytical simulations. The analytical and experimental results show that the proposed switching function can result in significant improvement of the slew maneuver performance. A closed loop switching function for single-axis slew maneuvers of spacecraft using on-off thrusters is investigated by analytical simulations and experimental demonstrations. The proposed switching function provides flexibility of controlling multiple firing and pointing errors in the presence of modelling errors and structural flexibility. The proposed switching functions for three-axis maneuver of a rigid body are also investigated by analytical simulations. The analytical and experimental results show that the proposed switching function can result in significant improvement of the slew maneuver performance. A closed loop switching function for single-axis slew maneuvers of spacecraft using on-off thrusters is investigated by analytical simulations and experimental demonstrations. The proposed switching function provides flexibility of controlling multiple firing and pointing errors in the presence of modelling errors and structural flexibility. The proposed switching functions for three-axis maneuver of a rigid body are also investigated by analytical simulations. The analytical and experimental results show that the proposed switching function can result in significant improvement of the slew maneuver performance. A closed loop switching function for single-axis slew maneuvers of spacecraft using on-off thrusters is investigated by analytical simulations and experimental demonstrations. The proposed switching function provides flexibility of controlling multiple firing and pointing errors in the presence of modelling errors and structural flexibility. The proposed switching functions for three-axis maneuver of a rigid body are also investigated by analytical simulations. The analytical and experimental results show that the proposed switching function can result in significant improvement of the slew maneuver performance. A closed loop switching function for single-axis slew maneuvers of spacecraft using on-off thrusters is investigated by analytical simulations and experimental demonstrations. The proposed switching function provides flexibility of controlling multiple firing and pointing errors in the presence of modelling errors and structural flexibility. The proposed switching functions for three-axis maneuver of a rigid body are also investigated by analytical simulations. The analytical and experimental results show that the proposed switching function can result in significant improvement of the slew maneuver performance

A complex exponential solution to the unified two-body problem

A complex exponential solution has been derived which unifies the elliptic and hyperbolic trajectories into a single set of equations and provides an exact, analytical solution to the unperturbed, Keplerian two-body problem. The formulation eliminates singularities associated with the elliptic and hyperbolic trajectories that arise from these orbits. Using this complex exponential solution formulation, a variation of parameters formulation for the perturbed two-body problem has been derived. In this paper, we present the analytical formulation of the complex exponential solution, numerical simulations, a comparison with classical solution methods, and highlight the benefits of this approach compared with the classical developments

Adaptive external torque estimation by means of tracking a Lyapunov function

A real-time method is presented to adoptively estimate three-dimensional unmodeled external torques acting on a spacecraft. This is accomplished by forcing the tracking error dynamics to follow the Lyapunov function underlying the feedback control law. For the case where the external torque is constant, the tracking error dynamics are shown to converge asypmtotically. The methodology applies not only to the control law used in this paper, but can also be applied to most Lyapunov derived feedback control laws. The adaptive external torque estimation is very robust in the presence of measurement noise, since a numerical integration is used instead of a numerical differentiation. Spacecraft modeling errors, such as in the inertia matrix, are also compensated for by this method. Several examples illustrate the practical significance of these ideas