Research On Dynamics And Control Of Lorentz Spacecraft

Electrostatically charged spacecraft accelerates when orbiting a central body with a magnetic field due to the induced Lorentz force, providing new means of propellantless electromagnetic propulsion to perform orbital maneuvers. Such spacecraft is referred to as Lorentz spacecraft, a conceptional space vehicle that could intentionally modulate the net charge on its surface to induce Lorentz force via interaction with the local magnetic field. Though the development of Lorentz spacecraft is complicated by the fact that the Lorentz force could only act in a direction perpendicular to the local magnetic field and the vehicle’s velocity with respect to the local magnetic, it will by no means inhibit the applications of Lorentz spacecraft in various space missions. To propose a systematic analysis and design of Lorentz-augmented space missions, this dissertation develops dynamical models that characterize, respectively, the absolute and relative orbital motion of Lorentz spacecraft, which are then applied to research on Lorentz-augmented spacecraft hovering, Lorentz-propelled rendezvous and formation reconfiguration.Firstly, assuming that the Earth’s magnetic field can be modeled as a tilted dipole corotating with Earth, dynamic equations for both two-body and J2-perturbed orbital motion of Lorentz spacecraft are derived using Lagrange mechanics. Dynamical models for two-body and J2-perturbed relative motion of Lorentz spacecraft are also developed via inclusion of the Lorentz acceleration into equations of spacecraft relative motion, which lead to the approximate analytical solutions for the orbital motion of Lorentz spacecraft with respect to near-circular inclined reference orbit. Compared with present relative motion models, these models are more accordant with the property of the Earth’s magnetic field, thus, presenting enhanced accuracy.Further, relative state estimation algorithms for Lorentz spacecraft are proposed. Using the information from line-of-sight observations and gyro measurements, coupled with the proposed relative motion model, both extended Kalman filter(EKF) and unscented Kalman filter(UKF) are designed to perform Lorentz spacecraft relative navigation. Comparisons between these two filters indicate that UKF presents more precise relative state estimation than EKF due to the increased nonlinearity of relative dynamics with incorporation of Lorentz force.Finally, dynamics and control of spacecraft hovering, rendezvous, and formation flying using the geomagnetic Lorentz force are investigated.1. Lorentz-augmented Spacecraft HoveringThe feasibility of using the geomagnetic Lorentz force as an auxiliary means of propulsion for spacecraft hovering is investigated. A nonlinear dynamical model for Lorentz-augmented hovering is first derived to analyze the required open-loop control acceleration for hovering. Based on this dynamical model, the hovering configurations that could achieve propellantless hovering and the corresponding required specific charge of a Lorentz spacecraft are presented. For other configurations, optimal open-loop control laws that minimize the control energy consumption are designed. Likewise, the optimal trajectories of required specific charge and control acceleration are both presented. The effect of orbital inclination on the expenditure of control energy is also analyzed. Further, a closed-loop control approach is developed for propellantless hovering. Numerical results prove the validity of proposed control methods. Typically, hovering radially several kilometers above a target in low Earth orbit(LEO) requires specific charges on the order of 0.1 C/kg. Meanwhile, the effect of J2 perturbations on Lorentz-augmented spacecraft hovering is also analyzed.2. Lorentz-propelled Spacecraft RendezvousThe constraints on present Lorentz-propelled rendezvous scheme obtained from a linearized dynamical model is first analyzed. Then, a close-loop linear quadratic regulator(LQR) is designed for such rendezvous strategy. Based on the proposed nonlinear dynamical model of relative motion, the Lorentz-propelled rendezvous problem is then formulated as a constrained trajectory optimization problem. Using Gauss pseudospectral method(GPM) to transcribe this trajectory optimization problem into a nonlinear programming problem(NLP), the resulted NLP is then solved by corresponding numerical optimization approaches. Numerical simulation results prove the validity and applicability of GPM in solving optimal Lorentz-propelled rendezvous problem, and indicate that rendezvous can be achieved at both fixed and free final time. Meanwhile, the influence of J2 perturbations on Lorentz-propelled rendezvous is also analyzed.3. Lorentz-propelled Spacecraft Formation FlyingBased on the dynamical model for the orbital motion of Lorentz spacecraft with respect to near-circular reference orbit, this dissertation investigates the feasibility of spacecraft formation establishment and reconfiguration propelled by the geomagnetic Lorentz force only. Likewise, this trajectory optimization problem is transcribed and discretized into NLP via GPM. Further, the final constraints are divided into two categories, fixed and free final constraints. The terminal relative states are set as priori determined fixed points for the first kind of final constraints. However, in the free final constraints, the final states are treated as variables in the optimization and it is only required that the final states satisfy the desired final geometry configuration constraints. Energy-optimal trajectories for Lorentz-propelled spacecraft formation establishment and reconfiguration with both kinds of final constraints are then derived using GPM, and comparisons are then made between these two kinds of results.To sum up, this dissertation studies the orbital dynamics of Lorentz spacecraft and its applications to space missions. Based on the proposed dynamical models of absolute and relative orbital motion, relative navigation algorithms for Lorentz spacecraft are designed to perform relative state estimation and control schemes are designed for the Lorentz-augmented space missions, which hold reference value for future propellantless space missions design.