Planning natural repointing manoeuvres for nano-spacecraft

In this paper the natural dynamics of a rigid body are exploited to plan attitude manoeuvres for a small spacecraft. By utilising the analytical solutions of the angular velocities and making use of Lax pair integration, the time evolution of the attitude of the spacecraft in a convenient quaternion form is derived. This enables repointing manoeuvres to be generated by optimising the free parameters of the analytical expressions, the initial angular velocities of the spacecraft, to match prescribed boundary conditions on the final attitude of the spacecraft. This produces reference motions which can be tracked using a simple proportional-derivative controller. The natural motions are compared in simulation to a conventional quaternion feedback controller and found to require lower accumulated torque. A simple obstacle avoidance algorithm, exploiting the analytic form of natural motions, is also described and implemented in simulation. The computational efficiency of the motion planning method is discussed

Planning natural repointing manoeuvres for nano-spacecraft

In this paper the natural dynamics of a rigid body are exploited to plan attitude manoeuvres for a small spacecraft. By utilising the analytical solutions of the angular velocities and making use of Lax pair integration, the time evolution of the attitude of the spacecraft in a convenient quaternion form is derived. This enables repointing manoeuvres to be generated by optimising the free parameters of the analytical expressions, the initial angular velocities of the spacecraft, to match prescribed boundary conditions on the final attitude of the spacecraft. This produces reference motions which can be tracked using a simple proportional-derivative controller. The natural motions are compared in simulation to a conventional quaternion feedback controller and found to require lower accumulated torque. A simple obstacle avoidance algorithm, exploiting the analytic form of natural motions, is also described and implemented in simulation. The computational efficiency of the motion planning method is discussed

Computationally light attitude controls for resource limited nano-spacecraft

Nano-spacecraft have emerged as practical alternatives to large conventional spacecraft for specific missions (e.g. as technology demonstrators) due to their low cost and short time to launch. However these spacecraft have a number of limitations compared to larger spacecraft: a tendency to tumble post-launch; lower computational power in relation to larger satellites and limited propulsion systems due to small payload capacity. As a result new methodologies for attitude control are required to meet the challenges associated with nano-spacecraft. This paper presents two novel attitude control methods to tackle two phases of a mission using zero-propellant (i) the detumbling post-launch and (ii) the repointing of nano-spacecraft. The first method consists of a time-delayed feedback control law which is applied to a magnetically actuated spacecraft and used for autonomous detumbling. The second uses geometric mechanics to construct zero propellant reference manoeuvres which are then tracked using quaternion feedback control. The problem of detumbling a magnetically actuated spacecraft in the first phase of a mission is conventionally tackled using BDOT control. This involves applying controls which are proportional to the rate of change of the magnetic field. However, real systems contain sensor noise which can lead to discontinuities in the signal and problems with computing the numerical derivative. This means that a noise filter must be used and this increases the computational overhead of the system. It is shown that a timedelayed feedback control law is advantageous as the use of a delayed signal rather than a derivative negates the need for such a filter, thus reducing computational overhead. The second phase of the mission is the repointing of the spacecraft to a desired target. Exploiting the analytic solutions of the angular velocities of a symmetric spacecraft and further using Lax pair integration it is possible to derive exact equations of the natural motions including the time evolution of the quaternions. It is shown that parametric optimisation of these solutions can be used to generate low torque reference motions that match prescribed boundary conditions on the initial and final configurations. Through numerical simulation it is shown that these references can be tracked using nanospacecraft reaction wheels while eigenaxis rotations, used for comparison, are more torque intensive. As the method requires parameter optimisation as opposed to optimisation methods that require numerical integration, the computational effort is reduced

Planar tilting maneuver of a spacecraft: singular arcs in the minimum time problem and chattering

In this paper, we study the minimum time planar tilting maneuver of a spacecraft, from the theoretical as well as from the numerical point of view, with a particular focus on the chattering phenomenon. We prove that there exist optimal chattering arcs when a singular junction occurs. Our study is based on the Pontryagin Maximum Principle and on results by M.I. Zelikin and V.F. Borisov. We give sufficient conditions on the initial values under which the optimal solutions do not contain any singular arc, and are bang-bang with a finite number of switchings. Moreover, we implement sub-optimal strategies by replacing the chattering control with a fixed number of piecewise constant controls. Numerical simulations illustrate our results.Comment: 43 pages, 18 figure

Applied Reachability Analysis for Time-Optimal Spacecraft Attitude Reorientations

Satellite attitude reorientation has been of significant interest in astronautical engineering, and being able to reorient in a time-optimal manner has been of exceeding interest since the 1970s. Ensuring a spacecraft mission set can be conducted within a certain amount of time begs the question of whether or not a certain maneuver can be completed with a bounded control. This thesis answers that question by using the concept of reachability to provide reachable sets for different spacecraft reorientation scenarios. The reachable sets generated provide a range of initial states that guarantee a satellite reach a desired end orientation given a certain time constraint. Prior research providing a formal approach of applying reachability to spacecraft attitude maneuvers has not been found. It was found that using Modified Rodriguez Parameters (MRPs) to generate reachable sets is more efficient than other attitude parameterizations. It was also found that the linearized MRP dynamics provide a valid time optimal solution for the true, nonlinear dynamics of medium angle attitude maneuvers. This linearized version of the dynamics was used to formulate an optimal control policy for spacecraft reorientations with bounded controls

Near Real-Time Closed-Loop Optimal Control Feedback for Spacecraft Attitude Maneuvers

Optimization of spacecraft attitude maneuvers can significantly reduce attitude control system size and mass, and extend satellite end-of-life. Optimal control theory has been applied to solve a variety of open-loop optimal control problems for terrestrial, air, and space applications. However, general application of real-time optimal controllers on spacecraft for large slew maneuvers has been limited because open-loop control systems are inherently vulnerable to error and the computation necessary to solve for an optimized control solution is resource intensive. This research effort is focused on developing a near real-time optimal control (RTOC) system for spacecraft attitude maneuvers on the Air Force Institute of Technology\u27s 2nd generation simulated satellite, SimSat II. To meet the end goal of developing a RTOC controller, necessary preliminary steps were completed to accurately characterize SimSAT II\u27s mass properties and attitude control system. Using DIDO, a pseudospectral-based optimal control solver package, to continuously solve and execute a sequence of optimized open-loop control solutions in near real-time, the RTOC controller can optimally control the state of the satellite over the course of a large angle slew maneuver. In this research, simulation and experimental results clearly demonstrate the benefit of RTOC versus other non-optimal control methods for the same maneuver

Control of large flexible spacecraft by the independent modal-space control method

The problem of control of a large-order flexible structure in the form of a plate-like lattice by the Independent Modal-Space Control (IMSC) method is presented. The equations of motion are first transformed to the modal space, thus obtaining internal (plant) decoupling of the system. Then, the control laws are designed in the modal space for each mode separately, so that the modal equations of motion are rendered externally (controller) decoupled. This complete decoupling applies both to rigid-body modes and elastic modes. The application of linear optimal control, in conjunction with a quadratic performance index, is first reviewed. A solution for high-order systems is proposed here by the IMSC method, whereby the problem is reduced to a number of modal minimum-fuel problems for the controlled modes

Numerical Analysis of Constrained, Time-Optimal Satellite Reorientation

Previous work on time-optimal satellite slewing maneuvers, with one satellite axis (sensor axis) required to obey multiple path constraints (exclusion from keep-out cones centered on high-intensity astronomical sources) reveals complex motions with no part of the trajectory touching the constraint boundaries (boundary points) or lying along a finite arc of the constraint boundary (boundary arcs). This paper examines four cases in which the sensor axis is either forced to follow a boundary arc, or has initial and final directions that lie on the constraint boundary. Numerical solutions, generated via a Legendre pseudospectral method, show that the forced boundary arcs are suboptimal. Precession created by the control torques, moving the sensor axis away from the constraint boundary, results in faster slewing maneuvers. A two-stage process is proposed for generating optimal solutions in less time, an important consideration for eventual onboard implementation

Study of conceptual deep space monitor communications systems using a single earth satellite. Volume III - Appendix Final report

Condensed technical survey for deep space monitor communications system using earth satellit

Some operational aspects of a rotating advanced-technology space station for the year 2025

The study of an Advanced Technology Space Station which would utilize the capabilities of subsystems projected for the time frame of the years 2000 to 2025 is discussed. The study includes tradeoffs of nuclear versus solar dynamic power systems that produce power outputs of 2.5 megawatts and analyses of the dynamics of the spacecraft of which portions are rotated for artificial gravity. The design considerations for the support of a manned Mars mission from low Earth orbit are addressed. The studies extend to on-board manufacturing, internal gas composition effects, and locomotion and material transfer under artificial gravity forces. The report concludes with an assessment of technology requirements for the Advanced Technology Space Station