Prospects of Relative Attitude Control Using Coulomb Actuation

Abstract

The relative attitude is studied between two charge controlled spacecraft being held at a fixed separation distance. While one body has a spherical shape, the 2nd body is assumed to be non-spherical and tumbling. The attitude control goal is to arrest the rotation of the 2nd body. While prior work has identified the existence of torques between charged bodies, this is the first analytical study on a charged feedback attitude control. Using the recently developed multi-sphere method to provide a simplified electrostatic force and torque model between non-spherical shapes, Lyapunov theory is used to develop a stabilizing attitude control using spacecraft potential as the control variable. Zero and non-zero equilibrium potentials are considered, with the later suitable for the electrostatic tug concept. With a pulling configuration, the cylinder will come to rest with the long axis aligned with the inter-vehicle axis in a stable configuration. For a pusher, the cylinder will settle 90 degrees rotated from this axis. Numerical simulations illustrate the control performance.

Prospects and challenges of touchless electrostatic detumbling of small bodies

“…Preliminary work has been performed considering 1-D constrained rotational motion and 3-D tumble, which are reviewed in this section. As shown in Schaub and Stevenson (2012), if the separation distance is larger than 2-3 craft radii, the potential and attitude influence on the electrostatic torque can be separated as shown in Eq. (4) where U represents the projection angle measure between the cylinder slender axis and the inter-spacecraft separation vector.…”

“…(4) can introduce errors that are less than 1%. Without loss of generality, it is assumed that the non-cooperative cylinder has the same potential magnitude, that is / 2 ¼ j/ 1 j, and is assumed to be always positive (Schaub and Stevenson, 2012). Thus, the voltage dependency function is set to:…”

“…The orientation angle dependency explored in Schaub and Stevenson (2012) presents Eq. (6) as the analytic representation.…”

“…A fixed separation distance is maintained using a continuous station keeping servo. The charging controller assumes the projection angle U and angle rate _ U are measured and the servicing spacecraft potential / 1 is the control variable as introduced in Schaub and Stevenson (2012). Generalized for 3-D rotation of a cylinder, the control law f ð/ 1 Þ is:…”

“…More recently, fast numerical electrostatic torque models were developed to explore applying electrostatic torques on a passive object (Stevenson and Schaub, 2013a,b;Schaub and Stevenson, 2012). Touchless electrostatic detumble, illustrated in Fig.…”