Mars exploration is currently in the focus of scientific community interests. The attempts for efficient exploration will probably include the unmanned aerial vehicle in the near future to explore ...the places inaccessible by rovers. Since the Mars atmospheric conditions render the conventional rotary and fixed wing aerial vehicles inefficient, the insect-type flapping concept emerged as a promising solution. This is due to the fact that insects on Earth fly efficiently at the same values of Reynolds number that the aerial vehicle for Mars exploration would exhibit. The paper proposes the novel design optimization algorithm for development of insect-type aerial vehicle capable of flight in Martian atmosphere. The optimization procedure utilizes the novel flapping pattern optimization based on a quasi-steady aerodynamic model, combined with the discrete mechanics and optimal control framework. A test case of a flapping vehicle with fruit fly-like wings, performing a standstill hovering on Mars, is analyzed in detail. The fruit fly wing is scaled with a wide range of uniform scaling factors and optimized for hovering on Mars in the conditions of bioinspired Reynolds number range. Apart from the single optimal combination for the standstill hovering with fruit fly-like wings, the algorithm also found different efficient flapping patterns for a wide range of scaling factors, providing directions for design of flapping aerial vehicles for Mars.
Outstanding aerial capabilities that insects present in nature inspire researchers to undertake a challenge to develop a flapping aerial vehicle with performances unmatched by any manmade object. ...However, the complex aerodynamic phenomena crucial for the insect flight are not easily understood, let alone modeled and utilized for flight. The researchers managed to develop a quasi-steady aerodynamic model capable of capturing the most important aspects of a fruit fly-like insect flight, while still being efficient enough to allow for the usage in the flapping mechanism optimization loop. This experimentally justified quasi-steady model is used in the paper as a building block for creating a novel optimization algorithm, based on the discrete mechanics and optimal control framework. When compared to the conventional approaches to design optimization, this framework includes the natural description of the energy cost function, while incorporating the physical laws in the form of a discrete Lagrange–d’ Alembert equations inherently in optimization constraints. This leads to the discrete description of the inherently continuous problem, allowing the algorithm to search for the optimal solutions in the whole domain. In other words, in contrast to the conventional approaches involving the assumption on the function family and subsequent optimization on the parameters of that function type, this approach is not constrained by the user input and is capable of yielding any solution that respects the physical laws. As presented by the numerical test cases, optimizing the flapping patterns of a fruit fly-like aerial vehicle in standstill hovering leads to both effective and robust optimization tool.
Three recently approved space missions are headed towards Venus, to help answer major questions about Venus atmosphere and geology. However, many existing questions cannot be properly addressed ...without direct in situ measurements from Venus surface or within the atmosphere. To this end, flapping wing vehicle concept is selected, optimized for Venus atmospheric flight, and evaluated using energy efficiency as performance criteria. Flapping wing vehicle computational model is derived based on discrete variational mechanics and quasi-steady aerodynamics, with all relevant aerodynamic phenomena included. Flapping wing vehicle computational model is then embedded within optimization algorithm, which is utilized to obtain energy efficient flapping patterns for forward flight in Venus surface atmospheric conditions. Numerical optimization is performed for different neutrally buoyant configurations, with wingspan ranging from 10 mm to 1 m. Different forward velocities are used as well, where maximum velocity is limited by an advance ratio of 0.5. Bumblebee and hummingbird-sized vehicles, with a wingspan of 30 mm and 30 cm, are selected as the most representative test cases and thoroughly studied. It is proved that flapping wing propulsion is a feasible and effective concept for Venus exploration purposes. Finally, based on a comparison of the selected test cases, general conclusions are drawn on the flapping wing dynamics and flight mechanics in the Venus atmosphere. Significant difference in the propulsion mechanism has been observed, based on the aerial vehicle size. In order to maximize propulsive efficiency, the smaller vehicle mostly exploited aerodynamic forces related to the leading edge vortex, while the larger vehicle relied more on added mass and rotational forces.
•Flapping wing vehicles can be used for Venus atmospheric flight and exploration.•Quasi-steady forward flight model can be used to model Venus flapping flight.•Flapping wing dynamics can be efficiently optimized using DMOC framework.•Added mass and rotational forces have strong impact on Venus flapping flight.
Unit quaternion representation is widely used in flight simulation to overcome the limitations of the standard numerical ordinary-differential-equations (ODEs) based on three-parameters rotation ...variables (such as Euler angels), as they may impose kinematic singularities during aircraft's attitude reconstruction. However, these benefits do not come without a price, since the classical way of integrating rotational quaternions includes solving of differential-algebraic equations (DAEs) that requires post-integration numerical stabilization of the additional algebraic constraint enforcing the quaternion unitary norm. This can pose a problem in the case of longer flight simulations since improper numerical treatment of the quaternion-normalization constraint may induce numerical drift into the simulation results. As a remedy, the proposed novel algorithm circumvents DAE problem of quaternion integration by shifting update-integration-process from configuration manifold to the local tangential level of the incremental rotations (reducing thus integration to standard three ODEs problem at tangential Lie algebra level). This can be done due to the isomorphism of the Lie algebras of the rotational SO(3) group and the configuration manifold unit quaternion Sp(1) group. Besides avoiding DAE formulation by reducing integration process to standard three ODEs problem, the proposed algorithm also exhibits numerical advantages as it is discussed in the presented example.
Insect flight research is propelled by their unmatched flight capabilities. However, complex underlying aerodynamic phenomena make computational modeling of insect-type flapping flight a challenging ...task, limiting our ability in understanding insect flight and producing aerial vehicles exploiting same aerodynamic phenomena. To this end, novel mid-fidelity approach to modeling insect-type flapping vehicles is proposed. The approach is computationally efficient enough to be used within optimal design and optimal control loops, while not requiring experimental data for fitting model parameters, as opposed to widely used quasi-steady aerodynamic models. The proposed algorithm is based on Helmholtz–Hodge decomposition of fluid velocity into curl-free and divergence-free parts. Curl-free flow is used to accurately model added inertia effects (in almost exact manner), while expressing system dynamics by using wing variables only, after employing symplectic reduction of the coupled wing-fluid system at zero level of vorticity (thus reducing out fluid variables in the process). To this end, all terms in the coupled body-fluid system equations of motion are taken into account, including often neglected terms related to the changing nature of the added inertia matrix (opposed to the constant nature of rigid body mass and inertia matrix). On the other hand—in order to model flapping wing system vorticity effects—divergence-free part of the flow is modeled by a wake of point vortices shed from both leading (characteristic for insect flight) and trailing wing edges. The approach is evaluated for a numerical case involving fruit fly hovering, while quasi-steady aerodynamic model is used as benchmark tool with experimentally validated parameters for the selected test case. The results indicate that the proposed approach is capable of mid-fidelity accurate calculation of aerodynamic loads on the insect-type flapping wings.
