Continuous Thrust Research Articles

Optimal circle-to-rectilinear orbit transfer with circumferential thrust

This paper investigates the optimal transfer trajectories from a circular parking orbit towards the apocenter of a rectilinear ellipse, where the spacecraft reaches a quasi-stationary condition relative to an inertial reference frame. The spacecraft is equipped with a propulsion system that provides a circumferential continuous propulsive acceleration, that is, an acceleration whose direction is perpendicular to the primary body-spacecraft line. The performance index to minimize is the total flight time, and an indirect method is used to analyze the transfer trajectories. In this context, the optimal transfer performance is obtained as a function of the spacecraft propulsive acceleration magnitude through an interpolation procedure of numerical simulations. The results obtained with a continuous thrust propulsion system are also compared with those derived from a multi-impulse transfer. Finally, the paper investigates a heliocentric mission scenario in which the spacecraft minimizes the flight time required to reach a rectilinear ellipse with a given value of the aphelion radius.

Construction of Frozen Orbits Using Continuous Thrust Control Theories Considering Earth Oblateness and Solar Radiation Pressure Perturbations

The problem of the artificial frozen orbits around the Earth is investigated. To design such orbits with arbitrary orbital parameters, six control strategies are discussed taking into account the main zonal harmonics up to J4 and solar radiation pressure (SRP). The effect in the argument of periapsis due to the main zonal harmonics is revealed to be about three orders of magnitude greater than that of SRP. Two comparisons are given. To obtain longer lifespan of the spacecraft, continuous variable low-thrust control is implemented. Radial and/or transverse thrusts are used to achieve these orbits. Furthermore, explicit formulas for refinement of the control thrusts are given in order to overcome errors due to approximations arising from long and short periodic variations of a and e. Some concluding remarks can be inferred from the presented simulation; e.g. the energy consumed is saved efficiently when using the root mean squares rather than using averages, also when using coupled radial and transverse thrusts instead of using single radial or transverse thrust. To minimize the fuel consumption more efficiently, three new techniques are suggested. The calculations illustrated that AFOT-F Technique, where the transverse control thrust is constant, has the minimum control thrust required.

Real-time trajectory planning for free-floating space robot in close range using continuous thrust

This paper investigates the trajectory planning problem of free-floating space robot in proximity with continuous thrust. Sampling-based motion planning algorithm is viewed as promising method in such high-dimensional, complex scenario. A novel, fast trajectory planning algorithm AGB-RRT* is proposed using linearized orbital dynamics, which is capable of preventing collisions efficiently. Several constraints are considered, such as obstacle avoidance, plume impingement and control feasibility. Two extensions of AGB-RRT* algorithm are made: adaptive sampling strategy and LQR steering method. Finally, the performance of proposed algorithm are tested in 2D planar case and 3D case. Simulation results indicate the real-time feasibility of the proposed AGB-RRT* algorithm and the collision-free trajectories are displayed.

Quantum-behaved particle swarm optimization for far-distance rapid cooperative rendezvous between two spacecraft

Focused on far-distance rapid cooperative rendezvous between two spacecraft under continuous large thrust, this paper presents a series of artificial intelligence algorithms for fuel and time optimization. The process of far-distance rapid cooperative rendezvous was optimized by a type of hybrid algorithm-integrated Quantum-behaved Particle Swarm Optimization (QPSO) and Sequential Quadratic Programming (SQP). The convergent co-state vectors were obtained by QPSO and subsequently set as the initial values of SQP to search for the exact solutions in a smaller area. Applications of non-coplanar cooperative rendezvous are provided to demonstrate that the QPSO-SQP algorithm has better performance than other popular algorithms in less time consumption, faster convergence rate and highly stable solutions.

Note: Precision balance for sub-miliNewton resolution direct thrust measurement.

We attempted to test the suitability of a commercial precision balance as a simple alternative sub-miliNewton resolution continuous thrust stand on a vertically oriented 300 W-class Hall thruster. The measured thrust data were in the range of 1-10 mN with a maximum error of 0.1 mN. The performance of the precision balance was compared to the performance of a hanging pendulum thrust stand. The measured thrust from the precision balance falls within the standard error of the hanging pendulum indicating good quantitative agreement.

Analytic Modeling for Precise Speed Tracking of Multilink Robotic Fish

In this paper, a novel analytical-based kinematic and dynamic modeling and control approach is developed for reference speed tracking of a multijoint robotic fish. The kinematic model is improved by the introduction of input signal for controlling body undulation amplitude without distorting the model structure. Next, the dynamic model is developed in the discrete-time domain primarily because fish swimming pattern generates oscillating continuous thrust where the effect of thrust over one cycle of undulation can be calculated through averaging. Hence, the dynamics can be discretized according to the undulation rate. The novelty in developing the discrete-time dynamical model is three fold. First, the thrust gradient is derived with assistance of Lighthill's large amplitude elongated body theory. More importantly, affine-in-control dynamical model form, essential for designing a real-time model-based control algorithm, is derived by inclusion of the updated kinematic model. Second, the thrust delay is studied via pulse input response of the motion system, and incorporated in the dynamical model. Third, drag force coefficient calculation is also proposed by comparing the thrust model and empirically recorded steady-state speeds of the robotic fish. Finally, discrete-time model-based sliding-mode control (SMC) is designed for speed tracking. Experimental results verify that SMC based on the proposed dynamical model, can significantly improve speed tracking performance of a multilink robotic fish.

Orbital plane change maneuver strategy using electric propulsion

The orbital dynamics basis for orbital plane change maneuver using chemical propulsion is the impulsive orbital change theory in practical engineering. The orbital plane change theory using continuous thrust suitable for electric propulsion is studied in this paper. A set of nonsingular orbital variational equations using quaternion is used to investigate the orbital motion of spacecraft under constant normal acceleration departing from a Keplerian circular orbit firstly. Results show that the orbit of spacecraft under continuous constant normal acceleration is a circular orbit over the gravitational center on the same spherical surface as the initial orbit, and it is tangent to the initial circular orbit at the initial position. Continuous and discontinuous maneuver strategies are then designed using the previous theory, and they are validated by numerical simulations. Results indicate that the strategy can work effectively.

Artificial Equilibrium Points near Irregular-Shaped Asteroids with Continuous Thrust

Artificial equilibrium points near irregular-shaped asteroids are generated by using continuous thrust to enlarge the feasible regions of body-fixed hovering missions. The dynamics of artificial equilibrium points and feasible sets with constraints of the control magnitude and direction are investigated. The linearized motion near artificial equilibrium points is derived with the generalized effective potential for analysis of topological classification, bifurcations, and stability. Collision and annihilation of equilibrium points and Hopf bifurcation are found during numerical continuation. A parametric study is conducted to investigate the influence of the control magnitude on the sets of artificial equilibrium points. The linearly stable regions are obtained by a grid searching. Moreover, a method based on the polyhedral model of asteroids is proposed to solve the feasible artificial equilibrium points with constraints of the control direction and observation. The observable area at feasible artificial equilibrium points is also obtained by the proposed method. In numerical simulations, 433 Eros is selected as a representative irregular-shaped asteroid to validate the effectiveness of the methods.

Continuous maneuvers for spacecraft formation flying reconfiguration using relative orbit elements

This paper presents the solutions to the spacecraft relative trajectory reconfiguration problem when a continuous thrust profile is used, and the reference orbit is circular. Given a piecewise continuous thrust profile, the proposed approach enables the computation of the control solution by inverting the linearized equations of relative motion parameterized using the mean relative orbit elements. The use of mean relative orbit elements facilitates the inclusion of the Earth's oblateness effects and offers an immediate insight into the relative motion geometry. Several reconfiguration maneuvers are presented to show the effectiveness of the obtained control scheme.

Analytical approach to spacecraft formation-flying with low-thrust relative spiral trajectories

This work addresses the growing need for an intuitive, systematic approach to low-thrust spacecraft formation flying by extending shape-based continuous thrust trajectory design methods to the relative motion of two spacecraft. There is widespread interest in distributed space systems for their low costs, broad capabilities, and high redundancy. This trend introduces a new challenge for trajectory design when combined with the increasing prevalence of low-thrust, high specific impulse electric propulsion systems. That challenge is met herein with a geometrically intuitive, semi-analytical solution to the low-thrust problem. Beginning with the equations of relative motion of two spacecraft, an unperturbed chief and a continuously-thrusting deputy, a thrust profile is constructed which transforms the equations into a form that is solved analytically. The resulting relative trajectories are the family of sinusoidal spirals, which provide diversity for design and optimization based upon a single thrust parameter. Closed-form expressions are derived for the trajectory shape and time-of-flight for two prescribed relative velocity behaviors, and used to develop a novel patched-spirals trajectory design and optimization method. The example problem of a servicer spacecraft establishing and reconfiguring a formation around a target in geostationary earth orbit is used to demonstrate the application of the patched spirals technique as well as the advantages of the relative spiral trajectories over impulsive maneuvers. The sensitivity of the trajectory solutions to deviations from the underlying assumptions, uncertainties in the state, and errors in thrust are studied through high-fidelity simulation.

Orbit period modulation for relative motion using continuous low thrust in the two-body and restricted three-body problems

This paper presents rich new families of relative orbits for spacecraft formation flight generated through the application of continuous thrust with only minimal intervention into the dynamics of the problem. Such simplicity facilitates implementation for small, low-cost spacecraft with only position state feedback, and yet permits interesting and novel relative orbits in both two- and three-body systems with potential future applications in space-based interferometry, hyperspectral sensing, and on-orbit inspection. Position feedback is used to modify the natural frequencies of the linearised relative dynamics through direct manipulation of the system eigenvalues, producing new families of stable relative orbits. Specifically, in the Hill–Clohessy–Wiltshire frame, simple adaptations of the linearised dynamics are used to produce a circular relative orbit, frequency-modulated out-of-plane motion, and a novel doubly periodic cylindrical relative trajectory for the purposes of on-orbit inspection. Within the circular restricted three-body problem, a similar minimal approach with position feedback is used to generate new families of stable, frequency-modulated relative orbits in the vicinity of a Lagrange point, culminating in the derivation of the gain requirements for synchronisation of the in-plane and out-of-plane frequencies to yield a singly periodic tilted elliptical relative orbit with potential use as a Lunar far-side communications relay. The Delta v requirements for the cylindrical relative orbit and singly periodic Lagrange point orbit are analysed, and it is shown that these requirements are modest and feasible for existing low-thrust propulsion technology.

Highly miniaturized FEEP propulsion system (NanoFEEP) for attitude and orbit control of CubeSats

A highly miniaturized Field Emission Electric Propulsion (FEEP) system is currently under development at TU Dresden, called NanoFEEP [1]. The highly miniaturized thruster heads are very compact and have a volume of less than 3 cm3 and a weight of less than 6 g each. One thruster is able to generate continuous thrust of up to 8 μN with short term peaks of up to 22 μN. The very compact design and low power consumption (heating power demand between 50 and 150 mW) are achieved by using Gallium as metal propellant with its low melting point of approximately 30 °C. This makes it possible to implement an electric propulsion system consisting of four thruster heads, two neutralizers and the necessary electronics on a 1U CubeSat with its strong limitation in space, weight and available power. Even formation flying of 1U CubeSats using an electric propulsion system is possible with this system, which is shown by the example of a currently planned cooperation project between Wuerzburg University, Zentrum fuer Telematik and TU Dresden. It is planned to use the NanoFEEP electric propulsion system on the UWE (University Wuerzburg Experimental) 1U CubeSat platform [2] to demonstrate orbit and two axis attitude control with our electric propulsion system NanoFEEP. We present the latest performance characteristics of the NanoFEEP thrusters and the highly miniaturized electronics. Additionally, the concept and the current status of a novel cold neutralizer chip using Carbon Nano Tubes (CNTs) is presented.

IRMA: a Graphical Tool for Interplanetary Mission Design

Designing an interplanetary mission is a complex task and requires the choice of the launch opportunity and of the exact launch and arrival dates. Depending on these choices, the trajectory must be defined and, in case of continuous thrust, also the thrust profile needs to be optimized.. Traditionally, these choices are made using some plots which allow to find a good compromise between the travel duration and the cost of the mission, which is often expressed in terms of initial mass in Earth orbit (IMLEO). IRMA (InterPlanetary Mission Analysis) code, based on the MATLAB®environment, is here described. It allows to deal with both impulsive propulsion (using the patched conics approach) and low continuous thrust (Solar or Nuclear electric or propellantless, like solar sails). A specific solver, based on indirect optimization techniques, has been developed specifically for this program, but IRMA can be used also as an interface for standard solvers, based on direct methods, like the FALCON.m code.

Model Predictive Control for Continuous Low Thrust Satellite Formation Flying

This paper presents a low thrust guidance and control strategy for distributed spacecraft systems flying in proximity in nearly circular Low Earth Orbit (LEO) using Model Predictive Control (MPC). It is designed to converge to arbitrary three dimensional (3D) force free formation topologies taking different constraints and system limitations into account. However it is also applicable to forced formations with the same given constraints. Its performance is evaluated using simulations of different typical 3D formation topologies.

Optimal Orbital Transfers to Asteroids

Many of the smaller asteroids between Mars and Jupiter have poorly determined orbits with high uncertainties. For successfully completing a transfer missions without consuming unacceptable amounts of fuel, a robust optimal design is needed. In this paper, the spacecraft trajectory planning problem is posed as an optimal control problem. The solutions of the problem is obtained by employing a computationally efficient algorithm, Model Predictive Static Programming (MPSP). The algorithm is used for generating nominal and adaptive trajectories. A comparison study is carried out with classical solutions. The results show that MPSP is highly reliable in generating computationally efficient low continuous thrust transfer trajectories particularly in situations where there are stringent time constraints and robustness is a need.

Economic Approach of Tinplate Production by Correlating Customers Demand and Production Parameters through Numerical Simulation

Competition to tinplate industry leads to continuous thrust on down gauging, improvement in mechanical properties, lesser coating without sacrificing preservative properties .This paper studies effect of temper rolling parameters and chemistry of HR coils and annealing parameters of low carbon steels for tinplate application, and critical assessment provides a solution of cost effective tinplate production as per customer’s requirements.

Novel and compact thermomagnetic actuator using temperature-sensitive magnetic materials

This paper describes the structure and characteristics of a novel compact actuator that uses a combination of temperature-sensitive magnetic materials (TSMMs) and permanent magnets (PMs). The actuator has the potential to generate a large force per volume, while the absence of a coil structure makes it easy to downsize. The structure and driving principles of the actuator were determined to exploit the advantages of this combination, and thrust force characteristics were examined through numerical analysis. The thrust force generated was measured based on the temperature of the TSMMs. The temperature characteristics were investigated experimentally and theoretically. In addition to thrust force, the energy consumption was experimentally examined with respect to the TSMM temperature. The results indicate that the proposed actuator performed better than a conventional electromagnetic actuator in generating a large continuous thrust force.

A simplex method for the orbit determination of maneuvering satellites

A simplex method of orbit determination (SMOD) is presented to solve the problem of orbit determination for maneuvering satellites subject to small and continuous thrust. The objective function is established as the sum of the nth powers of the observation errors based on global positioning satellite (GPS) data. The convergence behavior of the proposed method is analyzed using a range of initial orbital parameter errors and n values to ensure the rapid and accurate convergence of the SMOD. For an uncontrolled satellite, the orbit obtained by the SMOD provides a position error compared with GPS data that is commensurate with that obtained by the least squares technique. For low Earth orbit satellite control, the precision of the acceleration produced by a small pulse thrust is less than 0.1% compared with the calibrated value. The orbit obtained by the SMOD is also compared with weak GPS data for a geostationary Earth orbit satellite over several days. The results show that the position accuracy is within 12.0 m. The working efficiency of the electric propulsion is about 67% compared with the designed value. The analyses provide the guidance for subsequent satellite control. The method is suitable for orbit determination of maneuvering satellites subject to small and continuous thrust.

Fault-Tolerant Station-Keeping on Libration Point Orbits

This paper extends a linear quadratic regulator-based control scheme for station-keeping on libration point orbits to enable continued tracking in the event of thruster failure. In the first instance it is shown that by using an extended state observer the fault (as well as disturbances) can be measured and compensated for at each sampling period using continuous thrust. It is proved that this control yields asymptotic tracking to a small bounded region around the desired reference orbit in the presence of these uncertainties. In addition, it is demonstrated that by combining this method with a sliding mode or an adaptive control, asymptotic tracking can be achieved. An advantage of this method is that the required gain for asymptotic tracking of the sliding mode component is much smaller than traditional methods; the gain magnitude is required to be larger than the magnitude of the disturbance estimation error rather than the magnitude of the disturbance. A comparison of the controllers performance against an linear quadratic regulator control scheme is undertaken in an application to low-thrust station-keeping on a halo orbit in the Earth–Moon–spacecraft system in the presence of disturbances and various thruster faults.

Study of Arjuna-Type Asteroids for Low-Thrust Orbital Transfer

This paper investigates the accessible low-thrust transfer trajectories for a near-Earth asteroid transfer mission. The target asteroids considered are Arjuna-type asteroids, which are characterized by their Earth-like orbital paths including low eccentricity and low inclination. The asteroid range is characterized by a specific range of semimajor axes and transfer angles to provide an overall assessment of the potential Arjuna transfer domain. A single hovering ion beam spacecraft is employed for the task of asteroid redirection. The method uses a continuous thrust over the duration of the transfer maneuver to redirect the asteroid to an Earth-bound orbit. The transfer model employs a minimized form of Gauss’s variational equations to determine the available trajectories for asteroid redirection. The transfer model employs, in addition to the aforementioned orbital equations, spacecraft thruster and sizing metrics as well as mission cost analysis formulae. The system parameters and orbital transfer paths are assessed with regard to key mission parameters, namely, time frame for redirection, number of orbital revolutions, system mass, propellant mass, thrust, power, system cost, and financial return rate.