Control Allocation

Control Allocation is the process of distributing a desired total control effort (wrenches like forces and torques) across a set of redundant actuators. It is a fundamental problem in over-actuated systems like spacecraft, aircraft with multiple control surfaces, and underwater vehicles.

The Problem

Given a desired 6-DOF wrench (3 forces + 3 torques), how do you map this to individual actuator commands (throttle, deflection angles, etc.) when there are more actuators than degrees of freedom?

AEGIS Application

In AEGIS, the Control Allocator maps a desired 6-DOF wrench to engine throttles and gimbal angles. The system uses a pseudo-inverse approach:

u = pinv(B) * τ_desired

Where:

• B is the control effectiveness matrix (maps actuator commands to wrench)
• τ_desired is the desired 6-DOF wrench
• u is the actuator command vector (throttles and gimbal angles)

Fault-Tolerant Allocation

When engines fail, the allocator dynamically remaps by:

1. Detecting failed engines (via FDI)
2. Recomputing the pseudo-inverse with only surviving engines
3. Automatically throttling down engines opposite the failure to cancel torque _awhile throttling up adjacent engines to maintain vertical thrust

Numerical Safety

• Condition number check: If cond(B) > 1e4, raises AllocationDegenerateError
• Rank deficiency check: If rank(B) < 6, raises AllocationDegenerateError

Related Concepts

• Pseudo-inverse — The mathematical tool used for allocation
• Fault Detection and Isolation — Detects which engines have failed
• 6-DOF Control — Six degrees of freedom (position + attitude)
• Redundancy Management — Handling over-actuated systems
• Constrained Optimization — Alternative allocation methods using optimization

Sources

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