Abstract Non-spherical wrist manipulators are widely used in industrial settings, yet they lack effective inverse kinematics solutions. Current methods primarily rely on numerical iteration, which suffers from limitations such as sensitivity to initial values and convergence issues. Meanwhile, algebraic elimination methods require complex elimination techniques to obtain analytical solutions, restricting their practical engineering application. To address the limitations of these existing approaches, this paper innovatively proposes a novel analytical method based on conformal geometric algebra theory. The core of this method lies in utilizing the geometric characteristics of the manipulator to establish a polynomial equation for one of the joint variables, after which the remaining joint angles are solved according to the joint angle solution methodology. The correctness of the proposed method was verified using three sets of joint angles. Additionally, a comparative analysis with the Dixon elimination method was conducted using 100 sets of arbitrary initial joint angles. Example validation demonstrates that the proposed method exhibits significant advantages in computation time, solution completeness, and numerical accuracy, thereby providing a new theoretical tool and practical framework for the inverse kinematics analysis of robotic manipulators.

Abstract In this research, a hierarchical dynamic and kinematic modeling framework is proposed for a wheeled-legged manipulator (WLM), explicitly incorporating wheel slip and skid effects through the Gibbs–Appell formulation. Unlike traditional Lagrangian methods that depend on constraint multipliers, the proposed approach unifies the platform and manipulator dynamics while substantially reducing computational complexity. This integration enables efficient handling of nonholonomic constraints without compromising physical fidelity and offers a clear separation between subsystems, allowing the effects of wheel-ground interactions to be analyzed independently from manipulator motions. The proposed formulation is validated through a combination of MATLAB/Webots simulations and laboratory experiments conducted under both dry and wet (soapy ceramic) surface conditions. Experimental results indicate end-effector position deviations of 8–10.5% primarily due to wheel slip and initial joint torque discrepancies of 6.5–20% that progressively diminish as steady-state motion is reached. Comparative evaluation against a conventional Lagrangian model highlights the computational advantage of the Gibbs–Appell formulation, demonstrating reduced assembly time and fewer symbolic differentiation operations. Furthermore, a sensitivity analysis on friction coefficients and slip ratios confirms the robustness of the model to variations in surface conditions. Beyond accurate dynamic prediction, the hierarchical structure enables modular real-time implementation, supporting controller design, trajectory planning, and fault detection. Overall, the results demonstrate that the Gibbs–Appell-based hierarchical modeling framework combines analytical rigor with computational efficiency, providing a robust foundation for control and optimization in advanced wheeled-legged robotic manipulators.

Abstract Legged robots operating in irregular environments are often subjected to compound disturbances such as tilts and vibrations, which can degrade attitude stability and motion reliability. This paper presents a real-time disturbance-adaptive control framework for a hexapod robot. The proposed system integrates quaternion-based attitude estimation using an extended Kalman filter (EKF), a double-threshold pose classifier, and a modular gait library and is implemented on an embedded controller with a 2 ms control-loop latency. Analytical verification and laboratory experiments demonstrate that the proposed control loop achieves uniform ultimate boundedness (UUB) under deterministic hybrid disturbances composed of controlled tilt and vibration, with a mean recovery time of 5.7 s. These results demonstrate that a lightweight rule-based controller can ensure reliable posture recovery within the experimentally validated laboratory scenarios, providing a foundation for future extensions to more complex environments. The main contributions of this work are (1) a disturbance-adaptive gait selection architecture for quasi-static stabilization, (2) a noise-robust EKF-based attitude estimation and double-threshold pose determination scheme, and (3) a concise Lyapunov-based stability analysis demonstrating UUB of the closed-loop system.

Abstract Continuum robots inspired by biological life forms are favored for their flexibility, compliance, and adaptability to confined environments. However, flexible structure and coupled dynamics include challenges, especially under external forces. This paper presents a dynamic-model-based control framework for a two-section planar-to-spatial tendon-driven continuum manipulator (P2S-TDCM), which integrates a comprehensive Euler–Lagrange model that accounts for tendon stiffness, viscous damping, and backbone flexibility. A genetic algorithm (GA)-optimized PID controller is designed and tested on deterministic and robustness-oriented tuning modes. To further enhance real-time robustness against external disturbances, an online disturbance observer (DOB) is integrated into the control loop to estimate and compensate for unmeasured external wrenches. Numerical results showed that the robust tuning strategy achieved consistently lower RMSE (up to ∼ 25% improvement compared to the deterministic approach) and reduced sensitivity to parameter uncertainties such as vertebra mass by ±2%, backbone Young’s modulus by ±5% under external tip forces. Experimental validation of the deterministic controller further confirmed the model’s accuracy and feasibility. The combined GA-PID-DOB framework improves trajectory tracking stability and disturbance rejection, establishing a robustness-oriented control for P2S-TDCM. This work demonstrates that integrating DOB-based compensation with GA-optimized control enhances robustness and 3D trajectory tracking in TDCMs. Future work will extend the framework to account for distributed external forces along the manipulator body and explore adaptive or learning-based controllers for real-time uncertainty compensation.

Abstract In this paper, a novel series–parallel stable platform is proposed, and its kinematic and dynamic models are established. The relationship between the length, speed, and acceleration of rolling and pitching electric push rods is analyzed. The workspace of the series–parallel stable platform is determined, and the singularity and interference are analyzed. The state-machine-based control system of the stable platform is designed. An experimental environment of the principle of the real-time control system based on dSPACE was built. A position–speed double closed-loop experiment, simulating mounting carrier of the random signal tracking, and system comprehensive performance experiment were conducted to verify the accuracy of the kinematics and dynamics model of the series–parallel stable platform and the rationality and stability of the control system.

Abstract Lower limb-assisted exoskeletons can provide payloads and support, but the hip joints of current lower limb-assisted exoskeletons have problems such as single mechanisms, few degrees of freedom, and limitations in the types of gaits that can be acted upon. To address these problems, a novel double-cam hip joint assist mechanism is proposed for walking, running, and carrying gait situations. The double cam and two rectangular compression springs with different stiffness are used to satisfy the differences in exoskeleton assistance requirements in multiple gaits. First, biomechanical simulation of walking, running, and carrying movements is carried out with OpenSim to obtain the hip joint angle and torque data, and then the structural design of the assist mechanism is carried out. Hip joint angle planning and contour solving are carried out for the contour lines of the cams, so that the cam contour lines are assist according to different hip joint angles, and the stiffness of compression springs is determined by D’Alembert’s principle, and the assist torques are analyzed. Meanwhile, a human–machine coupling model was established for theoretical analysis. Finally, the muscle power change curves were exported using OpenSim, and the assistance was verified by comparison.

Abstract This paper focuses on six-degree-of-freedom (six-DOF) spatial cable-suspended parallel robots with eight cables (8-6 CSPRs) because the redundantly actuated CSPRs are relevant in many applications, such as large-scale assembly and handling tasks, and pick-and-place operations. One of the main concerns for the 8-6 CSPRs is the stability because employing cables with strong flexibility and unidirectional restraint operates the end-effector of the robot under external disturbances. As a consequence, this paper attempts to address two key issues related to the 8-6 CSPRs: the force-pose stability measure method and the stability sensitivity analysis method. First, a force-pose stability measure model taking into account the poses of the end-effector and the cable tensions of the 8-6 CSPR is presented, in which two cable tension influencing factors and two position influencing factors are developed, while an attitude influence function representing the influence of the attitudes of the end-effector on the stability of the robot is constructed. And furthermore, a new type of workspace related to the force-pose stability of the 8-6 CSPRs is defined and generated in this paper. Second, a force-pose stability sensitivity analysis method for the 8-6 CSPRs is developed with the gray relational analysis method, where the relationship between the force-pose stability of the robot and the 14 influencing factors (the end-effector’s poses and cable tensions) is investigated to reveal the sequence of the 14 influencing factors on the force-pose stability of the robot. Finally, the proposed force-pose stability measure method and stability sensitivity analysis method for the 8-6 CSPRs are verified through simulations.

Abstract In firefighting missions, human firefighters are often exposed to high-risk environments such as intense heat and limited visibility. To address this, firefighting robots can serve as valuable agents for autonomous navigation and flame perception. This paper proposes a novel visual Simultaneous Localization and Mapping (SLAM) framework, Fire SLAM , tailored for firefighting scenarios. The system integrates a flame detection and tracking thread-based on the YOLOv8n network and Kalman filtering-to achieve real-time flame detection, tracking, and 3D localization. By leveraging the detection results, dynamic flame regions are excluded from the SLAM front-end, allowing static features to be used for robust pose estimation and loop closure. To validate the proposed system, multiple datasets were collected from real-world and simulated fire environments. Experimental results demonstrate that Fire SLAM improves localization accuracy and robustness in fire scenes with flame disturbances, showing promise for autonomous firefighting robot deployment.

Abstract This study presents an innovative system for upper limb rehabilitation, combining a variable stiffness device, the ReHArm prototype, with a dynamic and engaging user interface, known as Arms Rehabilitation Management System. The proposed system offers a highly customisable approach to rehabilitation, ensuring real-time adaptability to patients’ specific needs while maintaining compactness and ease of use. Key features include a modular design allowing precise stiffness adjustments, a robust control architecture, and interactive rehabilitation phases designed to enhance user engagement. Extensive multidisciplinary analyses, including kinematic, dynamic, and structural evaluations, demonstrate the system’s ability to improve therapy effectiveness through tailored interaction and feedback. Validation tests demonstrated the prototype’s reliability and robustness, and initial usability assessments suggest its potential to improve rehabilitation outcomes. Further clinical studies involving patients will be necessary to fully evaluate its therapeutic effectiveness.

Abstract This paper presents a novel robust control method for a hip-assist exoskeleton robot’s joint module, addressing dynamic performance under variable loads. The proposed approach integrates traditional PID control with robust, model-based strategies, utilizing the system’s dynamic model and a Lyapunov-based robust controller to handle uncertainties. This method not only enhances traditional PID control but also offers practical advantages in implementation. Theoretical analysis confirms the system’s uniform boundedness and ultimate boundedness. A Matlab prototype was developed for simulation, demonstrating the control scheme’s feasibility and effectiveness. Numerical simulations show that the proposed fractional-order hybrid PD (FHPD) controller significantly reduces tracking error by 58.70% compared to the traditional PID controller, 55.41% compared to the MPD controller, and 32.32% compared to ADRC, highlighting its superior tracking performance and stability.