Now, a research team led by Zhe Sun, Shujie Hu, Xinan Miao, and Bo Chen of Zhejiang University of Technology in Hangzhou, China, together with Jinchuan Zheng and Zhihong Man of Swinburne University of Technology in Melbourne, Australia, and Tian Wang of Hangzhou RoboCT Technology Development Co. Ltd., has unveiled an integrated control framework that promises to make these agile robots far more capable of navigating cluttered environments on their own. Published in Frontiers in Control Engineering, their study tackles two of the most vital technologies for autonomous movement: trajectory planning and trajectory-tracking control. The work arrives at a moment when mobile robots are being deployed ever more widely, and when the ability to plan a path around obstacles in real time, and then follow that path with precision, separates a genuinely autonomous machine from a remote-controlled toy.

Trajectory planning, in essence, means generating a series of reference position-and-posture signals for a mobile robot based on environmental information perceived by its sensors, while respecting the robot’s kinematic constraints and accounting for surrounding obstacles. Planning strategies fall into two broad categories. Global planning algorithms require all environmental information in advance and take considerable time to execute, which makes them difficult to implement in real settings. Local planning, by contrast, possesses a stronger real-time property because it uses sensor-collected information to iteratively update the reference trajectory as the robot moves. Typical local planning approaches include fuzzy logic methods, neural network methods, and artificial potential field (APF) methods. The APF scheme is particularly elegant: it treats the target and obstacles as objects exerting virtual forces on the robot, with the target generating an attractive force and obstacles generating repulsive forces. The resultant of these virtual forces indicates the robot’s moving direction, guiding it smoothly around hazards and toward its destination. Because APF-based strategies offer smooth trajectory generation and real-time obstacle avoidance, they play a key role in mobile robot navigation.

The Zhejiang-led team harnessed this potential field concept with a thoughtful piecewise design. Their attractive-field function depends on the distance between the robot and the target at each sampling moment, modulated by an attractive-field parameter and a switching distance threshold. The purpose of the piecewise structure is to prevent an overlarge attractive force when the robot is far from its goal. If the attractive force were always proportional to distance, the robot would be forced to rush at high velocity from the starting point. Instead, a constant attractive force is exerted on the robot until it enters an area of predetermined radius around the destination, at which point the force becomes proportional to the remaining distance, allowing a gentle arrival. On the repulsive side, the field function depends on the distance between each obstacle and the robot, scaled by a repulsive-field coefficient and limited to a maximum acting range. Beyond that range, an obstacle exerts no influence at all, keeping the virtual force landscape clean and computationally efficient. The resultant force, decomposed along the X and Y axes, generates reference velocities that serve as the reference signal for the tracking control system.

Planning a trajectory is only half the battle; the robot must then follow it accurately despite disturbances, friction variations, and model uncertainties. For this task, the researchers turned to sliding mode control, a strategy widely utilized in mechatronic engineering practice owing to its superior performance and firm robustness in handling external disturbances and model uncertainties. Conventional sliding mode control, however, can only realize asymptotic convergence, meaning errors decay gradually rather than vanishing in finite time. To overcome this shortage, terminal sliding mode control was developed to enhance convergence speed and suppress the chattering phenomenon, and a subsequent non-singular terminal sliding mode method addressed the singularity problem inherent in the classical formulation, finding applications in systems ranging from vehicle steer-by-wire to servomotor-driven rigid robots.

The team’s contribution goes a step further by embracing the discrete nature of modern computer control. As embedded controllers grow more powerful, more control algorithms are implemented by computer systems that operate with sampling periods, during which the control input signal remains constant. This discrete reality creates a fundamental problem for sliding mode control: while discrete control inputs can bring system states close to the sliding surface, they usually cannot make the states stay on it. Directly applying a continuous sliding mode algorithm to a sampled-data system may harm stability and even result in loss of control. The researchers therefore designed a discrete integral terminal sliding mode (DITSM) control algorithm specifically suited to computer implementation, building on established concepts of quasi-sliding mode and quasi-sliding mode bands from the discrete-time variable structure control literature.

The DITSM controller operates on a velocity error defined as the difference between the reference velocity signal and the robot’s actual velocity. A sliding surface is constructed that combines the current error with an integral term of a fractional power, with parameters chosen as odd integers whose ratio approaches one. The closer this ratio is to one, the closer the surface is to a proportional one, yielding smoother control input but slower convergence. The researchers selected a ratio of three-fifths as a considered tradeoff. The total control input is composed of two parts: an equivalent control input, derived by temporarily neglecting the lumped parametric uncertainties, and a reaching control input that handles those uncertainties through a switching gain. A key practical merit of the design is that the switching gain is defined in terms of a single tunable parameter, which reduces the difficulty of tuning and simplifies the stability analysis considerably.

Stability was not left to intuition. The team constructed a discrete-time Lyapunov function and carried out a classified discussion covering all sign combinations of the sliding variables, proving that each component converges into a bounded region in finite steps and, once inside, cannot escape. Building on a lemma concerning discrete-time terminal sliding surfaces, they further showed that the tracking error itself converges into a bounded region after finitely many steps. The researchers also elaborated a detailed tuning guideline: increasing the integral coefficient accelerates convergence and keeps small steady-state errors, though an overlarge value may cause instability, while a larger boundary parameter accelerates error convergence at the cost of intensifying chattering. Benchmark controllers, a discrete conventional sliding mode controller and a discrete terminal sliding mode controller, were designed for comparison.

Simulations in MATLAB verified the framework in two scenarios. In the static-obstacle case, the robot started at the origin with a target fifteen meters away, and five static obstacles were scattered along the corridor. The attractive-field coefficient was set to 0.5, the repulsive-field coefficient to 8, the switching distance to 5 meters, and the maximum repulsive range to 3 meters, with motor output torque limited to 0 to 15 newton-meters to mimic motor protection and a sampling period of 0.01 seconds. The trajectory-planning algorithm updated every 20 sampling periods, balancing computation load and operational efficiency, while the robot’s heading angle remained fixed at zero to showcase its omnidirectional movement. Results showed the DITSM controller achieved the fastest convergence rate in X-axis velocity error, with the DTSM and DCSM controllers ranking second and slowest. Y-axis velocity errors exhibited oscillations because the planning algorithm updates every 20 sampling periods, but the oscillation amplitude under DITSM was the smallest, peaking at only 0.05 meters per second. The initial control action of the DITSM system was the strongest, explaining its fast convergence.

In the dynamic-obstacle case, the third and fourth obstacles were set in motion along the Y-axis at velocities of 1 meter per second and 0.5 meters per second respectively, within defined ranges. Screenshots of the robot’s trajectory at half-second intervals showed the APF-based planning scheme updating the reference trajectory according to the moving obstacles’ positions and guiding the robot around them. Under the DITSM control law, the robot realized satisfactory dynamic obstacle avoidance, with the fastest velocity-error convergence rate, the fastest transient response, and the smallest error oscillations compared with the benchmarks. The findings indicate that the proposed planning-and-control method achieves effective obstacle avoidance in both static and dynamic scenarios, with higher tracking accuracy and firmer robustness than the benchmark controllers. For a robot class already prized for moving in any direction without a swerve, this work adds the intelligence to do so safely among moving hazards, a combination that could accelerate deployment of MWOMRs in warehouses, factories, and beyond.

Subject of Research: Artificial potential field trajectory planning and discrete integral terminal sliding mode tracking control of a Mecanum-wheeled omnidirectional mobile robot

Article Title: Obstacle-avoidance trajectory planning and sliding mode-based tracking control of an omnidirectional mobile robot

Article References: Sun, Z., Hu, S., Miao, X., Chen, B., Zheng, J., Man, Z., & Wang, T. (2023). Obstacle-avoidance trajectory planning and sliding mode-based tracking control of an omnidirectional mobile robot. Frontiers in Control Engineering, 4, Article 1135258. https://doi.org/10.3389/fcteg.2023.1135258

Image Credits: AI Generated

DOI: 10.3389/fcteg.2023.1135258

Keywords: omnidirectional mobile robot, Mecanum wheels, obstacle avoidance, trajectory planning, trajectory tracking, sliding mode control, artificial potential field, discrete control, Lyapunov stability, autonomous robots, robotics, control engineering

The material at the heart of the work is the magnetorheological elastomer, or MRE, a class of smart composite in which micrometer-scale magnetic particles are suspended in an elastic polymer matrix. When an external magnetic field is applied, the particles align and interact, stiffening the material and shifting its effective stiffness and damping properties within milliseconds. This reversible, field-controlled behavior makes MREs attractive for semi-active vibration isolation, in which the isolator adjusts its own mechanical properties in real time rather than relying on a fixed spring-damper design or consuming large amounts of power like a fully active actuator. Because the device modifies an inherent property of its material rather than injecting energy into a structure, semi-active systems also carry inherent stability advantages that have made them popular in automotive suspensions, seismic protection, and machinery mounting.

Yet MREs bring a notorious complication: their behavior is strongly nonlinear and hysteretic. The relationship between the applied magnetic field, the deformation of the elastomer, and the resulting force does not follow a simple algebraic rule. Instead, the material’s response depends on its deformation history, and its stiffness changes with both field strength and the amplitude and frequency of vibration. A controller designed under one set of assumptions can perform poorly, or even destabilize the system, when excitation conditions change. This is precisely the challenge the research team set out to address, focusing on excitations whose frequency and amplitude vary over a realistic operating envelope.

The experimental platform described in the study is a purpose-built MRE isolator with an orthogonal magnetic flux configuration. In this arrangement, the magnetic field is directed perpendicular to the plane in which the elastomer is sheared or compressed, maximizing the interaction between the field and the embedded particles while making efficient use of the magnetic circuit. The team fabricated the isolator and then systematically characterized its dynamic behavior under harmonic excitation across a frequency range of 15 to 80 hertz. This range is significant for practical isolation problems, because it spans many resonant frequencies of machinery mounts, vehicle subframes, and structural components where vibration damage and comfort problems concentrate. Mapping the isolator’s response across this band revealed the frequency-dependent shifts in stiffness and damping that any controller would need to handle.

To exploit the material’s adaptability without falling victim to its unpredictability, the researchers designed a hybrid controller built from two complementary elements. The first is a radial basis function neural network, or RBF network, a machine learning architecture whose output is a weighted sum of responses from localized, bell-shaped basis functions distributed across the input space. Because each basis function responds strongly only to inputs near its center, RBF networks can approximate nonlinear, spatially varying relationships efficiently and can be trained or updated online. In this application, the network’s job is to learn and adaptively estimate the isolator’s nonlinearities and hysteresis as they manifest under changing vibration conditions, providing a continuously refined model of the plant that a fixed mathematical model could never supply.

The second element is the sliding mode controller, a robust control technique with a long pedigree in engineering practice. Sliding mode control drives the system’s state trajectory onto a deliberately chosen sliding surface, along which the desired dynamic behavior is guaranteed, and then holds it there using a discontinuous control action that is insensitive to matched uncertainties. Its strength is robustness: once on the sliding surface, the closed-loop system tolerates a defined class of modeling errors and disturbances. Its weakness is that aggressive switching can amplify noise and induce chattering, and it traditionally requires a reasonably accurate bound on system uncertainties. The hybrid design resolves this tension elegantly, with the neural network absorbing the burden of representing the nonlinear, hysteretic dynamics while the sliding mode framework guarantees stability and rejects residual disturbances.

The division of labor matters because vibration isolation is a moving target. As excitation frequency sweeps through the resonance region, the isolator’s transmissibility changes rapidly; as amplitude grows, hysteresis loops widen and effective damping shifts. A purely neural approach risks drifting toward inaccurate estimates when conditions move outside its training experience, while a purely sliding mode approach would demand conservative margins that sacrifice performance. By integrating the two, the controller adapts its internal estimate of the system in real time while the sliding mode law enforces stable tracking of the isolation objective. The researchers evaluated this architecture both in simulation and experimentally, providing converging lines of evidence that the scheme works not only on paper but on a physical device subjected to real harmonic excitation.

The headline result is the maximum vibration reduction of 55.8 percent achieved near the resonance region under the tested conditions, the operating point where conventional passive isolators typically struggle most. Near resonance, even modest input forces can produce large transmitted vibrations, so effective attenuation there is the gold standard for isolator performance. Equally important, the study reports that the semi-active MRE isolator maintained stable performance across the full range of investigated excitation frequencies, indicating that the hybrid controller did not merely optimize for one narrow condition but adapted gracefully as the excitation environment changed. Stable adaptive performance under varying frequency and amplitude is the property that distinguishes an engineering solution from a laboratory demonstration tuned to a single test case.

The implications extend across several industries. Automotive engineers could apply such isolators to engine mounts and suspension elements, where excitation frequency changes constantly with driving conditions. Aerospace and marine systems, which encounter broadband vibration from rotating machinery and fluid-structure interaction, could benefit from isolators that retune themselves without mechanical adjustment. Precision manufacturing and semiconductor fabrication equipment, which must sit motionless on floors that are never truly still, represent another natural application. In earthquake engineering, semi-active devices built on similar principles have already been explored for structural protection, and a controller that handles nonlinear material behavior robustly could strengthen the case for MRE-based seismic isolators. Because semi-active systems require only modest power to drive the magnetic field rather than to generate control forces, they remain practical for battery-backed or low-power installations.

The work also speaks to a broader trend in control engineering: the marriage of learning-based models with provably robust control laws. Purely data-driven controllers often struggle to offer formal guarantees, while classical robust controllers can be overly conservative when systems are too nonlinear for simple models. Hybrid architectures such as the one demonstrated here let each approach cover the other’s weaknesses, a pattern that is spreading through robotics, energy systems, and aerospace. For magnetorheological elastomers specifically, the study suggests that the material’s most daunting property, its hysteresis, can be converted from an obstacle into a managed characteristic. The authors position the framework as an effective solution for handling nonlinear dynamics and a route toward greater adaptability in smart vibration isolation systems. As smart materials mature and machine learning hardware becomes inexpensive enough to embed in everyday devices, the vision of structures that sense, decide, and quiet themselves in milliseconds moves closer to routine engineering practice, and this research offers a concrete, experimentally validated blueprint for how that quieting can be achieved.

Subject of Research: Hybrid neural network and sliding mode control of a magnetorheological elastomer vibration isolator under variable excitation conditions

Article Title: Hybrid RBF neural network–based sliding mode control for a magnetorheological elastomer isolator under variable frequency and amplitude excitations

Article References: Katari, K., Poojary, U. R., Hegde, A., & K. V., G. (2026). Hybrid RBF neural network–based sliding mode control for a magnetorheological elastomer isolator under variable frequency and amplitude excitations. PLOS One, 21(10), e0360069. https://doi.org/10.1371/journal.pone.0360069

Image Credits: AI Generated

DOI: 10.1371/journal.pone.0360069

Keywords: magnetorheological elastomer, vibration isolation, sliding mode control, radial basis function neural network, semi-active control, smart materials, hysteresis, nonlinear dynamics, adaptive control, resonance, magnetic field, PLOS One

The core challenge the researchers tackled is one that has haunted robotics engineers for decades. A robotic manipulator is a strongly coupled, nonlinear system: moving one joint changes the forces acting on every other joint, and the equations governing its motion involve inertia, Coriolis and centrifugal effects, gravity, and friction that all shift as the arm moves through space. When the actual mass or inertia of a link differs from the values in the controller’s internal model, when Coulomb and viscous friction resist motion in ways that are hard to characterize, or when external torques push on the arm, tracking accuracy degrades and stability can be compromised. The team, led by Xiaole Ma and corresponding author Chenghu Jing, built their approach on a rigorous mathematical model of the UR10 that explicitly accounts for these perturbations, lumping all the unknown dynamics into a single disturbance term that their controller must confront head-on.

Their solution rests on a division of labor between two complementary technologies. The first is a radial basis function neural network, a lightweight learning architecture prized for its simple structure and its ability to approximate any continuous nonlinear function within a defined region. Placed in the feedforward path of the controller, the network observes the robot’s state in real time and learns to predict the lumped unknown dynamics, from friction quirks to inertia mismatches. By absorbing the dominant nonlinearities before they can corrupt the motion, the network dramatically shrinks the size of the residual disturbance that the robust part of the controller must handle. This matters because the size of that residual directly determines how aggressive, and how energy-hungry, the robust control term needs to be.

That robust term is where the super-twisting algorithm enters the picture. Sliding-mode control is a classic robust technique: it drives the system’s tracking error onto a carefully chosen sliding surface and then uses aggressive switching to hold it there, making the system immune to a broad class of disturbances. The trouble is that conventional sliding-mode control relies on discontinuous switching, which produces the infamous phenomenon of chattering, a high-frequency oscillation in the control torque that excites unmodeled vibrations, wastes energy, and accelerates wear on actuators and gears. The super-twisting algorithm, a second-order sliding-mode technique, solves this problem elegantly. Instead of switching the torque itself, it applies a continuous combination of a term proportional to the square root of the sliding variable’s magnitude and an integral term, achieving the same finite-time convergence and disturbance rejection while producing a smooth, continuous control signal.

The Chinese team’s contribution is a carefully engineered synthesis of these two elements, backed by a rigorous stability proof. They defined a linear sliding surface based on the tracking error and its derivative, then constructed a control law with three modules: a nominal dynamic compensation term built from the robot’s known model, the neural network feedforward term for online approximation of unknown dynamics, and the super-twisting robust term to suppress residual disturbances. To keep the neural network’s weights from drifting to unbounded values, a common failure mode of adaptive schemes, they introduced a projection-based adaptive law that mathematically guarantees the weight estimates never exceed a preset safety boundary. Using Lyapunov stability theory, the researchers proved that both the sliding variable and the tracking error converge in finite time, with explicit gain conditions relating the super-twisting parameters to the disturbance bound.

The proof framework itself represents a departure from conventional practice. Rather than using the adaptive law to exactly cancel uncertainty terms, which can lead to gain drift and complicated derivations, the team adopted a decoupled design in which the neural network physically reduces the total disturbance bound. This allows the super-twisting gains to be substantially relaxed, cutting energy consumption and further suppressing chattering while preserving the finite-time stability guarantee. It is a design philosophy that treats the neural network and the robust controller as partners rather than competitors, each doing the job it is best suited for.

To test the approach, the researchers ran simulations on a full six-degree-of-freedom UR10 model using experimentally identified nominal parameters. They deliberately made the task hard: the masses of joints two and three were increased by twenty percent, centers of mass were shifted, inertias were perturbed by five percent, and a smooth sigmoidal friction model captured Coulomb and viscous effects in every joint. A sinusoidal external disturbance of 0.5 newton-meters was applied to all joints, and a fixed-gain study showed the method maintained tracking errors below 0.005 radians even when disturbances reached 2.0 newton-meters. The robot was commanded to move from one pose to another along a fifth-order polynomial trajectory over ten seconds, with a control period of one millisecond.

The results were emphatic. Under pure neural network control, lacking any robust term, the steady-state errors of the wrist joints ballooned to as much as 0.82 radians, with maximum errors exceeding one radian, an unacceptable failure. Conventional sliding-mode control fared far better, reducing steady-state errors to the thousandth-of-a-radian range, but the proposed composite controller cut them further still: joints four and five achieved steady-state errors of 0.0005 and 0.0017 radians, improvements of more than fifty percent and seventy-eight percent over pure sliding-mode control. All joints except one achieved steady-state errors better than one-thousandth of a radian. Measured by the integral of time-weighted absolute error, a standard metric combining response speed and steady-state accuracy, the composite controller outperformed pure sliding-mode control by 86.1 percent and pure neural network control by 99.7 percent. In Cartesian space, the end effector’s steady-state error shrank to 0.0002 meters, compared with 0.0007 meters for sliding-mode control and a disastrous 0.1031 meters for the network alone.

Just as important as the accuracy is the character of the control signals. The composite controller produced continuous, smooth torques free of the high-frequency chattering that traditional sliding-mode schemes generate, with peak torques around 62 newton-meters at joint two, comfortably below actuator saturation limits. The neural network’s weights, rather than growing without bound as they did under pure network control, stabilized at a low value after a brief transient, confirming that the super-twisting term was shouldering the main disturbance rejection burden while the network handled fine compensation. The method also proved its generality on continuous sinusoidal trajectories simulating industrial operation, with all joint root-mean-square errors below 0.003 radians. The authors note that future work will focus on experimental validation on a physical UR10 platform, adaptive optimization of the network structure, and integration of iterative learning with neural sliding-mode control. If hardware trials confirm the simulation results, this hybrid of learning and robust control could find a home in precision assembly, medical assistance, and any application where a robot arm must move exactly where it is told, even when the world pushes back.

Subject of Research: Composite neural network and super-twisting sliding-mode control for high-precision trajectory tracking of the UR10 robotic manipulator

Article Title: Trajectory-tracking control of the UR10 manipulator based on radial basis function neural network and super-twisting sliding mode

Article References: Ma, X., Jing, C., Zhang, K., Chen, C., & Wang, Y. (2026). Trajectory-tracking control of the UR10 manipulator based on radial basis function neural network and super-twisting sliding mode. Mechanical Sciences, 17(2), 759-767. https://doi.org/10.5194/ms-17-759-2026

Image Credits: AI Generated

DOI: 10.5194/ms-17-759-2026

Keywords: robotics, UR10 manipulator, trajectory tracking, sliding-mode control, super-twisting algorithm, radial basis function neural network, chattering suppression, adaptive control, Lyapunov stability, finite-time convergence, collaborative robots, nonlinear friction

The study, published in the International Journal of Aeronautical and Space Sciences, tackles a problem that has shadowed every membrane-based spacecraft concept since the earliest solar sail designs: the film itself deforms. When a sail twists under aerodynamic loading, its shape changes, and that change feeds back into the very torques that caused it. This coupling between torsional deformation and aerodynamic forces means that treating the sail as a rigid plate is not merely inaccurate, it can be fundamentally misleading. The research team, led by Shuiyuan Wu and Ming Xu with corresponding author Lincheng Li, built their analysis from the ground up, beginning with the physics of the film itself.

Their first step was to apply classical elasticity theory to calculate the torsional deformation of the thin membrane. Rather than stopping at an idealized analytical solution, the team cross-checked their results against a finite element simulation built on solid-shell elements, a numerical approach capable of capturing the behavior of structures that are thin in one dimension but extended in the other two. This dual verification matters because the deformation field directly determines how air molecules strike the surface, and therefore how much torque the sail experiences. An error of even a few degrees in the local surface inclination can shift the aerodynamic torque distribution across the entire membrane.

To translate the deformed geometry into forces, the researchers turned to the Schaaf–Chambre model, a foundational framework from the study of rarefied gas flows. At the altitudes where atmospheric sails operate, the air is so thin that molecules almost never collide with one another before hitting the spacecraft; the flow is instead governed by individual molecule-surface interactions. In this free molecular regime, the momentum transferred to the sail depends on how molecules reflect off the film, characterized by normal and tangential accommodation coefficients, and on the local angle of incidence. By integrating these molecular momentum exchanges over the deformed sail surface, the team derived the torques acting about all three axes and assembled a complete three-axis attitude dynamics model of the flexible sail.

One of the study’s quieter but more consequential findings is that the torques involved are remarkably small, all on the order of newton-meters. That may sound like good news, and in terms of structural loading it is, but it presents a severe challenge for control engineers. Actuators must respond to disturbances that are tiny, nonlinear, and constantly shifting as the membrane flexes. A controller that reacts too aggressively wastes precious energy and can excite vibrations in the film; one that reacts too sluggishly lets the sail drift off its intended attitude. The team’s answer to this dilemma is a composite scheme that pairs a radial basis function neural network, or RBFNN, with sliding mode control, a robust technique long favored for spacecraft attitude regulation.

Sliding mode control works by driving the system’s state onto a predefined sliding surface and then holding it there, offering strong guarantees against bounded disturbances. Its weakness is that it must treat unknown nonlinearities as disturbances to be overpowered, which demands larger control effort and can induce chattering. The RBFNN changes that equation. Because a radial basis function network can approximate arbitrary nonlinear functions given enough nodes, it can learn the unknown terms in the sail’s dynamics, specifically the nonlinear functions the researchers label f1(x), f3(x), and f5(x), and compensate for them directly. The simulations show that the network tracks these nonlinear terms rapidly and efficiently, effectively handing the sliding mode controller a much cleaner problem to solve.

The payoff is striking. When the RBFNN–SMC composite controller was applied, the torque required about the z-axis, Mz, dropped by as much as 55.2 percent compared with sliding mode control alone. Just as importantly, the physical motion of the sail films themselves became gentler. The rotation angles of the film segments, denoted β2, β3, and β4 in the study, were notably reduced under the hybrid scheme, with the motor rotation amplitude for β4 shrinking by 35.6 percent. For a membrane structure whose service life is limited by flexing, folding, and fatigue, smaller rotation angles translate directly into longer operational lifetimes. The researchers summarize this with an accumulated energy index, which came out lower under the composite controller, confirming that the neural network approach reduces total energy consumption rather than merely shifting it elsewhere in the system.

The implications extend well beyond a single simulation study. Atmospheric sails sit at the intersection of several pressing trends in space technology. Satellites destined for very low Earth orbit, where they can image the planet at higher resolution or serve as drag-based formation flyers, must constantly fight atmospheric drag, and sails offer a way to harness rather than resist it. Distributed drag sails have already been proposed for transverse satellite formation flying, and atmosphere-breathing electric propulsion concepts rely on the same rarefied flow physics that the Schaaf–Chambre model describes. Every one of these applications needs attitude control that is both precise and frugal, because small satellites cannot carry generous power budgets or oversized reaction hardware. A control scheme that cuts torque demand by more than half could be the difference between a feasible mission concept and an impractical one.

The study also contributes to a broader effort to model sail deformation rigorously. Previous work has examined the structural response of large solar sails during attitude maneuvers, analyzed wrinkling of solar-photon sails, and used point cloud methods to characterize sail deformation. What distinguishes the new research is its end-to-end treatment: the deformation is computed analytically, verified numerically, fed into a free molecular flow model to produce torques, and then closed into a full attitude dynamics loop where the controller must cope with the coupled torsional-aerodynamic effects. This chain matters because the coupling is precisely what makes deformable sails hard to control. A film that twists changes its own aerodynamic loading, which changes the torque, which changes the twist again. A controller blind to this loop would either fight it wastefully or be destabilized by it.

For now, the results come from simulation, and the transition to flight hardware will demand further validation, including how the neural network performs under model uncertainties, thermal-induced membrane vibrations, and the messy realities of actuator saturation. But the direction is clear. As membranes grow larger and spacecraft grow smaller, the era of treating flexible structures as rigid bodies is ending. Machine learning is increasingly finding its way into spacecraft control, from fault-tolerant attitude tracking with neural estimators to adaptive neural sliding controllers for rotorcraft and hypersonic vehicles. This study adds a compelling data point to that trend, showing that a well-trained network can shoulder the nonlinear burden of a flexing sail and leave the robust core of the controller free to do its job with a fraction of the effort. If atmospheric sails are to sweep through the thin air of low orbit in the years ahead, they may well do so with a neural network quietly trimming their course, saving energy with every gentle turn of the film.

Subject of Research: Energy-efficient neural network attitude control of deformable atmospheric sails under coupled torsional and aerodynamic effects

Article Title: Energy-Efficient RBFNN-SMC Attitude Control of Deformable Atmospheric Sail Under Coupled Torsional-Aerodynamic Effects

Article References: Wu, S., Xu, M., Li, L., Wang, H., & Meng, D. (2026). Energy-Efficient RBFNN-SMC Attitude Control of Deformable Atmospheric Sail Under Coupled Torsional-Aerodynamic Effects. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01241-4

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01241-4

Keywords: atmospheric sail, attitude control, RBF neural network, sliding mode control, torsional deformation, free molecular flow, very low Earth orbit, spacecraft dynamics, membrane structures, energy efficiency, aerodynamic torque, flexible spacecraft

The central challenge the researchers tackled is a fundamental tension in flight control. On one hand, engineers want to guarantee that the aircraft’s tracking errors stay within strict bounds, a property known as prescribed performance, so that the jet never strays outside a safe corridor during its descent. On the other hand, the aircraft’s control surfaces and engine thrust are physically limited. When a controller demands more deflection or thrust than the actuators can deliver, a condition called actuator saturation, the aircraft temporarily stops obeying commands and the error can breach the very boundaries the performance function was designed to enforce. Once those boundaries are violated, many prescribed performance controllers fail catastrophically, because their mathematics assumes the error always remains inside a constrained domain.

The Harbin team’s solution is elegantly pragmatic: rather than pretending saturation will never happen, they built a controller that bends without breaking. At the heart of the method lies a predefined-time prescribed performance function, a mathematical curve that dictates how quickly and how tightly the landing error must shrink. Unlike conventional exponential convergence guarantees, which depend on initial conditions, a predefined-time guarantee ensures the error converges within a time chosen by the designer, no matter where the aircraft starts. This is a significant advantage in carrier operations, where the approach window is short and unforgiving and where an autopilot that converges ‘eventually’ is not good enough.

To work with these constraints mathematically, the researchers employed an error transformation technique that converts the constrained error domain into an equivalent unconstrained one. In essence, the transformation warps the coordinate system so that as long as the transformed error remains bounded, the physical landing error is guaranteed to stay inside its prescribed funnel. This allows standard control design tools to be applied to a problem that would otherwise involve hard, nonlinear boundaries. The transformed error then feeds into a nonsingular fast terminal integral sliding mode controller, a robust control strategy renowned for its ability to reject external disturbances. The ‘terminal’ component drives errors to zero in finite time rather than merely asymptotically, while the ‘nonsingular’ design avoids the mathematical pitfalls, such as division by zero, that plague naive terminal sliding mode formulations.

The truly novel ingredient, however, is the flexible adjustment mechanism embedded within the performance function itself. When the controller detects that actuators are saturating, meaning the aircraft cannot fully execute the commanded deflections, the mechanism adaptively relaxes the local performance boundaries, giving the aircraft room to recover rather than demanding the impossible. Once the saturation episode passes, the boundaries tighten again, and the landing proceeds with its original accuracy targets intact. This adaptive flexibility prevents the boundary violations that would otherwise cause the error transformation to blow up and the controller to fail. Complementing this mechanism, the team designed an auxiliary system that maintains stability during saturation events, a well-known strategy in the control literature that the authors integrated carefully with their performance framework.

Disturbance rejection receives equally thorough treatment. The turbulent airwake behind a carrier’s island superstructure is modeled in the study as a set of external disturbances acting on the aircraft’s translational and rotational dynamics, with components that vary sinusoidally over time to mimic the chaotic flow field. To counter these, the researchers developed a predefined-time disturbance observer, an algorithm that estimates the unknown disturbance signals and feeds the estimates directly into the control law as compensation. Because the observer converges in predefined time, the compensation kicks in quickly enough to matter during the brief final approach. The team also introduced a predefined-time reference model to generate the command signals that the inner control loops track. This choice eliminates a chronic computational problem in conventional backstepping control designs, where repeated differentiation of command signals leads to ‘explosion of complexity,’ an exponential growth in the analytic terms that must be computed at each step.

The aircraft model used in the study is a full six-degree-of-freedom representation of a carrier-based aircraft, complete with the coupling between roll, pitch, and yaw dynamics that arises from the aircraft’s inertia properties, aerodynamic coefficients for lift, drag, and side force, and the contributions of the elevator, aileron, rudder, and direct lift flap. The guidance problem is framed as following a moving deck landing path, with the controller tasked with tracking the ship’s motion while respecting output constraints on altitude and attitude errors. This comprehensive modeling matters, because simplified models often hide exactly the coupling effects that make real carrier approaches so treacherous, particularly the way lateral gusts induce rolling moments that must be countered within fractions of a second.

To benchmark their approach, the authors compared FPTPPC against three competing strategies in simulation: dynamic inverse control, a classical technique that cancels the aircraft’s nonlinearities through model inversion; predefined-time control without prescribed performance; and standard prescribed performance control without the flexible saturation mechanism. The results showed that the proposed method reduced path following errors and improved overall landing accuracy relative to all three baselines. The simulations also demonstrated that the flexible adjustment mechanism kept the controller stable and accurate through saturation events that would have destabilized a rigid prescribed performance design. While the study is computational rather than flight-tested, the consistency of the improvements across the comparison set lends weight to the practical promise of the approach.

The implications extend beyond naval aviation. The core ideas, predefined-time convergence guarantees, flexible performance boundaries that tolerate actuator limits, and disturbance observers that compensate within a designer-chosen horizon, are directly transferable to other safety-critical control problems, including spacecraft attitude control, unmanned aerial vehicle operations in gusty conditions, and robotic systems with limited actuator authority. Related work in the same journal and elsewhere has begun applying predefined-time and anti-saturation techniques to fault-tolerant flight control, suggesting a broader research movement toward controllers that are honest about physical limits rather than assuming them away. For the moment, the Harbin team’s contribution stands as a careful piece of control engineering: a mathematically rigorous answer to the question of what an autopilot should do when the ideal command and the possible command diverge, at the worst possible moment, a few hundred feet above a moving flight deck.

Subject of Research: Automatic carrier landing control using flexible predefined-time prescribed performance control under output constraints, actuator saturation, and airwake disturbances

Article Title: Flexible Predefined-Time Prescribed Performance Control for Automatic Carrier Landing with Output Constraints and Actuator Saturation

Article References: Wang, Z., Zhu, Q., Kong, L., & Wang, L. (2026). Flexible Predefined-Time Prescribed Performance Control for Automatic Carrier Landing with Output Constraints and Actuator Saturation. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01239-y

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01239-y

Keywords: automatic carrier landing, prescribed performance control, predefined-time control, actuator saturation, sliding mode control, airwake disturbance, flight control systems, disturbance observer, carrier-based aircraft, nonlinear control, landing accuracy, Harbin Engineering University

The research, published in the International Journal of Aeronautical and Space Sciences by Qilong Wu of Huainan Normal University, Qidan Zhu of Harbin Engineering University, and their colleagues, including Lunpan Wei, Lipeng Wang, and Wenqiang Jiang of the China Ship Development and Design Center, tackles a problem that has long frustrated engineers: how to guarantee that a landing aircraft stays on its glide path within a strictly bounded error, and that it does so within a time window chosen in advance by the designer, regardless of where the aircraft starts its approach. The work was supported by the National Natural Science Foundation of China and other national and provincial funding bodies.

At the heart of the new scheme is what the authors call a predefined-time prescribed performance function, or PTPPF. Prescribed performance control is a technique that constrains the tracking error, the difference between where the aircraft should be and where it actually is, to remain inside a shrinking envelope. Think of it as a funnel around the ideal glide slope: the aircraft’s deviation is mathematically forbidden from escaping the funnel walls, and the funnel narrows as the aircraft nears the deck. What makes the new formulation distinctive is the predefined-time element. In many conventional designs, the convergence of the error depends on the initial conditions, meaning a jet that starts its approach far from the ideal path may take an unpredictable amount of time to settle. The PTPPF removes that dependency entirely, guaranteeing that the error converges within a time set by the control engineer before the mission even begins.

Guaranteeing a bounded error is only half the battle, however. The second pillar of the approach is a predefined-time sliding mode controller, or PTSMC. Sliding mode control is a well-established robust technique that drives a system’s state onto a chosen sliding surface and then forces it to slide along that surface toward the target, effectively ignoring matched uncertainties and external disturbances along the way. Its weakness has traditionally been the chattering phenomenon, in which the control signal oscillates rapidly, and the fact that classical finite-time versions offer convergence speeds that vary with initial conditions. The predefined-time variant designed by the team enhances robustness against the nonlinear uncertainties and external disturbances that plague carrier approaches, while ensuring that the sliding dynamics complete their work within the designer’s chosen deadline.

The third and perhaps most ingenious component is a prescribed-time extended state observer, or PTESO. Extended state observers are devices that treat all the unknown disturbances acting on a system, including unmodeled dynamics, wind gusts, and even actuator faults, as an additional augmented state to be estimated alongside the system’s physical states. Once estimated, these lumped disturbances can be cancelled out in real time within the control loop, a strategy known as active disturbance rejection. The prescribed-time version developed here goes further: it promises that its estimates of the combined disturbances and actuator faults become accurate within a prescribed time, allowing the controller to compensate for a failing elevator or a sudden shift in the ship’s turbulent wake almost as soon as it occurs, rather than gradually over the course of the approach.

To prove that this elaborate architecture is safe rather than merely plausible, the authors carried out a Lyapunov-based stability analysis. Lyapunov methods are the gold standard of nonlinear control theory: the designer constructs an energy-like function of the closed-loop system and demonstrates mathematically that this function decreases along the system’s trajectories, which implies that all signals remain bounded and that the tracking error behaves as intended. In this case, the analysis establishes two critical guarantees simultaneously: every closed-loop signal stays bounded, and the tracking error converges within the predefined time, no matter the initial conditions. That combination of boundedness and deadline-driven convergence is what separates this work from earlier prescribed performance designs, which typically offered only asymptotic or condition-dependent convergence.

The true test of any carrier landing control law comes in simulation that faithfully reproduces the hostile environment of a moving flight deck. The team’s carrier landing experiments incorporated three of the most punishing factors at once: the carrier air-wake, the turbulent and horizontally offset airflow generated by the ship’s island superstructure as it washes over the approaching aircraft; the deck motion, meaning the heave, pitch, and roll of the landing point as the ship responds to waves; and actuator faults, including partial loss of control effectiveness. These are precisely the coupled hazards that have caused past approaches to degrade, because a controller tuned for calm conditions can be overwhelmed when disturbances and hardware failures arrive together.

The results, according to the authors, show that the proposed method significantly improves transient performance, disturbance rejection, and landing accuracy compared with existing techniques. Transient performance matters enormously in this context: the moments right after the aircraft enters the glide path, or right after a fault occurs, are when deviations are largest and most dangerous. By confining the error inside the prescribed performance funnel from the very start and compensating disturbances through the observer in real time, the scheme keeps those dangerous excursions small and short-lived. The practical implication is a tighter, more predictable touchdown point on the deck, which translates directly into reduced structural stress on the airframe and lower risk of missing the arresting wires.

The significance of the predefined-time formulation becomes clearer when one considers the communication environment referenced in the study’s title. Carrier-based aircraft operate in data links with the ship, and guidance updates may arrive late or intermittently. A control law whose convergence time balloons when conditions are unfavorable offers no firm promise to the pilot or the mission planner. By contrast, a scheme in which the error is guaranteed to converge within a time fixed at design stage, independent of initial conditions, allows the entire approach to be choreographed against a known clock, which is essential when the landing window is dictated by the ship’s motion and the recovery schedule of the air wing.

The work also fits into a broader and rapidly accelerating research trend. Fixed-time and predefined-time control methods have recently swept through the control theory literature, with applications demonstrated for multiagent consensus, microgrid frequency regulation, hypersonic vehicles, spacecraft attitude stabilization, and quadrotor drones, including vehicles suffering actuator failures. Meanwhile, extended state observers have been combined with sliding mode and super-twisting techniques for carrier landing in a series of recent studies, and fault-tolerant control for carrier-based aircraft has evolved from fault reconstruction schemes to adaptive neural approaches. The new paper synthesizes these strands, wrapping a predefined-time prescribed performance function, a predefined-time sliding mode controller, and a prescribed-time extended state observer into a single fault-tolerant architecture with formal stability proofs.

For now, the results rest on simulation experiments rather than flight tests, and the authors note that the underlying code is not publicly available due to project confidentiality and institutional restrictions, though it can be requested from the corresponding author for academic purposes. The data supporting the findings are likewise available upon reasonable request with laboratory approval. Those caveats are standard for research at this stage, and the gap between simulated and real carrier operations remains a formidable one, involving sensor noise, actuator saturation limits, and the sheer unpredictability of the maritime environment. Nevertheless, the mathematical guarantees established in the paper, bounded closed-loop signals and deadline-driven error convergence under simultaneous air-wake disturbance, deck motion, and actuator faults, represent a meaningful step toward the long-sought goal of fully autonomous, fault-resilient carrier recoveries. If future flight validation confirms the simulation results, the technology could one day allow unmanned carrier-based aircraft, and perhaps crewed ones, to come aboard in conditions that today demand the finest human piloting skills in existence.

Subject of Research: Fault-tolerant predefined-time control for automatic aircraft carrier landing under air-wake disturbances and actuator faults

Article Title: Robust Predefined-Time Fault-Tolerant Prescribed Performance Control for Automatic Carrier Landing in Communication Environments Under Air-Wake Disturbances and Actuator Faults

Article References: Wu, Q., Zhu, Q., Wei, L., Wang, L., & Jiang, W. (2026). Robust Predefined-Time Fault-Tolerant Prescribed Performance Control for Automatic Carrier Landing in Communication Environments Under Air-Wake Disturbances and Actuator Faults. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01266-9

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01266-9

Keywords: automatic carrier landing, fault-tolerant control, predefined-time control, sliding mode control, prescribed performance, extended state observer, air-wake disturbance, actuator faults, Lyapunov stability, carrier-based aircraft, flight control systems, disturbance rejection

The challenge the researchers set out to solve is deceptively simple to state and fiendishly difficult to solve. A variable sweep wing aircraft undergoing rapid and continuous configuration switching is, from a control standpoint, a moving target. Its mass properties, aerodynamic coefficients, and stability derivatives all shift as the wings sweep. Worse, unsteady aerodynamic effects mean the forces and moments acting on the vehicle at any instant depend not just on the current wing position but on the history of how it got there. This produces aerodynamic hysteresis loops, in which lift, drag, and pitching moment trace different paths depending on whether the wing is sweeping in or sweeping out. Traditional control models that assume quasi-steady aerodynamics simply miss these dynamics, and the resulting tracking errors can compound dangerously in complex flight environments.

The research team, led by Yuequn Gao with Linfeng Tian, Ao Li, and corresponding author Luhua Liu, began by building a longitudinal dynamic model of the variable sweep wing aircraft that explicitly incorporates unsteady aerodynamic effects. Rather than treating the hysteresis as an unmodeled disturbance, they derived hysteresis correction terms and folded them directly into the equations of motion, alongside the additional forces and moments that morphing itself induces. By analyzing the mechanism behind the hysteresis loops, the team gained a mathematical handle on a phenomenon that has bedeviled morphing flight since early experimental studies of sweep-varying wings documented the same lagging behavior decades ago. This modeling foundation is what allows the rest of the control architecture to compensate for unsteadiness rather than merely react to its symptoms.

The true novelty of the approach lies in how it rethinks prescribed performance control. In the traditional framework, engineers define a fixed performance envelope, essentially a corridor of acceptable tracking error that shrinks exponentially toward a small final bound. As long as the error stays inside the corridor, guarantees on overshoot, convergence, and steady-state accuracy hold. But a rigid corridor is a poor fit for an aircraft whose dynamics swing wildly during wing sweep. Demanding ultra-tight tracking precisely when the aerodynamics are most pathological wastes control authority, invites aggressive actuation, and can even trigger the numerical singularities and high-frequency chattering that sliding mode controllers are notorious for. The team’s answer is a flexible prescribed performance factor constructed from the morphing rate and the instantaneous tracking error, allowing the performance boundary to widen when the aircraft is morphing hard and to tighten when conditions permit.

This adaptive envelope means the controller behaves like an experienced pilot rather than an inflexible autopilot. During calm flight, it holds the vehicle to exacting accuracy standards. During rapid configuration switching, it temporarily relaxes the corridor in proportion to the morphing rate and the risk of hitting the boundary, then snaps back to precision once the geometry stabilizes. The boundary adjustment is not heuristic guesswork; it is built into the error transformation that shapes the control law, so the guarantees of prescribed performance theory still apply, just with a moving target. The result is a control philosophy that spends its authority where it matters most, a principle the authors argue is essential for vehicles whose dynamics are inherently time-varying.

On top of this flexible envelope, the researchers constructed a novel fixed-time reaching law, the mechanism that drives the tracking error onto a sliding surface and holds it there. Fixed-time sliding mode control differs from its finite-time cousins in a crucial way: the convergence time bound does not depend on the initial conditions. No matter how far the aircraft has strayed from its reference trajectory, the theory guarantees the error system will converge within a fixed maximum settling time, an explicit expression combining the controller’s gain parameters. To achieve this, the team merged fast sliding mode dynamics with radial basis function neural networks, which learn and cancel the lumped uncertainties that neither the model nor any observer can predict, including residual unsteady effects and external disturbances such as wind gusts.

Practical flight also demands respect for hardware limits, and the control law addresses them head-on. Actuator saturation, the condition in which commanded deflections exceed what physical surfaces can deliver, is compensated through an anti-saturation term woven directly into the error system. This prevents the classic failure mode in which an aggressive controller demands more authority than the aircraft possesses, degrading tracking and potentially destabilizing the vehicle. The neural approximation further suppresses chattering, the high-frequency oscillation that plagues conventional sliding mode designs, by absorbing the discontinuous components of the disturbance estimate. Together, these elements let the controller achieve rapid tracking under unsteady aerodynamics, model uncertainties, actuator constraints, and external disturbances simultaneously, rather than handling each problem in isolation.

Rigor underpins the whole construction. The team proved fixed-time stability of the closed-loop system using Lyapunov theory, deriving explicit bounds on the settling time and demonstrating that the transformed tracking error remains strictly inside the flexible performance envelope for all time. The appendices of the paper walk through the inequalities that establish these guarantees, including a demonstration that the envelope transformation maps the error into a bounded interval, ensuring the prescribed performance constraints cannot be violated even during the most aggressive morphing maneuvers. Comparative simulations then pitted the proposed controller against three alternative fixed-time sliding mode designs. Across complex scenarios involving rapid wing sweep, unsteady aerodynamic hysteresis, and external disturbances, the new method maintained its performance constraints, suppressed control singularities and chattering, and delivered superior tracking accuracy, validating the theory in silico.

The implications reach well beyond one class of aircraft. Morphing flight vehicles, from variable-sweep waveriders and hypersonic glide vehicles to span-morphing drones, all share the same core dilemma: their performance envelope changes as fast as their shape. Flexible prescribed performance control, informed by morphing rate and boundary risk as demonstrated here, offers a template for how future flight control systems can adapt their own strictness in real time. The research was supported by the Science and Technology on Space Physics Laboratory, the Shenzhen Science and Technology Program, and the National Natural Science Foundation of China, and the authors report no competing interests. As morphing aircraft move from laboratory concepts toward operational platforms, controllers that can reason about unsteady aerodynamics, respect actuator limits, and guarantee convergence in a fixed time may prove to be the difference between a shape-shifting aircraft that flies and one that merely flails. This work marks a substantial step toward that operational future.

The distinction between fixed-time and finite-time convergence deserves further emphasis, because it explains why the choice of reaching law matters for real missions. In finite-time designs, the settling time bound grows with the magnitude of the initial tracking error, so a vehicle that begins a maneuver far from its commanded attitude may, in principle, take arbitrarily long to settle. Fixed-time formulations remove this dependency by structuring the error dynamics so that the worst-case convergence time is a constant determined solely by the controller gains. For a morphing aircraft, where large transient errors can appear suddenly each time the sweep angle changes, this property provides a uniform performance promise across the entire flight envelope rather than a promise that weakens precisely when the vehicle is most stressed.

The use of radial basis function neural networks also reflects a broader trend in flight control toward learning-based uncertainty rejection. Because the network approximates unknown nonlinear functions locally and can be trained online from the observed error signals, it does not require a precise parameterization of the hysteresis terms it compensates. This is valuable when unsteady aerodynamic models are derived from wind tunnel or computational data that may not match flight conditions exactly. The approximation residual is handled by the robust sliding mode component, creating a layered defense in which learning absorbs the predictable portion of the uncertainty and the discontinuous term guarantees boundedness of what remains.

Equally significant is the decision to treat actuator saturation within the stability proof itself rather than as an afterthought. Saturation is among the most common causes of loss of control in aggressive maneuvering, and control laws that ignore it can appear stable in simulation yet fail in hardware. By folding anti-windup compensation into the error transformation, the authors ensure that the fixed-time and performance guarantees remain meaningful when the surfaces reach their limits, addressing the gap between theoretical convergence and what a physical actuator can actually deliver during rapid wing sweep maneuvers.

Subject of Research: Adaptive fixed-time tracking control of variable sweep wing morphing aircraft under unsteady aerodynamic effects

Article Title: Adaptive Fixed-Time Tracking Control for Morphing Aircraft with Flexible Prescribed Performance Under Unsteady Aerodynamics Effects

Article References: Gao, Y., Tian, L., Li, A., & Liu, L. (2026). Adaptive Fixed-Time Tracking Control for Morphing Aircraft with Flexible Prescribed Performance Under Unsteady Aerodynamics Effects. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01294-5

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01294-5

Keywords: morphing aircraft, variable sweep wing, fixed-time control, sliding mode control, prescribed performance, unsteady aerodynamics, aerodynamic hysteresis, neural networks, actuator saturation, flight control, tracking accuracy, Lyapunov stability