Search Results (184)

This study introduces an innovative self-regulating intelligent optimal balancing control framework for inverted pendulum-type mechatronic platforms, designed to enhance reference tracking accuracy and improve disturbance rejection capability. The control procedure is synthesized by synergistically integrating a baseline Linear Quadratic Regulator (LQR) with a fuzzy controller via a customized linear decomposition function (LDF). The LDF dissociates and transforms the LQR control law into compounded state tracking error and tracking error derivative variables that are eventually used to drive the fuzzy controller. The principal contribution of this study lies in the adaptive modulation of these compounded variables using reconfigurable tangent hyperbolic functions driven by the cubic power of the error signals. This nonlinear preprocessing of the input variables selectively amplifies large errors while attenuating small ones, thereby improving robustness and reducing oscillations. Moreover, a model-free online self-tuning law dynamically adjusts the variation rates of the hyperbolic functions through dissipative and anti-dissipative terms of the state errors, enabling autonomous reconfiguration of the nonlinear preprocessing layer. This dual-level adaptation enhances the flexibility and resilience of the controller under perturbations. The robustness of the designed controller is substantiated via tailored experimental trials conducted on the Quanser rotary pendulum platform. Comparative results show that the prescribed scheme reduces pendulum angle variance by 41.8%, arm position variance by 34.6%, and average control energy by 28.3% relative to the baseline LQR, while outperforming conventional fuzzy-LQR by similar margins. These results show that the prescribed controller significantly enhances disturbance rejection and tracking accuracy, thereby offering a numerically superior control of inverted pendulum systems. Full article

A wheeled–legged robot has the advantage of stable and agile movement on flat ground and an excellent ability to overcome obstacles. However, when faced with a narrow footprint, there is a limit to its ability to move. We developed the control moment gyroscope (CMG) unicycle–legged robot to solve this problem. A scissored pair of CMGs was applied to control the roll balance, and the pitch balance was modeled as a double-inverted pendulum. We performed Linear Quadratic Regulator (LQR) control and model predictive control (MPC) in a system in which the control systems in the roll and pitch directions were separated. We also devised a method for controlling the rotation of the robot in the yaw direction using torque generated by the CMG, and the performance of these controllers was verified in the Gazebo simulator. In addition, forward driving control was performed to verify mobility, which is the main advantage of the wheeled–legged robot; it was confirmed that this control enabled the robot to pass through a narrow space of 0.15 m. Before implementing the verified controllers in the real world, we built a CMG test platform and confirmed that balancing control was maintained within $\pm 1^{\circ }$. Full article

In this study, a nonlinear dynamic model is developed to examine the stability and vibration behavior of a self-balancing electric Segway operating over irregular stochastic terrains. The Segway is treated as a three-degrees-of-freedom cart–inverted pendulum system, incorporating elastic and damping effects at the wheel–ground interface. Road irregularities are generated in accordance with international standard using high-order filtered noise, allowing for representation of surface classes from smooth to highly degraded. The governing equations, formulated via Lagrange’s method, are transformed into a Lorenz-like state-space form for nonlinear analysis. Numerical simulations employ the fourth-order Runge–Kutta scheme to compute translational and angular responses under varying speeds and terrain conditions. Frequency-domain analysis using Fast Fourier Transform (FFT) identifies resonant excitation bands linked to road spectral content, while Kernel Density Estimation (KDE) maps the probability distribution of displacement states to distinguish stable from variable regimes. The Lyapunov stability assessment and bifurcation analysis reveal critical velocity thresholds and parameter regions marking transitions from stable operation to chaotic motion. The study quantifies the influence of the gravity–damping ratio, mass–damping coupling, control torque ratio, and vertical excitation on dynamic stability. The results provide a methodology for designing stability control systems that ensure safe and comfortable Segway operation across diverse terrains. Full article

Underactuated systems, such as rotary and double inverted pendulums, challenge traditional control due to nonlinear dynamics and limited actuation. Classical methods like state-feedback and Linear Quadratic Regulators (LQRs) are commonly used but often require high gains, leading to excessive control effort, poor energy efficiency, and reduced robustness. This article proposes a generalized state-feedback controller with its own internal dynamics, offering greater design flexibility. To automate tuning and avoid manual calibration, we apply Bayesian Optimization (BO), a data-efficient strategy for optimizing closed-loop performance. The proposed method is evaluated on two benchmark underactuated systems, including one in simulation and one in a physical setup. Compared with standard LQR designs, the BO-tuned state-feedback controller achieves a reduction of approximately 20% in control signal amplitude while maintaining comparable settling times. These results highlight the advantages of combining model-based control with automatic hyperparameter optimization, achieving efficient regulation of underactuated systems without increasing design complexity. Full article

The control of a biped robot is a challenging task due to the hard-to-stabilize dynamics. Generating a suitable walking reference trajectory is a key aspect of this problem. This article proposes a novel method of generating walking patterns for biped robots. The method integrates the double support phase and the single support phase into one step, and uses this step as the unit for trajectory generation through quadratic optimization with terminal constraints based on the Linear Inverted Pendulum Model, enabling us to shorten the optimization horizon while still generating natural walking trajectories. Moreover, by restricting the position and acceleration of the center of mass (COM) in the vertical direction, an excessive constraint is formed on the Zero Moment Point (ZMP) to offset the nonlinear effects of the COM’s vertical motion on the ZMP. This allows the COM of the robot to change in the vertical direction while maintaining the linearity of the optimization problem. Finally, the performance of the proposed method is validated by simulations and experiments of walking on flat ground and stairs using a position-controlled biped robot, Neubot. Full article

Gait analysis plays a crucial role in assessing and monitoring the progress of individuals undergoing rehabilitation. This preliminary validation study aims to compare the performance of a new wearable system, NeuroSkin^®, equipped with embedded sensors (inertial measurement unit and pressure sensors), with the non-wearable gold standard, GAITRite^®, in assessing spatio-temporal parameters during gait. Data was collected from nine healthy participants wearing the NeuroSkin while walking on the GAITRite walkway. Temporal parameters were calculated using the pressure sensors of the NeuroSkin^® to detect heel strike (HS) and toe off (TO) on both sides. Distances were calculated using vertical hip acceleration with an inverted pendulum method. We found that the level of agreement between NeuroSkin^® and GAITRite^® measures was excellent for speed, cadence, as well as length and duration of stride and step (lower bound of intraclass correlation coefficients (ICCs) > 0.95), and moderate to excellent for stance and swing durations (ICC > 0.5). These levels of agreement are comparable to the known test–retest reliability of GAITRite^® measures. These results demonstrate the potential of NeuroSkin^® as an embedded gait assessment system for healthy subjects. As this study was conducted exclusively in healthy adults, the results are not directly generalizable to clinical populations. Thus, future studies are needed to investigate its use in patients. Full article

This paper presents a comprehensive study of an ESP32 microcontroller-based self-balancing mobile robot system designed in conjunction with an Android app for Bluetooth control. The robot employs an MPU6050 accelerometer/gyroscope to execute dynamic equilibrium control for robotic balance. This study explores the design of a system composed of an ESP32-based dual-platform architecture. The firmware for the ESP32 executes real-time motor control and sensor processing, while the Android application provides the user interface, data visualization, and command transmission. The system achieves stable operation with tilt angle variations of ±2.5° ($\sigma =0.8°$, n = 50 trials) during normal operation with a PID controller tuned to KP = 6.0, KI = 0.1, and KD = 1.5. In experimental tests, control latency was measured at 38–72 ms (mean = 55 ms, $\sigma =12$ ms) over distances of 1–10 m with a robust Bluetooth connection. Extended operational tests indicated the reliability of both autonomous obstacle avoidance mode and manual control exceeding 95%. Key contributions include gyro drift compensation using a progressive calibration scheme, intelligent battery management for operational efficiency, and a dual-mode control interface to facilitate seamless transition between manual and autonomous operation. Processing of real-time telemetry on the Android application allows visualization of important parameters like tilt angle, motor speeds, and sensor readings. This work contributes to a cost-effective mobile robotics platform (total cost: USD 127) through the provision of detailed design specifications, implementation strategies, and performance characteristics. Full article

This study introduces a novel model reference adaptive control (MRAC) framework that incorporates fractional-order gradients (FGs) to regulate the displacement of an inverted pendulum-cart system. Fractional-order gradients have been shown to significantly improve convergence rates in domains such as machine learning and neural network optimization. Nevertheless, their integration with fractional-order error models within adaptive control paradigms remains unexplored and represents a promising avenue for research. The proposed control scheme extends the classical MRAC architecture by embedding Caputo fractional derivatives into the adaptive law governing parameter updates, thereby improving both convergence dynamics and control flexibility. To ensure optimal performance across multiple criteria, the controller parameters are systematically tuned using a multi-objective Particle Swarm Optimization (PSO) algorithm. Two fractional-order error models (FOEMs) incorporating fractional gradients (FOEM2-FG, FOEM3-FG) are investigated, with their stability formally analyzed via Lyapunov-based methods under conditions of sufficient excitation. Validation is conducted through both simulation and real-time experimentation on a physical pendulum-cart setup. The results demonstrate that the proposed fractional-order MRAC (FOMRAC) outperforms conventional MRAC, proportional-integral-derivative (PID), and fractional-order PID (FOPID) controllers. Specifically, FOMRAC-FG achieved superior tracking performance, attaining the lowest Integral of Squared Error (ISE) of $2.32\times {10}^{-5}$ and the lowest Integral of Squared Input (ISI) of 6.40 in simulation studies. In real-time experiments, FOMRAC-FG maintained the lowest ISE ($5.11\times {10}^{-6}$). Under real-time experiments with disturbances, it still achieved the lowest ISE ($1.06\times {10}^{-5}$), highlighting its practical effectiveness. Full article

This study introduces a novel control strategy tailored to nonlinear systems with non-minimum phase (NMP) characteristics. The framework leverages reinforcement learning within a cascade control architecture that integrates an Actor–Critic structure. Controlling NMP systems poses significant challenges due to the inherent instability of their internal dynamics, which hinders effective output tracking. To address this, the system is reformulated using the Byrnes–Isidori normal form, allowing the decoupling of the input–output pathway from the internal system behavior. The proposed control architecture consists of two nested loops: an inner loop that applies input–output feedback linearization to ensure accurate tracking performance, and an outer loop that constructs reference signals to stabilize the internal dynamics. A key innovation in this design lies in the incorporation of symmetry principles observed in both system behavior and control objectives. By identifying and utilizing these symmetrical structures, the learning algorithm can be guided toward more efficient and generalized policy solutions, enhancing robustness. Rather than relying on classical static optimization techniques, the method employs a learning-based strategy inspired by previous gradient-based approaches. In this setup, the Actor—modeled as a multilayer perceptron (MLP)—learns a time-varying control policy for generating intermediate reference signals, while the Critic evaluates the policy’s performance using Temporal Difference (TD) learning. The proposed methodology is validated through simulations on the well-known Inverted Pendulum system. The results demonstrate significant improvements in tracking accuracy, smoother control signals, and enhanced internal stability compared to conventional methods. These findings highlight the potential of Actor–Critic reinforcement learning, especially when symmetry is exploited, to enable intelligent and adaptive control of complex nonlinear systems. Full article

Balance control in pirouettes has previously been characterized by constraint of the topple angle. However, there is a paucity of research using the margin of stability (MoS) as a dynamic measure of balance related to pirouettes. Therefore, this study aimed primarily to examine the MoS as a metric of balance during a single-turn en dehors pirouette in healthy female amateur ballet dancers. Four participants performed pirouettes until five successful pirouettes were achieved without hopping or loss of balance. Three-dimensional motion capture was used to record the motion trajectories of anatomical markers based on the Plug-in-Gait and Oxford Foot models. Motion synchronized with ground reaction forces was used to calculate the center of pressure (CoP), base of support (BoS), center of the pivot foot, center of mass (CoM), and extrapolated center of mass (XCoM) throughout the turn phase, using laboratory (LCS) and virtual left foot (LFT) coordinate systems. In the LCS and LFT coordinate system, the excursions and patterns of motion of both the CoM and XCoM relative to the CoP were similar, suggesting a neurological relationship. Two different measures of the margin of stability (MoS) in the LFT coordinate system were tabulated: the distance between the (1) XCoM and CoP and (2) XCoM and BoS center. The magnitude of both versions of the MoS was greatest at turn initiation and toe-touch, which was associated with two foot contacts. The MoS values were at a minimum approximately 50% of the stance during the turn phase: close to zero along the anteroposterior (A/P) axis and approximately 50 mm along the mediolateral (M/L) axis. On average, MoS magnitudes were reduced (mean across participants: approximately 20 mm) along the A/P axis, and larger MoS magnitudes (mean across participants: approximately 50 mm) along the M/L axis throughout the turn phase. Although all turns analyzed were completed successfully, the larger MoS values along the M/L axis suggest a fall potential. The variability between trials within a dancer and across participants and trials was documented and showed moderate inter-trial (16% to 51%) and across-participant CV% (range: 10% to 28%), with generally larger variations along the A/P axis. Although our results are preliminary, they suggest that the MoS may be useful for detecting faults in the control of dynamic balance in dehors pirouette performance, as a part of training and rehabilitation following injury. Full article

Virtual synchronous generator (VSG) control has been increasingly utilized for the grid integration of the voltage source inverter (VSI). Under large disturbances, such as voltage sags and grid faults, the VSG synchronization dynamic is highly nonlinear and cannot be evaluated by small-signal-based approaches. Conventionally, the equal area criterion (EAC) is utilized to analyze the transient stability of a synchronous machine or a VSG. However, it is found that the EAC is only valid under special scenarios when the damping effect is ignored. In this case, the EAC will provide conservative predictions and therefore put stringent requirements on the fault-clearing time. This paper reveals that the motion of a pendulum is essentially the same as the VSG swing equation. Due to this, the phase portrait approach, which was used to predict the pendulum motion, can be similarly applied for the VSG transient stability study. Based on the analogical phase portrait analysis, a damping coefficient tuning guideline is proposed, which always guarantees the synchronization stability as long as an equilibrium exists. The aforementioned theoretical findings are finally verified through a grid-connected VSG under the hardware-in-loop (HIL) environment. Full article

A collaborative inter-laboratory study was conducted to characterise the performance of the novel 250 W External Discharge Plasma Thruster (XPT) with a channel-less Hall effect-type thruster designed to address lifetime limitations and lower-power efficiency challenges in conventional Hall effect thrusters. This study aimed to validate performance measurements across different facilities and thrust stands, investigating potential facility effects on thrust characterisation. Performance testing was conducted both at the University of Surrey using a torsional thrust balance and at the University of Southampton with a double inverted pendulum thrust stand, providing independent verification of the thrust and efficiency metrics. The comparison highlighted the importance of cross-facility testing with differing background pressures, calibration methods, and thrust balance types. These differences provide valuable insights, ensuring more robust and reliable low-power thruster characterisation. The XPT thruster demonstrated consistent performance across both the University of Surrey and University of Southampton facilities, with thrust levels ranging from 1.60 mN to 11.8 mN, specific impulses from 327 s to 1067 s, and anode efficiencies up to 11%. Higher anode voltages and mass fluxes at Southampton enabled extended operational envelopes, revealing performance plateaus at elevated powers, particularly for flow rates above 8 sccm. Cross-facility testing highlighted facility-dependent influences, with Southampton achieving a higher thrust and specific impulse at lower flow rates (5–6 sccm) due to increased anode currents, while discrepancies between test sites of up to 25% were observed at higher flow rates (8–10 sccm) and powers above 200 W. Characterisation identified an optimal operating range at 200 W of anode power with a mass flux below 8 sccm. This work underscores the importance of inter-laboratory validation in electric propulsion testing and provides insights into the best practices for assessing next-generation Hall effect-type thrusters. Full article

This work will present an algorithmic approach for robust control focusing on hydraulic–mechanical systems. The approach is applied to a hydraulic actuator driving a cart with an inverted pendulum. The algorithmic approach aims to satisfy two robust control requirements for single input single output (SISO) linear systems with nonlinear uncertain structure. The first control requirement is robust stabilization, and the second is robust asymptotic command following for arbitrary reference signals. The approach is analyzed in two stages. In the first stage, the stability regions of the controller parameters are identified. In the second stage, a Particle Swarm Optimization Algorithm (PSO) is applied to find suboptimal solutions for the controller parameters in these regions, with respect to a suitable performance cost function. The application of the approach to a hydraulic actuator, driving a cart with an inverted pendulum, satisfies the goal of achieving precise control of the pendulum angle, despite the system’s inherent physical uncertainties. Full article

Sustainability and resource optimization have spurred interest in giving a second life to used equipment, often discarded after limited use. Within this framework, we conducted a multidisciplinary, final-year engineering project to explore the reverse engineering and repurposing of commercial hoverboards for an auto-stabilizing, modular robotic platform, with emphasis on medical applications such as transporting medication. The innovation lies in recycling hoverboards to develop a teleoperated, stabilized base that can accommodate additional modules—for instance, a multifunctional arm or a transport shelf—akin to existing commercial robots. Our methodology involves disassembling and reprogramming the hoverboard’s motor controllers and sensors to maintain horizontal stability. Control is realized through the sensor fusion of accelerometer and gyroscope data, processed by a Kalman filter and implemented in a Proportional-Integral-Derivative (PID) loop. A user-friendly Human-Machine Interface (HMI), hosted on an ESP32 microcontroller, enables remote operation and monitoring. Experimental results show that the platform autonomously balances, carries payloads, and achieves high energy efficiency, highlighting its potential as a sustainable and versatile solution in modular robotic applications. Full article

This research article tackles the control problem of an inverted pendulum, also known as the Furuta pendulum, mounted on a velocity-controlled robot manipulator in two configurations: the rotary pendulum and the translational pendulum. Differently from most of the existing control architectures where the motor actuating the pendulum motion is torque-controlled, the proposed control architecture exploits the inner velocity loop usually available on industrial robots, thus easing the implementation of an inverted pendulum. Another aspect investigated in this paper and mostly overlooked in the literature is the digital implementation of the control and, specifically, the latency introduced by the digital controller. The proposed control solution explicitly models such effects in the control design phase, improving the closed-loop performance. The additional novelty introduced by this paper is the friction compensation that is essential in the swing-up phase of the inverted pendulum, whereas classical control strategies for the nonlinear swing-up usually neglect this effect, and their solutions lead to control failures in practical systems. This paper presents detailed modeling and experimental identification phases followed by the control design of both the nonlinear swing-up algorithm and the linear stabilization controller, both experimentally validated on a Meca500 robotic arm controlled via an EtherCAT communication protocol by a mini PC featuring a Xenomai real-time operating system. The overall system showcases the potential of high-performance digital control systems in industrial robotic applications. Full article