# Drag-Aware Aerodynamic Manipulability for Torque-Limited Redundant Multirotors: Aerodynamic Promptness based on the Symmetric Acceleration Capacity

arXiv: https://arxiv.org/abs/2603.07998 · HTML: https://mlsanity.com/paper/2603.07998/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 32 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Builds on (most cited first, 6 of 6)

- [A Comparative Study of Nonlinear MPC and Differential-Flatness-Based Control for Quadrotor Agile Flight](https://mlsanity.com/paper/2109.01365/) (2021)
- [Time-Optimal Planning for Quadrotor Waypoint Flight](https://mlsanity.com/paper/2108.04537/) (2021)
- [Performance, Precision, and Payloads: Adaptive Nonlinear MPC for Quadrotors](https://mlsanity.com/paper/2109.04210/) (2021)
- [Downwash-aware Control Allocation for Over-actuated UAV Platforms](https://mlsanity.com/paper/2207.09645/) (2022)
- [Feasible Wrench Set Computation for Legged Robots](https://mlsanity.com/paper/2202.01628/) (2022)
- [Muscle Coactivation in the Sky: Geometry and Pareto Optimality of Energy vs. Aerodynamic Promptness and Multirotors as Variable Stiffness Actuators](https://mlsanity.com/paper/2602.14222/) (2026)

## Abstract (arXiv)

Aerodynamic promptness quantifies how rotor-speed variations generate multirotor wrench variations, but its Euclidean formulation assigns the same local cost to a given rotor acceleration at every operating speed. This work develops a capacity-aware extension for redundant multirotors with arbitrary numbers of heterogeneous rotors and wrench components. Under bounded motor torque and aerodynamic drag, each generally asymmetric instantaneous rotor-acceleration interval contains a largest zero-centered subset whose radius defines the symmetric acceleration capacity (SAC). The SAC induces a Riemannian metric on the positive-capacity rotor-speed region. Propagating its co-metric through the nonlinear rotor-speed-to-wrench differential yields a state-attached task-rate capability matrix and ellipsoid. The corresponding inverse quadratic form equals the minimum normalized rotor-acceleration effort required to realize a prescribed wrench rate, while the ellipsoid volume defines the drag-aware aerodynamic manipulability (DAAM) index. Fiberwise DAAM maximization provides a task-coordinate-invariant criterion for selecting task-equivalent actuator states; its maximizing set exists on compact regular domains and can be nonconvex and set valued. Low-dimensional two- and three-rotor studies make the resulting fiberwise geometry and parameter dependence directly visible. A complementary two-rotor use case shows how DAAM can inform a continuous allocation section subject to directional motor-torque feasibility. For two heterogeneous propulsion systems, the resulting sections reduce saturation-induced force-tracking degradation relative to the pseudoinverse in the faster command bands