Chris Blanksby

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.

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.

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.

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.

Heating and modeling effects in tethered aerocapture missions

The influence of thermomechanical and tether flexibility effects on tethered aerocapture missions is examined. The focus of these missions is capturing a system, consisting of an orbiter and tether-connected probe, from a hyperbolic to an elliptical orbit via aerodynamic braking. Two temperature-dependent dynamic models of the tether are included: a two-dimensional, straight, massive, extensible tether model derived via Lagranges equations and a three-dimensional lumped mass model derived via Kanes equations. The dynamics of the aerocapture maneuver are shown to be affected by tether extensibility due to the change in system rotational inertia. If not properly accounted for, this can result in non-capture. The effect of thermal variations on the dynamics of the aerocapture maneuver is shown to be influenced strongly by the thermal properties of the tether material. As a consequence, these thermal variations can decrease the viability of certain proposed tethered aerocapture missions and should be accounted for during design.

Prolonged Payload Rendezvous Using a Tether Actuator Mass

8Reilly, J. P., Ballantyne, A., and Woodroffe, J. A., “Modeling of Momentum Transfer to a Surface by Laser Supported Absorption Waves,” AIAA Journal, Vol. 17, No. 10, 1979, pp. 1098–1105. 9Simons, G. A., “Momentum Transfer to a Surface When Irradiated by a High-Power Laser,” AIAA Journal, Vol. 22, No. 3, 1984, pp. 1275–1280. 10Sedov, L. I., Similarity and Dimensional Methods in Mechanics, Academic Press, New York, 1959. 11Katsurayama, H., Komurasaki, K., Momozawa, A., and Arakawa, Y., “Numerical and Engine Cycle Analyses of a Pulse Laser Ramjet Vehicle,” Transaction of JSASS Space Technology, Vol. 1, No. 1, 2003, pp. 9–16.

OPTIMAL CONTROL OF FLEXIBLE TETHERS

A method for determining optimal trajectories for tethered systems is presented based on a parameterization of the tension control input. Three separate models of the tether system are used to compare the effects of different cost functions on optimal trajectories. The parameterization of the control is based on a rigid tether model, while the optimal trajectories are determined using a model that discretizes the tether into 4 point masses connected by massless inextensible strings. The effect of various cost functions and terminal times are compared for deployment and retrieval. The effect of various cost functions are also studied for a tether-assisted sample return problem. It is shown that a cost function that minimizes the tether reel acceleration maintains the tether essentially straight when simulated in a fully flexible model of the system, whereas several other cost functions result in significant bending of the tether.

Tether Assisted Rendezvous with for Satellites with Small Relative Inclinations

Rendezvous and capture of a payload at the end of a librating or rotating space tether is an exciting concept whose implementation would see revolutionary changes in space utilization. This paper addresses two of the most important control problems affecting the feasibility of this concept. The first problem, how to control the tether motion to enable rendezvous even when there is some small relative inclination between the primary satellite and the target payload, proves to be an extremely complex task. Conventional optimal control solution methods are not suitable for the job; the only successful approach is to combine an homotopy and Legendre pseudospectral method. With this approach, rendezvous with relative inclinations of up to 1.5 may be achieved in as few as 2 orbits. The second problem, how to control the tether dynamics following capture when some residual relative velocity exists between the tether tip and the payload, is solved using a wave-absorbing controller. Using tether offset at the primary satellite, the waveabsorbing controller can damp out a relative impact velocity of 7.5m/s normal to the tether. The effect of these two innovations is a significant advance in the cause of tether assisted rendezvous. INTRODUCTION The concept of using tethers to catch a payload in orbit is now well known. Despite the appeal in terms of its elegance and potential for dramatic reductions in launch costs, this application appears to have recently lost favor. There are two primary reasons for this, one of which is a somewhat conservative political climate that must ultimately change in time. The second and more important cause is a better understanding of the complex dynamics and control challenges faced by this concept. Some of these challenges are addressed in this paper. At the outset, when initial studies into this concept were presented, the promise was fantastic. By making a range of (not unreasonable) assumptions, it was possible to show that capture was achievable and that it could enable transfer from a ballistic trajectory into higher orbits, or even to the Moon or Mars. These wide-ranging studies of the effect of various feasible scenarios set a firm basis for the further development of the concept but did not adequately address control issues related to capture, particularly in light of likely perturbations. Particular problems that remain to be addressed include how to control the tether to rendezvous with a passive payload that does not approach with the desired trajectory (note that an active payload does not necessarily solve this problem as the fuel required to correct the trajectory is likely to be large). The authors have developed a guidance algorithm for inplane capture, but no out-of-plane solution has yet been presented in the literature. The out-of-plane case is a particularly difficult one since even a small difference in the relative inclination of the satellite and payload can result in significant relative velocity in the out-of-plane direction. Also, the development of a robust, effective and reusable capturing mechanism remains an issue. Associated with this is the need to allow adequate time for docking. This was addressed by Stuart and the authors for the inplane case, however, out-of-plane effects have so far been ignored. Finally, there is the need to address post-capture dynamics that may arise from the impact of a payload with a small relative velocity at the tether tip. In this paper, we attempt to address the question of whether rendezvous and capture is still possible if there is some small relative inclination between the primary satellite (with the tether) and the target payload. Various algorithms, including conjugate gradient and simulated annealing were applied to this problem, using only tether tension as an input and assuming some small, initial out-of-plane component. The effectiveness of these algorithms was severely limited by the long guidance interval. This limitation was overcome via the application of a Legendre 1 54th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law 29 September 3 October 2003, Bremen, Germany IAC-03-A.P.09 Copyright