Pavel Trivailo

Libration Control of Flexible Tethers Using Electromagnetic Forces and Movable Attachment

This paper proposes utilising the distributed Lorentz forces that are induced in an electromagnetic tether as a control actuator for controlling the tether motion. The control input governing the magnitude of the applied actuator force is the current being conducted within the tether. A wave-absorping controller is also proposed to suppress the unstable high order modes that tend to be initiated by electromagnetic forces. The absorption of travelling waves along the tether may be achieved by proper movement of the tether attachment point on the main satellite. A mission function control law is presented for controlling the tether length and in- and out-of-plane librations, derived from a model that treats the tether as an inextensible rigid rod. The control law is numerically simulated in a continuum model of the tether system. It is shown that the out-of-plane motion of the tether can be effectively damped by appropriate control of the tether current for inclined orbits. The effect of tether flexibility does not significantly alter the time history of the tether librations, but causes significant bowing that grows into instability of the lateral modes. It is shown that this instability can be effectively suppressed by applying the proposed waveabsorbing controller.

Dynamics of Circularly Towed Aerial Cable Systems, Part I: Optimal Configurations and Their Stability

When a long cable. is towed in a circular flight path, the system can exhibit quasi-stationary solutions for which the cable tip appears to remain stationary relative to the orbiting aircraft. For applications involving pickup and delivery of payloads, tighter turns at high speeds lead to nearly stationary motion of the cable tip in an inertial frame. This work studies the dynamics of such a system, focusing on the stability and equilibria of solutions. A numerical analysis of the system is carried out using a discretized lumped mass model of the cable. By using constrained numerical optimization, practical towing solutions that achieve small motion of the towed body are obtained.

Nonlinear control of librational motion of tethered satellites in elliptic orbits

A method to control the librational motion of a tethered satellite system in an elliptic orbit is presented. To simplify the analysis, gravity is treated as the only external force affecting the tethered satellite system, only in-plane motion is considered, and the flexibility and mass of tethers are neglected. The tethered satellite system treated in this paper consists of two subsatellites and a mother satellite, such as the space shuttle, connected together in series via massless tethers. This type of tethered satellite system has very important applications in Earth observation, space observation, communications, and satellite constellations. The librational motion of the tethered satellite system in an elliptic orbit is known to be chaotic and can be stabilized to undergo periodic motion by the delayed feedback control method. The periodic motion of a tethered satellite in a circular orbit is employed as the reference trajectory for tracking by the actual tethered satellite, which is in an elliptic orbit. The decoupling and model tracking control methods, based on differential geometric control theory are combined with the delayed feedback control method in a new approach to controlling the librational motion of the tethered satellite system in elliptic orbits. The results of numerical simulations show that the proposed control scheme has good performance in controlling the librational motion of a tethered satellite system in an elliptic orbit.

On the Optimal Deployment and Retrieval of Tethered Satellites

*† The deployment and retrieval processes of a tethered satellite system are studied from the point-of-view of optimal control. In the past, the application of various optimality criteria such as minimum tension or minimum libration angles have been applied in the determination of open-loop deployment and retrieval trajectories. This paper demonstrates by way of numerical examples that these criteria are inappropriate for defining the control system. By applying various optimality criteria, such as minimum tension rate, minimum length acceleration, and so on, as well as minimax optimal control techniques, it is shown that the best control objectives should incorporate minimization of system accelerations. Both inelastic and elastic tethers are considered, and it is proven that the deployment and retrieval processes are symmetrical under certain conditions. A large number of numerical examples are presented to illustrate the importance of selecting the right cost function for optimizing the deployment/retrieval processes.

Tethered planetary capture maneuvers

A new concept for the application of space tethers in planetary exploration and payload transfer is presented. We propose the deployment of a payload on a spinning tether in a hyperbolic orbit to provide it with a sufficient velocity change so that it is captured in an elliptical orbit at the destination planet. This concept of using tethers for planetary capture is investigated by conducting numerical simulations of a simplified tether system. The tether mass required to prevent rupture of the tether is optimized using numerical and iterative techniques for each of the major planets in the solar system. It is demonstrated that significant mass savings can be achieved when compared to the requirements for chemical propulsion. Finally, it is shown that controlling the tether length during the maneuver can be used to correct errors in the system trajectory for both spinning and nonspinning capture cases.

Optimal Control of an Aircraft-Towed Flexible Cable System

The control of an aerial-towed flexible cable system for precision rendezvous and snatch pickup of payloads is considered. In past studies of related systems, optimal trajectories have been determined assuming that the cable remains straight. However, aerodynamic drag and deployment forces can cause bowing of the cable that can significantly alter the position of the cable tip relative to the aircraft. To account for this, the cable is modeled using lumped masses connected via rigid links. Multiple rendezvous sequences using only cable winch control and including features such as collision avoidance and variable winds are solved by multiple-phase direct transcription methods. Numerical results show that for some multiple rendezvous scenarios it is necessary to use the cable lateral dynamics and swing motion to avoid impact with elevated terrain. The effect of different wind speeds and directions are also studied.

Spin-axis stabilisation of underactuated rigid spacecraft under sinusoidal disturbance

Spin-axis stabilisation of spacecraft is a problem of partial stabilisation for non-linear dynamical systems. In this article the analysis of spin-axis stabilisation of underactuated rigid spacecraft in the presence of sinusoidal disturbances is presented. By using the Euler–Poisson form to describe the equations of motion and assuming the disturbances in three axes are decoupled with known frequencies, the paper first studies the problem of the underactuated rigid axisymmetric spacecraft by applying the internal modal principle to eliminate the sinusoidal disturbance. Then the paper turns to the more complicated asymmetric spacecraft, where the boundedness of the angular velocity for the underactuated axis is analysed in detail. The paper also proves the global asymptotic stability of the closed-loop systems for both axisymmetric spacecraft and asymmetric spacecraft by combining the Lyapunov direct method with the LaSalles theorem. The simulation results show that the proposed control law is effective in the presence of sinusoidal disturbance.

Tethered planetary capture: Controlled maneuvers

Abstract A new concept for the application of space tethers in planetary exploration and payload transfer is presented. It is proposed that a payload be deployed on a spinning tether in a hyperbolic orbit in order to provide a sufficient delta-v such that it is captured in an elliptical orbit at the destination planet. Due to conservation of momentum, the main spacecraft gains a “momentum-enhanced gravity-assist”. This concept is investigated by conducting numerical simulations of a simplified system. The mathematical model is derived using Lagranges equations including tether mass, but neglects tether vibrations. The feasibility of the concept in the constant length case is demonstrated by numerically integrating the equations of motion. The required tether mass to prevent rupture is optimized using numerical and iterative techniques. These results are validated through mass and force contour plots. The optimum tether length, diameter and mass are determined for each of the major outer planets in the solar system. Finally, it is shown that controlling the tether length during the maneuver is preferable to maintaining the tether at a constant length. The control problem is posed as one of minimizing a performance functional, and a solution method is proposed utilizing nonlinear programming with direct integration.

Dynamics of Circularly Towed Cable Systems, Part 2: Transitional Flight and Deployment Control

When the towpoint of an aerial cable system moves in a tight circular path, the drogue at the cable tip moves towards the center of the circle, and its altitude decreases relative to its equilibrium position in forward flight. Such a system has both military and civilian applications, including remote pickup and delivery of payloads. This work studies the transitional dynamics of such a system as the aircraft changes from straight flight to circular flight. The system dynamics are modeled using a discretized cable model, allowing the cable to take on zero tension values. Numerical simulation results show that the cable becomes slack during the transition if the aircraft turns too rapidly. Parametric studies of the towpath are performed for both tow-in and tow-out maneuvers. Tension waves can be reduced by appropriate control of the towpoint. Simulated annealing is used to optimize some parameters used to specify the tow-in maneuver. Alternatively, a deployment controller is developed using fuzzy logic that avoids some of these problems by deploying the cable while I the aircraft orbits. Instability of deployment for certain combinations of cable length and length rate are observed.

Motion Planning for an Aerial-Towed Cable System

*† ‡ This paper studies the coupled motion of an aircraft towing a cable for applications such as precision deployment or retrieval of payloads, or close surveying of land/ocean environments. There is a complex interaction between the motion of the cable tow point, aerodynamic drag, and tension forces on the motion of the cable tip. The path planning algorithm involves determining the motion of the aircraft, as well as the cable deployment rate, to achieve precision “hits” of the cable tip with known ground targets in a three dimensional space. By utilizing the motion of the towed-body as a differentially flat output, the aircraft controls and/or reel rate are computed via an inverse technique. The motion of the towed-body is approximated using Chebyshev polynomials so as to pass through the desired points while minimizing the curvature of the curve. The open-loop control algorithm is successfully combined with a simple feedback control methodology in closedloop simulations. The application of the system for real-time regeneration of trajectories due to payload pickup and drop-off, as well as changes in the steady-wind strength is demonstrated.