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In a multi-modal system which combines thruster and legged locomotion such our state-of-the-art Harpy platform to perform dynamic locomotion. Therefore, it is very important to have a proper estimate of Thruster force. Harpy is a bipedal robot capable of legged-aerial locomotion using its legs and thrusters attached to its main frame. we can characterize thruster force using a thrust stand but it generally does not account for working conditions such as battery voltage. In this study, we present a momentum-based thruster force estimator. One of the key information required to estimate is terrain information. we show estimation results with and without terrain knowledge. In this work, we derive a conjugate momentum thruster force estimator and implement it on a numerical simulator that uses thruster force to perform thruster-assisted walking., Comment: Submitted to ACC 2025. arXiv admin note: text overlap with arXiv:2411.12968

Our work aims to make significant strides in understanding unexplored locomotion control paradigms based on the integration of posture manipulation and thrust vectoring. These techniques are commonly seen in nature, such as Chukar birds using their wings to run on a nearly vertical wall. In this work, we show quadratic programming with contact constraints which is then given to the whole body controller to map on robot states to produce a thruster-assisted slope walking controller for our state-of-the-art Harpy platform. Harpy is a bipedal robot capable of legged-aerial locomotion using its legs and thrusters attached to its main frame. The optimization-based walking controller has been used for dynamic locomotion such as slope walking, but the addition of thrusters to perform inclined slope walking has not been extensively explored. In this work, we derive a thruster-assisted bipedal walking with the quadratic programming (QP) controller and implement it in simulation to study its performance., Comment: Submitted to ACC2025. arXiv admin note: text overlap with arXiv:2406.14799

Wing-assisted inclined running (WAIR) observed in some young birds, is an attractive maneuver that can be extended to legged aerial systems. This study proposes a control method using a modified Variable Length Inverted Pendulum (VLIP) by assuming a fixed zero moment point and thruster forces collocated at the center of mass of the pendulum. A QP MPC is used to find the optimal ground reaction forces and thruster forces to track a reference position and velocity trajectory. Simulation results of this VLIP model on a slope of 40 degrees is maintained and shows thruster forces that can be obtained through posture manipulation. The simulation also provides insight to how the combined efforts of the thrusters and the tractive forces from the legs make WAIR possible in thruster-assisted legged systems., Comment: 6 pages, 8 figures, submitted to the Humanoids 2025 conference

Legged-aerial multimodal robots can make the most of both legged and aerial systems. In this paper, we propose a control framework that bypasses heavy onboard computers by using an optimization-free Explicit Reference Governor that incorporates external thruster forces from an attitude controller. Ground reaction forces are maintained within friction cone constraints using costly optimization solvers, but the ERG framework filters applied velocity references that ensure no slippage at the foot end. We also propose a Conjugate momentum observer, that is widely used in Disturbance Observation to estimate ground reaction forces and compare its efficacy against a constrained model in estimating ground reaction forces in a reduced-order simulation of Husky., Comment: 6 pages, 10 figures, submitted to American Control Conference 2025

Despite major advancements in control design that are robust to unplanned disturbances, bipedal robots are still susceptible to falling over and struggle to negotiate rough terrains. By utilizing thrusters in our bipedal robot, we can perform additional posture manipulation and expand the modes of locomotion to enhance the robot's stability and ability to negotiate rough and difficult-to-navigate terrains. In this paper, we present our efforts in designing a controller based on capture point control for our thruster-assisted walking model named Harpy and explore its control design possibilities. While capture point control based on centroidal models for bipedal systems has been extensively studied, the incorporation of external forces that can influence the dynamics of linear inverted pendulum models, often used in capture point-based works, has not been explored before. The inclusion of these external forces can lead to interesting interpretations of locomotion, such as virtual buoyancy studied in aquatic-legged locomotion. This paper outlines the dynamical model of our robot, the capture point method we use to assist the upper body stabilization, and the simulation work done to show the controller's feasibility., Comment: Submitted and to be presented at IEEE AIM 2024. arXiv admin note: substantial text overlap with arXiv:2103.15952

In this study, our aim is to evaluate the effectiveness of thruster-assisted steep slope walking for the Husky Carbon, a quadrupedal robot equipped with custom-designed actuators and plural electric ducted fans, through simulation prior to conducting experimental trials. Thruster-assisted steep slope walking draws inspiration from wing-assisted incline running (WAIR) observed in birds, and intriguingly incorporates posture manipulation and thrust vectoring, a locomotion technique not previously explored in the animal kingdom. Our approach involves developing a reduced-order model of the Husky robot, followed by the application of an optimization-based controller utilizing collocation methods and dynamics interpolation to determine control actions. Through simulation testing, we demonstrate the feasibility of hardware implementation of our controller., Comment: 7 pages, 7 figures, submitted to CDC 2024 conference. arXiv admin note: text overlap with arXiv:2405.06070

This research concentrates on enhancing the navigational capabilities of Northeastern Universitys Husky, a multi-modal quadrupedal robot, that can integrate posture manipulation and thrust vectoring, to traverse through narrow pathways such as walking over pipes and slacklining. The Husky is outfitted with thrusters designed to stabilize its body during dynamic walking over these narrow paths. The project involves modeling the robot using the HROM (Husky Reduced Order Model) and developing an optimal control framework. This framework is based on polynomial approximation of the HROM and a collocation approach to derive optimal thruster commands necessary for achieving dynamic walking on narrow paths. The effectiveness of the modeling and control design approach is validated through simulations conducted using Matlab., Comment: arXiv admin note: text overlap with arXiv:2312.12586

To maintain full autonomy, autonomous robotic systems must have the ability to self-repair. Self-repairing via compensatory mechanisms appears in nature: for example, some fish can lose even 76% of their propulsive surface without loss of thrust by altering stroke mechanics. However, direct transference of these alterations from an organism to a robotic flapping propulsor may not be optimal due to irrelevant evolutionary pressures. We instead seek to determine what alterations to stroke mechanics are optimal for a damaged robotic system via artificial evolution. To determine whether natural and machine-learned optima differ, we employ a cyber-physical system using a Covariance Matrix Adaptation Evolutionary Strategy to seek the most efficient trajectory for a given force. We implement an online optimization with hardware-in-the-loop, performing experimental function evaluations with an actuated flexible flat plate. To recoup thrust production following partial amputation, the most efficient learned strategy was to increase amplitude, increase frequency, increase the amplitude of angle of attack, and phase shift the angle of attack by approximately 110 degrees. In fish, only an amplitude increase is reported by majority in the literature. To recoup side-force production, a more challenging optimization landscape is encountered. Nesting of optimal angle of attack traces is found in the resultant-based reference frame, but no clear trend in amplitude or frequency are exhibited -- in contrast to the increase in frequency reported in insect literature. These results suggest that how mechanical flapping propulsors most efficiently adjust to damage of a flapping propulsor may not align with natural swimmers and flyers.

Robot designs can take many inspirations from nature, where there are many examples of highly resilient and fault-tolerant locomotion strategies to navigate complex terrains by using multi-functional appendages. For example, Chukar and Hoatzin birds can repurpose their wings for quadrupedal walking and wing-assisted incline running (WAIR) to climb steep surfaces. We took inspiration from nature and designed a morphing robot with multi-functional thruster-wheel appendages that allows the robot to change its mode of locomotion by transforming into a rover, quad-rotor, mobile inverted pendulum (MIP), and other modes. In this work, we derive a dynamic model and formulate a nonlinear model predictive controller to perform WAIR to showcase the unique capabilities of our robot. We implemented the model and controller in a numerical simulation and experiments to show their feasibility and the capabilities of our transforming multi-modal robot.

Some animals exhibit multi-modal locomotion capability to traverse a wide range of terrains and environments, such as amphibians that can swim and walk or birds that can fly and walk. This capability is extremely beneficial for expanding the animal's habitat range and they can choose the most energy efficient mode of locomotion in a given environment. The robotic biomimicry of this multi-modal locomotion capability can be very challenging but offer the same advantages. However, the expanded range of locomotion also increases the complexity of performing localization and path planning. In this work, we present our morphing multi-modal robot, which is capable of ground and aerial locomotion, and the implementation of readily available SLAM and path planning solutions to navigate a complex indoor environment.

We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of approximating solution operators to systems of partial differential equations through data alone. The learned FNO solution operator can be evaluated in milliseconds, potentially enabling faster-than-real-time modeling for predictive flow control in physical systems. Here we use FNOs to predict how physical fluid flows evolve in time, training with particle image velocimetry measurements depicting cylinder wakes in the subcritical vortex shedding regime. We train separate FNOs at Reynolds numbers ranging from Re = 240 to Re = 3060 and study how increasingly turbulent flow phenomena impact prediction accuracy. We focus here on a short prediction horizon of ten non-dimensionalized time-steps, as would be relevant for problems of predictive flow control. We find that FNOs are capable of accurately predicting the evolution of experimental velocity fields throughout the range of Reynolds numbers tested (L2 norm error < 0.1) despite being provided with limited and imperfect flow observations. Given these results, we conclude that this method holds significant potential for real-time predictive flow control of physical systems., Comment: 12 pages, 6 figures

The feasibility of performing airborne and ground manipulation, perception, and reconnaissance using wheeled rovers, unmanned aerial vehicles, CubeSats, SmallSats and more have been evaluated before. Among all of these solutions, balloon-based systems possess merits that make them extremely attractive, e.g., a simple operation mechanism and endured operation time. However, there are many hurdles to overcome to achieve robust loitering performance in balloon-based applications. We attempt to identify design and control challenges, and propose a novel robotic platform that allows for the application of balloons in the reconnaissance and perception of Mars craters. This work briefly covers our suggested actuation and Model Predictive Control design framework for steering such balloon systems. We propose the coordinated servoing of multiple unmanned ground vehicles (UGVs) to regulate tension forces in a cable-driven balloon to which an underactuated hanging payload is attached.

There have been several successful implementations of bio-inspired legged robots that can trot, walk, and hop robustly even in the presence of significant unplanned disturbances. Despite all of these accomplishments, practical control and high-level decision-making algorithms in multi-modal legged systems are overlooked. In nature, animals such as birds impressively showcase multiple modes of mobility including legged and aerial locomotion. They are capable of performing robust locomotion over large walls, tight spaces, and can recover from unpredictable situations such as sudden gusts or slippery surfaces. Inspired by these animals' versatility and ability to combine legged and aerial mobility to negotiate their environment, our main goal is to design and control legged robots that integrate two completely different forms of locomotion, ground and aerial mobility, in a single platform. Our robot, the Husky Carbon, is being developed to integrate aerial and legged locomotion and to transform between legged and aerial mobility. This work utilizes a Reference Governor (RG) based on low-level control of Husky's dynamical model to maintain the efficiency of legged locomotion, uses Probabilistic Road Maps (PRM) and 3D A* algorithms to generate an optimal path based on the energetic cost of transport for legged and aerial mobility

Mid-Air Helicopter Delivery (MAHD) is a new Entry, Descent and Landing (EDL) architecture to enable in situ mobility for Mars science at lower cost than previous missions. It uses a jetpack to slow down a Mars Science Helicopter (MSH) after separation from the backshell, and reach aerodynamic conditions suitable for helicopter take-off in mid air. For given aeroshell dimensions, only MAHD's lander-free approach leaves enough room in the aeroshell to accommodate the largest rotor option for MSH. This drastically improves flight performance, notably allowing +150\% increased science payload mass. Compared to heritage EDL approaches, the simpler MAHD architecture is also likely to reduce cost, and enables access to more hazardous and higher-elevation terrains on Mars. This paper introduces a design for the MAHD system architecture and operations. We present a mechanical configuration that fits both MSH and the jetpack within the 2.65-m Mars heritage aeroshell, and a jetpack control architecture which fully leverages the available helicopter avionics. We discuss preliminary numerical models of the flow dynamics resulting from the interaction between the jets, the rotors and the side winds. We define a force-torque sensing architecture capable of handling the wind and trimming the rotors to prepare for safe take-off. Finally, we analyze the dynamic environment and closed-loop control simulation results to demonstrate the preliminary feasibility of MAHD., Comment: Accepted in 2022 IEEE Aerospace Conference

Mid-Air Deployment (MAD) of a rotorcraft during Entry, Descent and Landing (EDL) on Mars eliminates the need to carry a propulsion or airbag landing system. This reduces the total mass inside the aeroshell by more than 100 kg and simplifies the aeroshell architecture. MAD's lighter and simpler design is likely to bring the risk and cost associated with the mission down. Moreover, the lighter entry mass enables landing in the Martian highlands, at elevations inaccessible to current EDL technologies. This paper proposes a novel MAD concept for a Mars helicopter. We suggest a minimum science payload package to perform relevant science in the highlands. A variant of the Ingenuity helicopter is proposed to provide increased deceleration during MAD, and enough lift to fly the science payload in the highlands. We show in simulation that the lighter aeroshell results in a lower terminal velocity (30 m/s) at the end of the parachute phase of the EDL, and at higher altitudes than other approaches. After discussing the aerodynamics, controls, guidance, and mechanical challenges associated with deploying at such speed, we propose a backshell architecture that addresses them to release the helicopter in the safest conditions. Finally, we implemented the helicopter model and aerodynamic descent perturbations in the JPL Dynamics and Real-Time Simulation (DARTS)framework. Preliminary performance evaluation indicates landing and helicopter operation scan be achieved up to 5 km MOLA (Mars Orbiter Laser Altimeter reference).

The dynamics of a cantilever plate clamped at its trailing edge and placed at a moderate angle ($\alpha \leq 30^{\circ}$) to a uniform flow are investigated experimentally and numerically, and a large experimental data set is provided. The dynamics are shown to differ significantly from the zero-angle-of-attack case, commonly called the inverted-flag configuration. Four distinct dynamical regimes arise at finite angles: a small oscillation around a small-deflection equilibrium (deformed regime), a small-amplitude flapping motion, a large-amplitude flapping motion and a small oscillation around a large-deflection equilibrium (deflected regime). The small-amplitude flapping motion appears gradually as the flow speed is increased and is consistent with a limit-cycle oscillation caused by the quasi-steady fluid forcing. The large-amplitude flapping motion is observed to appear at a constant critical flow speed that is independent of angle of attack. Its characteristics match those of the large-amplitude vortex-induced vibration present at zero angle of attack. The flow speed at which the plate enters the deflected regime decreases linearly as the angle of attack is increased, causing the flapping motion to disappear for angles of attack greater than $\alpha \approx 28^{\circ}$. Finally, the effect of aspect ratio on the plate dynamics is considered, with reduced aspect ratio plates being shown to lack sharp distinctions between regimes., Comment: Submitted to Journal of Fluid Mechanics

The stability of a cantilevered elastic sheet in a uniform flow has been studied extensively due to its importance in engineering and its prevalence in natural structures. Varying the flow speed can give rise to a range of dynamics including limit cycle behaviour and chaotic motion of the cantilevered sheet. Recently, the "inverted flag" configuration - a cantilevered elastic sheet aligned with the flow impinging on its free edge - has been observed to produce large-amplitude flapping over a finite band of flow speeds. This flapping phenomenon has been found to be a vortex-induced vibration, and only occurs at sufficiently large Reynolds numbers. In all cases studied, the inverted flag has been formed from a cantilevered sheet of rectangular morphology, i.e. the planform of its elastic sheet is a rectangle. Here, we investigate the effect of the inverted flag's morphology on its resulting stability and dynamics. We choose a trapezoidal planform which is explored using experiment and an analytical theory for the divergence instability of an inverted flag of arbitrary morphology. Strikingly, for this planform we observe that the flow speed range over which flapping occurs scales approximately with the flow speed at which the divergence instability occurs. This provides a means by which to predict and control flapping. In a biological setting, leaves in a wind can also align themselves in an inverted flag configuration. Motivated by this natural occurrence we also study the effect of adding an artificial "petiole" (a thin elastic stalk that connects the sheet to the clamp) on the inverted flag's dynamics. We find that the petiole serves to partially decouple fluid forces from elastic forces and increases the freedom by which the flapping dynamics can be tuned. These results highlight the intricacies of the flapping instability and account for some of the varied dynamics of leaves in nature., Comment: 21 pages, 10 figures, 1 table

Mid-Air Helicopter Delivery (MAHD) is a new Entry, Descent and Landing (EDL) architecture to enable in situ mobility for Mars science at lower cost than previous rover missions. It uses a jetpack to slow down a Mars Science Helicopter (MSH) after separation from the backshell, and reach aerodynamic conditions suitable for helicopter take-off in mid air. MAHD's lander-free approach leaves enough room in the aeroshell to accommodate larger rotors. This drastically improves flight performance compared to heritage EDL approaches, notably +60\% science payload mass. MAHD also brings cost savings, a simpler architecture, improved surface access and can reach higher elevations on Mars. This paper introduces a design for the MAHD system architecture and operations. We present a mechanical configuration which fits both MSH and the jetpack within the 2.65-m Mars heritage aeroshell, and a jetpack control architecture which fully leverages the available helicopter avionics. We discuss preliminary numerical models of the flow dynamics resulting from the interaction between the jets, the rotors and the side winds. We define a force-torque sensing architecture capable of handling the wind and trimming the rotors to prepare for safe take-off. Finally, we analyze the dynamic environment and closed-loop control simulation results to demonstrate the preliminary feasibility of MAHD.

Over the past few decades, superhydrophobic materials have attaracted a lot of interests, due to their numerous practical applications. Among various superhydrophobic materials, carbon nanotube arrays have gained enormous attentions simply because of their outstanding properties. The impact dynamic of water droplet on a superhydrophobic carbon nanotube array is shown in this fluid dynamics video., Comment: Videos included

This fluid dynamics video shows three-dimensional vortex formation process for plates in impulsive motion which is investigated experimentally by using defocusing digital particle image velocimetry (DDPIV). Rigid and flexible plate cases are compared in order to study the effect of flexibility on 3D vortex formation and associated hydrodynamic forces. This study was motivated by the general question of how the flexibility of flapping propulsors in flying and swimming animals affects vortex formation and propulsive force. For translating and rotating motion, the flexible plate generates a vortex morphology which is drastically different from that of the rigid plate. We identified the deflection of the tip region as the source of this difference. The flexible plate does not produce a large peak for the hydrodynamic force at the impulsive start and stop. This force trend is correlated with smooth vortex formation and shedding processes.