Minimizing cost reveals natural underactuation in fully actuated drones
Emergent Underactuation in Fully Actuated Multirotors by Minimizing a Homogeneous Allocation Cost
Robotics
Summary
Flying drones can control both their position and orientation if they have enough motors. However, this paper shows that when only position is important, choosing minimal effort naturally makes the drone behave as if it had fewer controls, restricting its movement in certain ways. This explains why even fully powered drones often move like simpler ones in normal flight but still use their full capabilities to handle disturbances or quick changes. The authors mathematically analyze how minimizing certain cost functions leads to this behavior.
What this means in practice
- •For drone control engineers: Design control algorithms that exploit natural underactuated-like motions in fully actuated drones to improve efficiency during position-only flight.
- •For robotics system designers: Develop multirotor platforms that use full actuation primarily for disturbance handling and transient maneuvers while minimizing energy during normal position tracking.
Authors
Antonio Franchi, Barbara Bazzana
Abstract
Full actuation is commonly valued for independent position and attitude tracking. This work establishes a complementary principle: when only a position trajectory is prescribed, minimizing a positively homogeneous allocation cost selects underactuated-like behavior on a fully actuated multirotor. This cost class includes norms and power laws, including standard minimum-norm pseudoinverse allocation. We use fiberwise infimization to transport the actuator-output cost to wrench space, yielding a homogeneous infimal allocation cost. Restriction to unit zero-moment forces defines a directional landscape whose minimizing directions are independent of force magnitude. We show that aligning any fixed minimizing direction with the required world-frame force minimizes instantaneous and integrated zero-moment allocation costs. The resulting body force remains in a fixed one-dimensional subspace without transverse components. We derive an exact optimality-gap decomposition quantifying the additional cost of every other attitude trajectory and characterizing the minimum-cost class. When a disturbance or prescribed-motion change modifies the required-force direction, a fully actuated platform can immediately generate the modified force using transverse authority and reorient toward the new minimum-cost family. A structurally underactuated platform must reorient before generating that force. Thus, homogeneous allocation-cost minimization explains why optimal nominal motion can be underactuated-like, while full actuation remains valuable for disturbance rejection and transient force generation.