Attitude determination and control (ADCS)

Definition

An attitude determination and control system (ADCS) measures where the body axes of a spacecraft point and drives them to the target the mission needs. The determination side turns sensor readings into an attitude estimate; the control side computes the torque that closes the gap between estimate and target and commands the actuators[1]. Pointing a camera or an antenna, turning arrays to the Sun and firing a thruster along the right axis all depend on this loop.

Classes of missions

The pointing requirement spans several orders of magnitude:

• Passive or detumbling only. Most amateur-radio and educational missions only need to slow the spin. Passive magnetic stabilization with a permanent magnet and hysteresis dampers belongs here.
• Coarse pointing (a few degrees). Magnetometer, cosine Sun sensors and magnetorquers point arrays at the Sun or an antenna at nadir.
• Fine pointing (below a degree). Reaction wheels, fine Sun sensors and star trackers serve Earth observation, optical communication and astronomy.

Integrated ADCS units in the NASA report declare pointing between 0.002° and 5°; a unit of this class flew on the 6U MarCO and ASTERIA missions[2].

The control loop

flowchart TB
  S["Sensors"] --> K["Attitude estimation"]
  K --> C["Control law"]
  C --> A["Actuators"]
  A --> D["Spacecraft dynamics"]
  B["Disturbance torques"] --> D
  D -->|"measurement"| S

After separation a spacecraft usually spins at a few to a few tens of degrees per second. The first job is to remove that spin (detumbling). The magnetic B-dot law reduces the rate with nothing more than a magnetometer and magnetorquers, without an attitude estimate[3].

Approaches flown on PocketQubes

ADCS is where the size, weight and power limits of PocketQubes bite hardest, and where off-the-shelf parts and published design data are scarcest[4]:

Sensors

The Sun sensor, gyroscope, star tracker and GPS rows are manufacturer figures from the summary table of the report, which also notes that low-cost star trackers only solve at rates up to about 0.3°/s[2].

Actuators

Magnetorquers can only produce torques perpendicular to the local field[2]. Reaction wheels give precise three-axis control, but the momentum that disturbance torques build up must be dumped regularly with magnetorquers or thrusters. At PocketQube scale a 7 g reaction wheel with 25 mW steady-state consumption has been developed at TU Delft[5].

Attitude determination

From two vector measurements, such as the magnetic field and the Sun direction, the attitude follows from deterministic methods like TRIAD or from the optimal solutions of Wahba’s problem, the q-method and QUEST. The multiplicative extended Kalman filter (MEKF) is the standard way to fuse noisy, intermittent vector measurements with gyroscope data[1].

B-dot detumbling

The B-dot law commands a magnetic dipole opposite to the rate of change of the field measured in the body frame:

The nadir lab. simulation of a 1U CubeSat and a 1P PocketQube from the same initial rate of about 9.6°/s at 500 km gives:

The derivation, the gain choice and the full time histories are in the B-dot article. Flight designs report similar orders of magnitude. Bouwmeester et al. recommend sizing PocketQube detumbling for initial rates of up to 180°/s and a target below 5°/s, the requirement adopted for Delfi-PQ[5]; POQUITO, with magnetorquers printed in the inner layers of its boards, detumbled from 20°/s within one orbit[6].

Inertia shrinks faster than torque

The principal moment of inertia of a homogeneous cube, $I=M{L}^2/6$, scales with the fifth power of size under geometric similarity. A PocketQube therefore has only 3–5% of the inertia of a 1U CubeSat[7]. Disturbance torques do not shrink as fast: the aerodynamic torque scales with the cube of size, so the angular acceleration it produces is about four times larger in a PocketQube, and the torque of a residual magnetic dipole does not depend on size at all.

Magnetic cleanliness

In a 50 mm cube every magnetic part sits close to the sensors and dampers: nickel underplating, Kovar leads, steel fasteners, battery cans and current loops all add to the residual dipole. The PocketQube Standard has no magnetic-cleanliness requirement, so non-magnetic fasteners and a measured residual dipole are advisable for any magnetic attitude design[7]. Permanent magnets can also disturb the other passengers of a deployer; the CubeSat Design Specification limits the field of a magnet outside the static envelope to 0.5 gauss above the Earth’s field[8].

Sensor and actuator interaction

Active magnetorquers corrupt the magnetometer reading while they run. The usual cure is to separate measurement and actuation in time: switch the coils off, measure the field, then apply the new dipole. With a permanent magnet the problem is permanent, as the PMAC entry shows.

Verification

Attitude software must be verified in simulation before flight and then with hardware (Helmholtz coils, air bearings, Sun simulators). A simple polarity test proving that every sensor and actuator axis has the right sign prevents the most common reason for a spacecraft that spins up instead of down.