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

A domain wall between single-mode and bimodal states and its transition to dynamical behavior in inhomogeneous systems

We consider domain walls (DW's) between single-mode and bimodal states that occur in coupled nonlinear diffusion (NLD), real Ginzburg-Landau (RGL), and complex Ginzburg-Landau (CGL) equations with a spatially dependent coupling coefficient. Group-velocity terms are added to the NLD and RGL equations, which breaks the variational structure of these models. In the simplest case of two coupled NLD equations, we reduce the description of stationary configurations to a single second-order ordinary differential equation. We demonstrate analytically that a necessary condition for existence of a stationary DW is that the group-velocity must be below a certain threshold value. Above this threshold, dynamical behavior sets in, which we consider in detail. In the CGL equations, the DW may generate spatio-temporal chaos, depending on the nonlinear dispersion.Comment: 16 pages (latex) including 11 figures; accepted for publication in Physica

Nonlocal feedback in nonlinear systems

A shifted or misaligned feedback loop gives rise to a two-point nonlocality that is the spatial analog of a temporal delay. Important consequences of this nonlocal coupling have been found both in diffusive and in diffractive systems, and include convective instabilities, independent tuning of phase and group velocities, as well as amplification, chirping and even splitting of localized perturbations. Analytical predictions about these nonlocal systems as well as their spatio-temporal dynamics are discussed in one and two transverse dimensions and in presence of noise.Comment: 13 pages, to be published in EPJ