Muscle Coactivation in the Sky: Geometry and Pareto Optimality of Energy vs. Aerodynamic Promptness and Multirotors as Variable Stiffness Actuators
For multirotor designers and control engineers, this provides a principled geometric framework to navigate the energy-agility trade-off, replacing heuristic methods.
This paper formalizes the trade-off between energy consumption and aerodynamic promptness in multirotors, showing that cooperative actuation yields bounded Pareto fronts while antagonistic actuation enables unbounded fibers for extreme agility at the cost of endurance. It establishes an isomorphism between aerodynamic co-contraction and variable stiffness actuators, introducing a 'flying muscle' paradigm.
In robotics and biomechanics, trading metabolic cost for kinematic readiness is a well-established principle. This paper formalizes this concept for aerial multirotors through the introduction of aerodynamic promptness -- a dynamic metric analogous to dynamic manipulability in robotics. By formulating redundancy resolution as a geometric multi-objective optimization along task fibers, we rigorously characterize the topological trade-off between energy consumption and promptness. We demonstrate that this interplay is fundamentally governed by fiber geometry. Cooperative actuation regime yields compact fibers with bounded, compatible Pareto fronts. Conversely, antagonistic actuation regime unlocks unbounded fibers, enabling aerodynamic co-contraction that drives promptness to hardware limits at the expense of flight endurance. We establish a structural isomorphism between aerodynamic co-contraction and biologically inspired variable stiffness actuators, introducing a dynamic ``flying muscle'' paradigm. Ultimately, this framework transitions multirotor allocation from heuristic energy minimization to principled, geometry-aware Pareto navigation, laying foundational theory for the design and control of highly agile aerial platforms.