Search Results (193)

This paper studies the issues of human balancing and stability in the sagittal plane using fractional and integer order time delay feedback control. The neural-mechanical model of human balance is represented as an inverted pendulum controlled by torque. We present a finite-time stability (FTS) analysis for closed-loop neutral time delay systems (NFOTDSs) with fractional order $1<\beta <\alpha \le 2$. By employing a generalized Gronwall inequality, we derive new FTS criteria for these systems in terms of the Mittag-Leffler function. Finally, a suitable numerical example is presented to show the effectiveness of the proposed method. Full article

A second-order nonsingular terminal sliding mode control (SONTSMC) is proposed to solve the stabilization and tracking problems of an inverted pendulum. Although, a first-order sliding mode controller with the integral of the cart position can eliminate the offset in the cart position caused by incorrect calibration of the pendulum angle while balancing the pendulum at the upright equilibrium position, its control precision and chattering reduction can be improved by using a higher-order sliding mode controller. Therefore, the SONTSMC is designed by combining nonsingular sliding mode control and first-order sliding mode control to construct a second-order sliding mode controller that enhances tracking accuracy and reduces the chattering problems associated with sliding mode control. The performance of the proposed control is compared with that of the linear quadratic regulator sliding mode control (LQRSMC) and the integral linear quadratic regulator sliding mode control (ILQRSMC) for CIP’s stabilization and tracking. The results indicate that SONTSMC significantly increases the control performance of CIP while efficiently utilizing control energy. Full article

This paper proposes a Takagi–Sugeno–Kang Elliptic Type-2 Fuzzy Brain-Imitated Neural Network (TET2FNN)-based decoupling control strategy for nonlinear underactuated mechanical systems subject to uncertainties. A sliding-mode framework is employed to construct a decoupled control architecture, in which an intermediate variable is introduced to separate two second-order sliding surfaces, thereby forming a decoupled slip surface. The TET2FNN acts as the main controller and approximates the ideal control law online, while a robust compensator is incorporated to suppress approximation errors and guarantee closed-loop stability. Simulation studies conducted on a double inverted pendulum system demonstrate that the proposed method achieves improved tracking accuracy and disturbance rejection compared with representative state-of-the-art controllers. Furthermore, the computational burden remains reasonable, indicating that the proposed scheme is suitable for real-time implementation and practical nonlinear control applications. Full article

Step length is a fundamental parameter for gait assessment, reflecting complex neuromuscular and biomechanical behavior. Accurate step-length estimation is clinically relevant for monitoring populations with neurological or musculoskeletal conditions, as well as older adults. This study presents a novel biomechanical model, inspired by the inverted double pendulum, for step-length estimation under asymmetric gait conditions using a single inertial sensor on the lower back. Unlike models that assume symmetry, the proposed model explicitly incorporates pelvic rotation, enabling more accurate step length estimation, particularly in individuals with gait impairment. The model was validated against a gold standard OptiTrack^® (Corvallis, OR, USA) system with 33 adults: 21 participants without and 12 with gait impairment. Results show that the model achieved low Median Absolute Errors (MdAE), below 0.04 m in participants without gait impairment and remaining within 0.06 m in those with impairment. Statistical validation confirmed a strong correlation with the reference system (R = 0.96, R² = 0.93) and a clinically trivial mean bias (0.64 cm) from Bland-Altman analysis. These results validate the model’s effectiveness under various gait conditions, suggesting its technical feasibility and strong potential for clinical and real-world applications, particularly for the longitudinal monitoring of patients with functional impairments. Full article

This work investigates the viability of using NNs to select an appropriate controller for a dynamic system based on its current state. To this end, this work proposes a method for training a controller-scheduling policy using several learning algorithms, including deep reinforcement learning and evolutionary strategies. The performance of these scheduler-based approaches is evaluated on an inverted pendulum, and the results are compared with those of NNs that operate directly in a continuous action space and a backpropagation-based Control Scheduling Neural Network. The results demonstrate that machine learning can successfully train a policy to choose the correct controller. The findings highlight that evolutionary strategies offer a compelling trade-off between final performance and computational time, making them an efficient alternative among the scheduling methods tested. Full article

This paper addresses the problem of stabilizing an inverted pendulum actuated by a reaction wheel, a system relevant for robotic balancing platforms and aerospace applications. The study compares several state-space representations of the system and examines their implications for controller synthesis and parameter identification. A unified nonlinear model formulation is introduced, enabling a structural Lyapunov-based robustness analysis that reveals how variations in the gravitational gain affect closed-loop stability. Control strategies based on pole placement and Linear Quadratic Regulator (LQR) design are implemented and compared across the different representations. The analysis highlights a robustness–fidelity trade-off between model complexity and sensitivity to parameter uncertainty, providing insight that extends beyond the specific laboratory setup. Theoretical results are validated on a real laboratory platform. The controllers are evaluated in both upright and downward equilibrium configurations, and the influence of parameter shifts is assessed experimentally using global identification and performance indices. The work offers general modeling and robustness guidelines for reaction-wheel-based stabilization systems and related underactuated nonlinear mechanisms. Full article

Attempting to make machines mimic human walking, grasping, balancing, and other behaviors is a deep exploration of cognitive science and biological principles. Due to the existing prediction lag problem, an error compensation mechanism that integrates historical motion data is proposed. By constructing a humanoid autonomous walking control system, this paper aims to use a three-dimensional linear inverted pendulum model to plan the general framework of motion. Firstly, the landing point coordinates of the single foot support period are preset through gait cycle parameters. In addition, it is substituted into dynamic equation to solve the centroid (COM) trajectory curve that conforms to physical constraints. A hierarchical whole-body control architecture is designed, with a task priority based on quadratic programming solver used at the bottom to decompose high-level motion instructions into joint space control variables and fuse sensor data. Furthermore, the numerical iterative algorithm is used to solve the sequence of driving angles for each joint, forming the control input parameters for driving the robot’s motion. This algorithm solves the limitations of traditional inverted pendulum models on vertical motion constraints by optimizing the centroid motion trajectory online. At the same time, it introduces a contact phase sequence prediction mechanism to ensure a smooth transition of the foot trajectory during the switching process. Simulation results demonstrate that the proposed framework improves disturbance rejection capability by over 30% compared to traditional ZMP tracking and achieves a real-time control loop frequency of 1 kHz, confirming its enhanced robustness and computational efficiency. Full article

Positional accuracy is crucial in target tracking for various robotic applications, where precise movement and response are essential. Geared electromechanical actuators, widely used in robotic systems, offer significant advantages but are susceptible to backlash, particularly during direction reversals. This backlash can introduce unwanted oscillations and disturbances, especially in systems with swinging loads, thereby compromising tracking performance. This study proposes a novel backlash compensation technique for inverted pendulum systems utilizing observer estimators. The proposed method effectively estimates and mitigates the disturbances caused by backlash, enhancing the system’s ability to maintain accurate target tracking. RMSE turns out to be 0.18 and settling time is quite minimal 2.4sec.Simulation results demonstrate that this approach significantly improves tracking performance, ensuring robust and reliable operation in dynamic environments. Full article

This study proposes a discrete multi-agent Q-learning framework for the online tuning of PID controllers in continuous dynamic systems with limited observability. The approach treats the adjustment of each PID gain ($k_p$, $k_i$, $k_d$) as an independent learning process, in which each agent operates within a discrete state space corresponding to its own gain and selects actions from a tripartite space (decrease, maintain, or increase its gain). The agents act simultaneously under fixed decision intervals, favoring their convergence by preserving quasi-stationary conditions of the perceived environment, while a shared cumulative global reward, composed of system parameters, time and control action penalties, and stability incentives, guides coordinated exploration toward control objectives. Implemented in Python, the framework was validated in two nonlinear control problems: a water-tank and inverted pendulum (cart-pole) systems. The agents achieved their initial convergence after approximately 300 and 500 episodes, respectively, with overall success rates of $49.6\%$ and $46.2\%$ in 5000 training episodes. The learning process exhibited sustained convergence toward effective PID configurations capable of stabilizing both systems without explicit dynamic models. These findings confirm the feasibility of the proposed low-complexity discrete reinforcement learning approach for online adaptive PID tuning, achieving interpretable and reproducible control policies and providing a new basis for future hybrid schemes that unite classical control theory and reinforcement learning agents. Full article

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