How a CubeSat points: magnetorquers and reaction wheels.

What attitude control has to do

After release from the launcher, a CubeSat tumbles. The attitude determination and control system (ADCS) first stops that spin, called detumbling. Then it points the spacecraft: solar panels at the Sun, antennas at a ground station, a camera at its target.

Between those jobs it holds attitude against small, steady disturbances. In low Earth orbit around 500 km, thin-air drag usually gives the largest disturbance torque on a CubeSat, followed by the spacecraft's own residual magnetism. Solar pressure and gravity gradient are smaller.

Magnetorquers: a coil that pushes on the Earth's field

A current loop is a magnet. Its magnetic moment is turns × current × enclosed area, and in the Earth's field it feels a torque τ = m × B. A magnetorquer is simply a coil driven so that this torque turns the spacecraft the way you want.

The cross product carries the catch: there is never any torque about the direction of the local field. At any instant one axis cannot be controlled. In a near-polar orbit the field direction swings round about twice per orbit, so every axis becomes controllable over time, but too slowly for fine pointing. Magnetorquers alone give coarse pointing.

Rods with a soft-iron core give the most dipole per watt. Flat air-core coils, including coils etched into a circuit board, give less, but leave no residual magnetism when switched off. For a given footprint the dipole grows with the square root of power times copper volume, so doubling the power buys only about 41% more dipole, while heavier copper and more layers help directly.

Detumbling with the B-dot law

The classic detumble law, B-dot, drives the coils against the measured rate of change of the magnetic field, or equivalently against the spin rate crossed with the field. The spacecraft's rotational energy can only fall.

Only the part of the spin perpendicular to the field is damped, though. With too much gain the controller removes that part almost at once and then drags the remaining spin axis along with the slowly turning field, and detumbling stalls. Matching the gain to the orbit rate and the field's inclination (Avanzini and Giulietti, 2012) gives a steady decay, typically within an orbit or so.

Reaction wheels: moving momentum inside the spacecraft

Spin a wheel up one way and the body turns the other way. The exchange is internal, so a set of three wheels can torque any axis at any instant. Three-axis pointing for imaging depends on that.

Wheels cannot remove momentum from the spacecraft. Every external disturbance adds to the total, so the wheels creep towards their speed limit. For a small satellite the wheels are sized mostly by that storage margin. Slew speed is rarely the limit.

Momentum dumping: coils and wheels together

The magnetorquers apply a small external torque that opposes the momentum stored in the wheels. The attitude loop holds the body still against it, which slows the wheels, and the momentum leaves through the Earth's field.

Dumping only has to keep pace with the disturbances, so it needs far less dipole than pointing with coils alone. That is why wheels and flat PCB coils make a good pair: the wheels do the fast, precise work, and the coils do the slow bookkeeping.

Wheels and image jitter

A wheel with a small static imbalance shakes the spacecraft at the wheel's rotation frequency. The force grows with the square of speed, but so does the body's resistance at that frequency, so the jitter amplitude comes out independent of speed. It is set by the imbalance, the lever arm and the spacecraft's inertia, which makes wheel balancing a direct lever on image sharpness.

Magnetic cleanliness

The magnetometer that detumbling and dumping rely on also hears every magnet on board: wheel rotor magnets, energised coils and current loops in the solar-cell strings. A magnet's field falls off with the cube of distance, so doubling the distance to the magnetometer cuts the error eightfold. Coil torquing and magnetometer sampling are usually taken in turns so the sensor reads a clean field.

What we are building

Our 3U design uses three reaction wheels and three magnetorquers. Our 1U uses magnetorquers only, and we are studying magnetorquer coils built into the body-panel circuit boards plus small reaction wheels on flat PCB motors, which would give a 1U full three-axis control. Attitude knowledge comes from our star camera.