Propulsive Force Research Articles

Does the flutter kick increase hand propulsion in front crawl swimming?

ABSTRACT This study aimed to investigate the effect of the flutter kick on the propulsive force generated by a stroke. Eight male swimmers performed 20 m front crawl trials under two conditions: the Whole Condition, involving maximum effort (T100%) and stroke frequencies at 70, 80, and 90% of T100%, and the Arm Condition, which excluded the flutter kick and matched stroke frequencies with the Whole Condition. Various parameters, including swimming velocity, stroke frequency, stroke length, three-dimensional (3D) resultant hand speed, and hand propulsion were calculated based on underwater 3D motion analysis and hand pressure distribution measurements. A two-way repeated-measures ANOVA was conducted to assess differences, considering the conditions and instructed frequencies as the two factors. There was no significant interaction between the condition and intensity for any of the variables. There was a significant main effect of condition on swimming velocity and stroke length, with these variables being 16.9–18.5% higher and 17.3–19.5% longer, respectively, in the Whole Condition compared to the Arm Condition. However, there was no difference in hand propulsion between the conditions, and it was clarified that the flutter kick did not affect hand propulsion at any swimming velocity.

Breaststroke and butterfly intercycle kinematic variation according to different competitive levels with Statistical Parametric Mapping analysis

Breaststroke and butterfly are complex swimming techniques requiring refined motor skills to perform successfully, with coordinated and consistent interaction between propulsive and resistive forces being decisive when considering swimmers expertise. The current study analysed those techniques intercycle kinematic variation in two swimmers cohorts. Twenty elite and 15 national level swimmers performed one 25 m breaststroke and one 25 m butterfly sprints, with an underwater camera recording images at 120 Hz in the sagittal plane. Mean velocity, maximum and minimum velocities, stroke rate and length, intracycle velocity variation and phases relative duration were calculated for consecutive cycles (elite: five breaststroke/butterfly, national level: eight breaststroke/seven butterfly). The two highest peaks and the lower peak in between in breaststroke were also addressed. Intercycle and inter-groups analysis were performed using ANOVA, ANCOVA and Statistical Parametric Mapping. Elite and national level differed regarding breaststroke mean and maximum velocities, 1st and 2nd peaks and minimum between peaks (1.30 ± 0.02 vs 1.15 ± 0.02 m/s, 2.13 ± 0.05 vs 1.88 ± 0.06 m/s, 1.63 ± 0.05 vs 1.48 ± 0.05 m/s, 2.13 ± 0.05 vs 1.86 ± 0.05 m/s, 1.33 ± 0.04 vs 1.23 ± 0.04 m/s), and butterfly mean, maximum and minimum velocities, stroke rate and intracycle velocity variation, respectively (1.65 ± 0.01 vs 1.50 ± 0.01 m/s, 2.20 ± 0.04 vs 2.09 ± 0.04 m/s, 1.12 ± 0.04 vs 0.79 ± 0.04 m/s, (57.9 ± 0.9 vs 54.9 ± 1.0cycles/min, 18.4 ± 1.3 vs 23.7 ± 1.3 %). Elite and national level swimmers showed consistent breaststroke intercycle kinematic variation, but a butterfly mean velocity decay, with the upper limbs release and recovery, and the outsweep phases originating variability between butterfly cycles. Skill levels contrasted in technical and strategic features at sprint breaststroke and butterfly but showed similar velocity variability between consecutive swimming cycles.

Course control in a self-consistent model of cuttlefish movement

We developed a simulation model to mimic cuttlefish movement. We developed a simulation model to mimic cuttlefish movement, representing an elongated body with two undulatory fins that generate propulsive forces for underwater movement. Our mathematical model concurrently solved equations for both body mechanics and fluid dynamics, using the Navier–Stokes equations to describe the latter. To implement this self-consistent model, we utilized deformable mesh techniques. This enabled us to compute both the apparatus’s movement performance characteristics and hydrodynamic flow parameters, such as vorticity and pressure fields. Our study focused on examining how oscillations of the left and right fins, each with different parameters, impact the apparatus’s maneuverability. We found that differences in frequencies between the left and right fins resulted in a peak turning angle velocity. We also explored how the interplay between hydrodynamic forces influences the apparatus’s course control.

A model for micro-scale propulsion using flexible rotating flagella

Micro-scale propulsion by rotating helical flagella is of interest for the study of bacteria and robotic micro-swimmers. The propulsive thrust and torque produced by the rotating flagella are usually estimated assuming that they are rigid. In this paper we assume the flagella to be deformable elastic rods and compute propulsive forces and torques by enforcing local equilibrium of the rod within the context of resistive force theory. The torque-speed characteristics of the flagellar motor driving the rotation are taken into account. We show that the problem can be cast as a system of algebraic equations if the flagella are assumed to be helical before and after deformation when no spontaneous curvature is included. If the assumption of helical shape is dropped then we show that the propulsion problem can be cast as a system of first order differential equations that can be solved numerically. Our results in both cases agree reasonably well with experimental observations of bacterial propulsion and deviate from the predictions of Purcell depending on the mechanical properties of the flagellum.

Optimal replicator dynamic controller for semi active control of long span cable stayed bridge with considering special variability of seismic excitations

Cable-stayed bridges are lifeline infrastructures. However, due to their design and structural characteristics, they are sensitive to the vibrations. Thus, vibration control in these structures is essential. Semi-active control systems have gained significant attention due to their high performance and adaptability. However, the implementation of these systems has always faced serious challenges particularly when it comes to developing appropriate control algorithms because semi active devices have complex and non-linear characteristics. Inspired by evolutionary game theory, the author utilizes the replicator dynamic controller concept to optimize the performance of MR dampers to improve the vibration reduction of cable-stayed bridges. Two key parameters in the proposed control methodologies using replicator dynamics are the total population (total available resources or the sum of actuator forces) and the growth rate. Instead of using the sensitivity analysis that has been done in previous studies for vibration reduction of highway bridges using a replicator controller, the author used an evolutionary algorithm named the nondominated sorting genetic algorithm (NSGA-II) to create an optimal replicator dynamic controller for more effective vibration reduction. The proposed methodology is evaluated through its numerical application to a second-generation benchmark example based on the Bill Emerson Memorial Bridge, which considers a more realistic behavior of the cable-stayed bridge by accounting for multiple support excitations. The study indicates that the optimal replicator dynamic controller improves the vibration reduction performance of MR dampers. Specifically, deck displacement is reduced by 46 % compared to passive control system and shear forces at the tower base are reduced by 33 % compared to active control systems for the El Centro earthquake. The results indicate that the proposed Replicator Dynamic Controller optimized through NSGA-II provides a robust and effective solution for improving seismic resilience of cable-stayed bridges.

Feeders and expellers, two types of animalcules with outboard cilia, have distinct surface interactions

Within biological fluid dynamics, it is conventional to distinguish between “puller” and “pusher” microswimmers on the basis of the forward or aft location of the flagella relative to the cell body: typically, bacteria are pushers and algae are pullers. Here we note that since many pullers have “outboard” cilia or flagella displaced laterally from the cell centerline on both sides of the organism, there are two important subclasses whose far-field is that of a stresslet, but whose nearfield is qualitatively more complex. The ciliary beat creates not only a propulsive force but also swirling flows that can be represented by paired rotlets with two possible senses of rotation, either “feeders” that sweep fluid toward the cell apex, or “expellers” that push fluid away. Experimental studies of the rotifer in combination with earlier work on the green algae show that the two classes have markedly different interactions with surfaces. When swimming near a surface, expellers such as scatter from the wall, whereas a feeder like stably attaches. This results in a stochastic “run-and-stick” locomotion, with periods of ballistic motion parallel to the surface interrupted by trapping at the surface. Published by the American Physical Society 2024

A novel mobile robot with origami wheels designed for navigating sandy terrains

Abstract Sand robots play a vital role as mobile tools for human exploration of desert regions, facilitating resource transportation and exploration. However, desert areas primarily consist of beaches or dunes, resulting in a highly diverse and complex terrain environment that demands enhanced adaptability from sandy mobile robots. Traditional wheeled robots currently face challenges such as skidding, limited climbing ability, and inadequate obstacle avoidance capabilities in sandy environments. To address these issues and enable effective adaptation to the intricate sand environment, we propose a novel sandy mobile robot equipped with Kresling origami wheels. The origami wheel can dynamically adjust its width and morphology through Kresling origami folding. Experimental tests were conducted to illustrate the impact of width variation on the robot’s mobility velocity, propulsive force, climbing performance, and carrying capacity. The self-folding malleability of the origami wheel empowers the robot to efficiently accomplish diverse tasks, including swift movement on flat sand surfaces, seamless crossing of narrow channels, and intelligent obstacle avoidance. By successfully completing these multimodal tasks while adapting to varying requirements, our robot demonstrates promising prospects for practical applications of mobile robots equipped with origami wheels – paving the way for wider adaptation and utilization of sand mobile robots.

A Machine Learning–Based Ergonomic Assessment of Wireless Hand Control System for Lower‐Limb Disabled Tractor Operators and Abled Female Agricultural Workers

ABSTRACTTractor being the most used power source for agricultural operations needs hand control (HC) and foot control (FC) to maneuver it. FCs restrict lower‐limb disabled agricultural workers from participating in tractor operation, and high requirement of actuation forces to operate FCs may create overexertion and early fatigue to female agricultural workers. Therefore, a sensor‐based HC system has been developed to assist them in tractor operation with minimal actuating force. This study focuses on ergonomic assessment of the HC system to assess the suitability for the abled and disabled agricultural workers, including physiological, psychophysical, and muscle fatigue parameters. Heart rate (HR) of abled male and female, and disabled male and female was observed in the range of 83–118, 85–117, 93–118, and 92–114 beats/min, respectively, during tractor operation. Energy expenditure rate (EER) during tractor operation with FCs (9.7–17.4 kJ/min) was observed higher than with the HC system (7.3–16.5 kJ/min). Body parts discomfort was observed highest for the right hand of all the subjects (4.9–5.3) and maximum overall discomfort was experienced by abled females during the operation with FCs (5.4) as they have to exert higher force. The root mean square (RMS) value of the electromyography signal obtained for extensor digitorum muscle was found to be higher for all the subjects and with both HC and FC (abled male, 17.37–40.43 µV; abled female, 14.76–45.29 µV; disabled male, 15.49–40.23 µV; disabled female, 30.32–54.29 µV) than other upper arm muscles middle deltoid, flexor carpi radialis, and brachioradialis. Muscle workload for all the selected muscles of all the subjects was observed within the recommended limit during the tractor operation with a developed HC system (< 30%). Categorization of overall discomfort rating (ODR) of the subjects using HR, EER, and RMS through machine learning algorithms such as k‐nearest neighbor (KNN), random forest classifier, and support vector machine predicted the ODR with accuracies in the range of 77%–83%. KNN algorithm was found to be most accurate with prediction accuracy of 83%. The developed HC system provides assistantship to the lower‐limb disabled agricultural workers (1%–100% disability of lower limbs) and allows female workers to operate the tractor with minimal physical exertion.

Static and dynamic characteristics of electrostatically coupled MEMS beams under asymmetric actuation conditions

Abstract Electrostatically actuated microbeams have gained prominence due to their applications as micro-actuators and ultrasensitive sensors. In this study, we investigate the dynamic behavior of electrostatically coupled microbeams, specifically focusing on the effects of asymmetric actuation conditions. Our investigation encompasses both static and dynamic characteristics of the coupled microbeam system, considering various gap ratios between the beams and the fixed electrodes. Within the coupled system, two doubly clamped microbeams are positioned between two fixed electrodes. We develop a reduced-order model (ROM) to investigate static and dynamic responses of the coupled system. To validate the ROM, we rigorously compare its results with finite element (FE) simulations. Our findings reveal that the gap ratios play a pivotal role in shaping the system’s response. Notably, first two natural frequencies are important for design of micro-resonators and they exhibit complex variation with respect to the applied DC voltage. Moreover, we explore resonance frequency tunability and investigated interplay between geometric nonlinearity and nonlinear electrostatic actuation forces. These insights contribute significantly to the efficient design of MEMS resonators.

Wind tunnel testing and performance modeling of an atmospheric ion thruster

Abstract In this work a complete atmospheric electro–hydro-dynamic (EHD) thruster is tested in a subsonic wind tunnel, with the purpose of evaluating changes in performance due to simulated flight conditions and, for the first time, comparing them with a physical model of the drift region. An aerodynamic frame was designed to accommodate the electrodes inside the wind tunnel. Propulsive force and electrical measurements were conducted to assess performance exploiting dimensionless coefficients derived from one-dimensional theory. The results, on top of validating the theory, show how EHD thrusters can operate with a non-zero bulk velocity and highlight the importance of optimized frames and electrodes to enhance the capabilities of flying demonstrators. The test campaign revealed that the operating voltage envelope extends with increasing bulk velocity, leading to an increase in maximum thrust.

Submaximal force–velocity relationships during mountain ultramarathon: Data from the field

ABSTRACT This study presents a novel method for evaluating the submaximal velocity-force (V(F)) relationship in mountain ultramarathon races using crowdsourced data from Strava.com. The dataset includes positional data from 408 participants of the 171-km UTMB® 2023 race (9,850-m D+). The race was divided into 100-m segments. The mean net propulsive force and velocity were computed for each segment to describe the submaximal V(F) relationship as a rational function of three parameters. F1: propulsive force at 1 m · s−1; V0: theoretical maximum velocity on flat terrain; C: curvature parameter (the lower C, the more linear the V(F) relationship). The V(F) profile parameters were found to be F1 = 1.80 ± 0.33 N · kg−1, V0 = 2.36 ± 0.42 m · s−1, and C = 0.66 ± 1.81, with good independence between the parameters within a group of homogeneous performance. The best athletes had the highest F1, V0, and C values. V(F) parameters were affected by fatigue during the race, with decreases of 20.9%, 32.0%, and 59.8% between the first and second parts of the race respectively. These findings suggest that the V(F) relationship is an interesting original approach for studying performance and fatigability during mountain ultra-endurance races.

Propulsion and energy extraction performance of wave-powered mechanism considering wave and current

Wave-powered mechanism can extract wave energy as propulsion, enabling long-term ocean observation. The kinematic properties of wave propulsion mechanisms are susceptible to ocean current loads in addition to wave effects, presenting complex dynamic behaviors. In this paper, to understand the effects of ocean currents on the kinematic performances of wave propulsion mechanism, the dynamic performance of a wave propulsion mechanism in the combined condition of wave and current is analyzed based on numerical simulation method for fluid-rigid body coupling and experimental methods. The performance of the propulsion mechanism against the current under counter-current conditions and the contribution of flow to the propulsion performance under co-current conditions are discussed. The intrinsic relationship between wave height, current velocity and current direction is investigated, and the energy extraction performance of wave propulsion mechanism is analyzed. According to the results, the ability of propulsion mechanism to resist counter-current is obtained, and it is found that as the counter-current velocity increases, the hydrofoil will stall and the propulsion force and efficiency decreases significantly. Whilst, the co-current has a promoting effect on the forward of the mechanism, but within a certain range of co-current speed, the mechanism will be negatively affected by the shedding vortex. And the discrimination mechanisms for wave-dominated propulsion and current-dominated propulsion are obtained. This work reveals the combined effect of waves and currents on the motion performance of wave propulsion mechanism, providing a reference for the development of surface vehicles that utilize multiple ocean energies for synergistic propulsion.

A parallel mechanism-based virtual biomechanical shoulder robot model: Mechanism design optimization and motion planning

This paper presents the design and optimization process of a Virtual Biomechanical Shoulder Robot Model (VBSRM) based on a 6-4 parallel mechanism. To address the challenges posed by parallel manipulators and the specific biomechanical constraints of the shoulder joint, a comprehensive design analysis is conducted. First, a kinematic model of the VBSRM is developed, followed by an investigation of its geometric model. To obtain an optimal VBSRM design, performance objectives such as condition number, norm of actuator force, and stiffness are identified and optimized. Initially, only condition number of the robot mechanism is optimized using Genetic Algorithm and performance objectives from the optimal design are analyzed. Later, the three objectives are grouped to form a single function and a single objective-based optimization is also conducted. However, further investigation revealed the conflicting nature of the objectives and hence these were simultaneously optimized using the Non-dominated Sorting Genetic Algorithm (NSGA II). The results obtained from various optimization routines are compared and it is found that the results from the NSGA II provide a better tradeoff between the performance objectives. The motion trajectories from the optimal design of the VBSRM are later analyzed vis-à-vis human shoulder motions for its intended use as a robotic model of the human shoulder joint in various applications.

Static Model of the Underwater Soft Bending Actuator Based on the Elliptic Integral Function

Underwater soft manipulators are increasingly used for grasping underwater organisms and cultural relics due to their compliance and ability to protect delicate objects. Unlike rigid manipulators, these soft manipulators feature underwater soft bending actuators that deform under external forces, making their shape and output force challenging to predict. Consequently, classical beam theory is no longer applicable. To address these issues, this article models the underwater soft bending actuator as a cantilever beam and establishes its shape and output force using elliptic integral functions. Additionally, this article proposes a method for determining the unknown parameters of the driver shape and output force model using optimization techniques and introduces a solution process based on the particle swarm optimization framework. Given the role of tensile and bending stiffness in the actuator’s performance, this paper employs a parameter identification method based on length and bending angle information. Tests demonstrate that the proposed method effectively estimates the deformation and output force of the underwater soft bending actuators, confirming its accuracy.

Development of Assistance Level Adjustment Function for Variable Load on a Forearm-Supported Robotic Walker.

With the progression of an aging society, the importance of walking assistance technology has been increasing. The research and development of robotic walkers for individuals requiring walking support are advancing. However, there was a problem that the conventional constant support amount did not satisfy the propulsion force required for the walking speed that users wanted. In this study, in order to solve this problem, we propose an algorithm for determining the support amount to maintain the walking speed when the average walking speed of each user is set as the target speed. A robotic walker was developed by attaching BLDC motors to an actual walker, along with a control algorithm for assistance based on sampling-type PID control. The effectiveness of the assistance determination algorithm and the usefulness of the parameters were demonstrated through experiments using weights loaded on the forearm support and target speeds. Subsequently, subject experiments were conducted to verify the ability to maintain target speeds, and a questionnaire survey confirmed that the assistance did not interfere with actual walking. The proposed algorithm for determining the assistance levels demonstrated the ability to maintain target speeds and allowed for adjustments in the necessary level of assistance.

Dissimilar Resistance Welding of NiTi Microwires for High-Performance SMA Bundle Actuators

Shape memory alloys (SMAs) are becoming a more important factor in actuation technology. Due to their unique features, they have the potential to save weight and installation space as well as reduce energy consumption. The system integration of the generally small-diameter NiTi wires is an important cornerstone for the emerging technology. Crimping, a common method for the mechanical and electrical connection of SMA wires, has several drawbacks when it comes to miniaturization and high-force outputs. For high-force applications, for example, multiple SMA wires in parallel are needed to keep actuation frequencies high while scaling up the actuation force. To meet these challenges, the proposed study deals with the development of a resistance-welding process for manufacturing NiTi wire bundles. The wires are welded to a sheet metal substrate, resulting in promising functional properties and high joint strengths. The welding process benefits from low costs, easy-to-control parameters and good automation potential. A method for evaluating the resistance-welding process parameters is presented. With these parameters in place, a manufacturing process for bundled wire actuators is discussed and implemented. The welded joints are examined by peel tests, microscopy and fatigue experiments. The performance of the manufactured bundle actuators is demonstrated by comparison to a single wire with the same accumulated cross-sectional area.

Kineto-static analysis of a hybrid manipulator consisting of rigid and flexible limbs with locking function for planar shape morphing

The incorporation of lockable passive backbones into active compliant morphing systems efficiently results in lightweight, high-load, and large deformation systems. However, there exist challenges in kineto-static analysis due to the interaction between rigid reconfigurable kinematic constraints and the nonlinear deformation of actuated flexible limbs. This paper addresses these issues by developing a kineto-static method to analyze the motion in a novel planar 3-DOF shape-morphing manipulator. The manipulator features two actuated flexible limbs with a lockable variable geometry truss (LVGT). In this study, two isostatic topologies are selected for reconfigurable motion control under external tip loads. A multi-step sequential control strategy is proposed to maneuver the manipulator's platform for desired poses. Then, a constrained-trajectory-based kinematic model is proposed for an inverse kinematic solution considering motion planning. Subsequently, a kineto-static model is introduced, considering constraints from rigid and flexible limbs, aiming to distribute distributing redundant actuation forces. Finally, nonlinear finite element analysis (FEA) and experiments are carried out to validate the effectiveness of the proposed method.

Sulphonated-graphene oxide nanocomposite membranes with PVA-ZnO nanostructures and mechanized agitation-enhanced pt coating for soft robotics bending actuator

Ionic Polymer-Metal Composite (IPMC) actuators have garnered significant scientific attention in robotics and artificial muscles for their ability to operate at low voltage, high strain capacity, and lightweight construction. The lack of uniform bending in IPMC actuators undermines their control precision and restricts their range of potential applications. This study utilized the unique properties of nanoscale materials and Polyvinyl alcohol (PVA) to develop a membrane for soft robotic bending actuation. Subsequently, a platinum coating was applied to the membrane to mitigate the limitations of IPMCs in soft robotics applications. Herein, mechanized agitation was employed during the solution-casting process to enhance platinum metal (Pt-metal) coating on zinc oxide (ZnO) nanostructures within a PVA- sulphonated graphene oxide nanocomposite, achieving enhanced soft robotics bending actuation capabilities. The resultant membrane composed of sulphonated-graphene oxide and polyvinyl-zinc oxide coated with pt (PsGZ-Pt) was examined by exploring advanced analytical techniques such as Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and X-ray diffraction spectroscopy (XRD). Furthermore, the ionic exchange capacity (IEC), proton conductivity (PC), water uptake and water loss characteristics were evaluated to be 2.1 meq. g−1, 1.95 × 10−3 Scm−1, 59.62% at 45 °C and water loss at 9 min immersion found 38%, respectively. Electromechanical studies of the PsGZ-Pt membrane (size 30 mm length, 10 mm width, 0.07 mm thickness) showed an actuation force of 0.3253 mN and a displacement of roughly 22.8 mm at ± 3 VDC. These findings highlighted the PsGZ-Pt membrane’s potential as a low-cost alternative to expensive commercial IPMC actuators based on polymers. These results presented a straightforward, low-cost approach for synthesizing PsGZ-Pt utilizing conventional technologies. The PsGZ-Pt membrane shows promise for generating low-cost, high-performance actuation materials with a wide range of industrial applications.

Should individuals with unilateral transtibial amputation carry a load on their intact or prosthetic side?

Carrying side loads often occurs during activities of daily living. As walking is most unstable mediolaterally, side load carriage may further compromise gait biomechanics, especially for transtibial amputees (TTAs). This study investigated the effects of side load carriage on gait kinetics during steady-state walking to determine which side, intact or prosthetic, TTAs should carry a load. Twelve unilateral TTAs wore a passive-elastic foot and carried a side load of 13.6 kg while walking at their self-selected speed. Kinetic metrics, including ground reaction force peaks and impulses, loading and unloading rates, and joint moments and powers, were analyzed. TTAs had smaller propulsive forces on their intact limb during the prosthetic side load condition. During the intact side load condition, they exhibited smaller hip flexor moment in late stance and smaller knee flexor moment at the end of swing on their intact limb. They had higher hip and knee abductor moments on their intact limb and prosthetic limb in early and late stance during the contralateral side load condition. TTAs generated higher hip extensor power at weight acceptance during the ipsilateral side load. Significant interactions were observed in hip extensor power and abductor moment, suggesting strong associations between hip extensor power generation and the ipsilateral side load and between hip abductor moment and the contralateral side load. These mixed results demonstrate some kinetic changes due to side load carriage and suggest that the side TTAs should carry a load depends on the desired effects, primarily on their intact limb.

Piecewise-scheduled thrust command control for in-service thrust performance improvement of gas turbine aero-engines: A hybrid fast design approach

Gas turbine aero-engines including turbofans, as the dominant powerplant for modern civil aircraft, convert the fossil energy in the jet fuel to propulsive forces via the thermo-dynamic cycle. Unfortunately, thrust regulation capabilities of gas turbine aero-engines are inevitably affected by uncertainties in measurements and gas path degradation during the life cycle, while quantification efforts for these uncertainties by traditional random analysis methods are usually considerable. In this paper, a piecewise-scheduled thrust command controller is proposed based on the improvement of the industrial baseline controller and current measurement levels, aiming at enhancing in-service thrust performance within a tolerable computational burden for engine fleets against these uncertainties. The proposed controller is equipped with a bank of embedded thrust maps for different flight cycle segments, which is fulfilled by a hybrid fast design approach incorporating a random analysis part and an analytical design part, as a new uncertainty quantification method. An industrial baseline controller with the identified thrust mode is also designed as the comparison basis. Simulations are carried out on a validated aero-thermal turbofan engine model with publically accessible uncertainty statistics. Simulation time for constructing the embedded thrust maps of the proposed controller is decreased by 99.8% on a desktop computer, compared to Monte-Carlo approach. Meanwhile, simulation results show that the proposed controller owns a bounded and tight thrust distribution for both new and severely degraded engine fleets at the take-off state within the permitted safety margin of the engine, which mitigates the significant under-thrust consequences from the baseline controller. Hence, the uncertainty control benefits of the proposed controller and its design efficiency are guaranteed.