Emergent Underactuation in Fully Actuated Multirotors by Minimizing a Homogeneous Allocation Cost

TL;DR

Minimizing a homogeneous allocation cost on a fully actuated multirotor leads to underactuated-like behavior in position tracking, where the body force stays within a fixed 1D subspace. This optimal behavior emerges naturally without structural underactuation and enables efficient force generation. The method provides a precise characterization of cost-optimality gaps and explains how full actuation supports rapid disturbance response.

Why It Matters

This work reveals that full actuation can achieve underactuated-like efficiency in nominal motion, improving energy efficiency and trajectory planning. It also clarifies the advantage of full actuation in transient response and disturbance rejection, guiding better control design for multirotor systems.

Key Findings

• Minimizing a positively homogeneous allocation cost results in a fixed one-dimensional force subspace, mimicking underactuated behavior despite full actuation.
• The optimal force direction is independent of magnitude and can be determined via a directional landscape in wrench space.
• Full actuation enables immediate force adaptation to changes in required direction, unlike structurally underactuated systems that require reorientation first.