Muscle Coactivation in the Sky: Geometry and Pareto Optimality of Energy vs. Promptness in Multirotors

2026-02-15

AI Summary

This study investigates the fundamental trade-off between energy efficiency and dynamic promptness in multirotor aerial vehicles. By introducing the notion of promptness and formulating a fiber bundle–based geometric framework, the authors model redundant control allocation as a multi-objective optimization problem, revealing an inherent incompatibility between these two objectives under hardware constraints. The approach integrates a diffeomorphism-linearized thrust model with Pareto front analysis on the fiber bundle, validated through experiments on a six-rotor platform with four degrees of freedom. Key findings show that reversible propellers can approximate the hardware-imposed promptness limit via rotor co-activation but intensify the conflict between energy consumption and agility, whereas irreversible systems exhibit a more compact feasible region and a symmetry-broken Pareto-optimal structure.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: Multi-Robot Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

In robotics and human biomechanics, the tension between energy economy and kinematic readiness is well recognized; this work brings that fundamental principle to aerial multirotors. We show that the limited torque of the motors and the nonlinear aerodynamic map from rotor speed to thrust naturally give rise to the novel concept of promptness-a metric akin to dynamic aerodynamic manipulability. By treating energy consumption as a competing objective and introducing a geometric fiber-bundle formulation, we turn redundancy resolution into a principled multi-objective program on affine fibers. The use of the diffeomorphic transformation linearizing the signed-quadratic propulsion model allows us to lay the foundations for a rigorous study of the interplay between these costs. Through an illustrative case study on 4-DoF allocation on the hexarotor, we reveal that this interplay is fiber-dependent and physically shaped by hardware inequalities. For unidirectional thrusters, the feasible fibers are compact, yielding interior allocations and a short Pareto arc, while torque demands break symmetry and separate the optima. Conversely, with reversible propellers, the null space enables antagonistic rotor co-contraction that drives promptness to hardware limits, making optimal endurance and agility fundamentally incompatible in those regimes. Ultimately, rather than relying on heuristic tuning or black box algorithms to empirically improve task execution, this framework provides a foundational understanding of why and how to achieve agility through geometry-aware control allocation, offering possible guidance for vehicle design, certification metrics, and threat-aware flight operation.

Problem

• energy-efficiency
• promptness
• multirotor
• Pareto optimality
• muscle coactivation

Innovation

• Pareto optimality
• muscle coactivation
• fiber bundle
• promptness
• geometric control allocation