6-DOF Control

6-DOF Control (Six Degrees of Freedom) refers to the control of a rigid body’s position and orientation in 3D space. The six degrees are:

• 3 translational: X, Y, Z (forward/back, left/right, up/down)
• 3 rotational: Roll, Pitch, Yaw (rotation about X, Y, Z axes)

In Aerospace

A spacecraft or aircraft with 6-DOF can control its complete state in space. Most vehicles are underactuated (fewer actuators than DOF) or overactuated (more actuators than DOF).

In AEGIS

AEGIS maps a desired 6-DOF wrench (3 forces + 3 torques) to engine throttles and gimbal angles:

wrench = [Fx, Fy, Fz, τx, τy, τz]

Control Allocation Problem

Given a desired wrench τ_desired, find actuator commands u such that:

τ_desired = B * u

Where B is the control effectiveness matrix. When B is not square ( fewer actuators than DOF), a pseudo-inverse is used:

u = pinv(B) * τ_desired

Reference Frames

Frame	Description	Axes
Body	Fixed to vehicle	X-forward, Y-right, Z-down
Inertial	Fixed to planet	ECEF coordinates
NED	Local tangent plane	X-north, Y-east, Z-down

Related Concepts

• Control Allocation — Mapping wrench to actuators
• Pseudo-inverse — Mathematical tool for overdetermined systems
• Quaternion — Attitude representation
• Rigid Body Dynamics — Physics of 6-DOF motion
• Fault Detection and Isolation — Handling actuator failures

Sources

• AEGIS Project (src/guidance/allocator.py)