This paper presents the development of a kinematic model for the lower limb of a quadruped walking robot. The key feature of the model is the placement of all actuators within the hip joint housing, where torque from the drive shaft is transmitted to the shin via a lever mechanism. The advantage of this design is the reduced mass of the lower limb, which enhances the limb’s response speed to control signals and increases the overall maneuverability of the robot. The disadvantage is the increased kinematic complexity, which necessitates deriving the relationships between the angular displacements of the components. The aim of this work is to develop a complete kinematic model of the lower limb of a quadruped robot, with the actuators for both the thigh and shin segments located within a single hip joint unit, where torque from the drive shaft is transmitted to the shin through a lever mechanism. This approach reduces the mass of the lower limbs and overcomes the drawbacks inherent to classical kinematic configurations. In this study, the relationship between the actuator shaft rotation angle and the resulting shin deflection relative to the thigh was derived. To validate the model, equations describing the ankle point trajectory during the walking process were formulated. Using the obtained coordinates, the angular variations were calculated by solving the inverse kinematics problem. The resulting graphs of these angular changes are smooth and continuous, which is a necessary condition for ensuring impact-free motion of the lower limb. Verification using a 3D solid model in SolidWorks confirmed the absence of mechanical interference (collisions) between links across all calculated positions. The obtained results constitute a complete mathematical framework for the design and control of energy-efficient limbs for walking robots. Thus, this work lays the foundation for creating lighter and more dynamic robotic platforms applicable in inspection, monitoring, and autonomous navigation tasks in complex environments.

The current level of development of technology and engineering, demands of society determine the need to develop unmanned vehicles and systems. Today, there is a wide variety of theoretical methods for planning the motion of robots, which differ in their efficiency in various conditions. Among the methods of motion planning, a group of methods based on the use of artificial potential fields (APF) stands out. In practice, various problems may arise in which the robot must find itself in the end point with the required linear velocity within the allotted time. The use of APF methods for such problems leads to a significant complication of the type of the potential energy function of the field. In addition, such methods are characterized by the problem of local field minima and oscillations of the robot near an obstacle. In this paper, a particular method is proposed that differs from existing methods, which eliminates this problem, allowing the robot to reach the target point in the allotted time for the extreme case. As the extreme case, the location of the obstacle center, the initial and final points of the robot’s center of mass and its velocity vector on one straight line is considered. The proposed private method VC/APF₂ + BC_τ⁰ of optimal planning of robot motion with bypass of a static obstacle is based on: the combined use of variational calculus (VC) and an artificial potential field (repelling the robot from the obstacle boundaries), the lines of force of which are perpendicular to the robot velocity vector (APF₂); on dividing the robot motion along the horizontal plane into stages (modes) for given initial and final coordinates and zero robot velocities, its travel time (BC_τ⁰).

The paper presents a static model for estimating the minimum required vacuum pressure in the suction gripper of a climbing robot when it is held on an inclined surface by a single supporting gripper. The system configuration is described by the surface inclination angle β , the platform rotation angle γ , as well as the geometric parameters and the position of the center of mass. An analytical expression Δ P_min( β , γ ) is obtained, taking into account three limiting mechanisms of stability loss: detachment, slippage, and overturning. The minimum vacuum is determined as the maximum of the corresponding

force and moment constraints with the introduction of a safety factor that accounts for atmospheric pressure reduction, variations in the friction coefficient, and dynamic disturbances. To consider the spatial orientation of the center of mass, a quaternion-based rotation formalism is employed. An experimental test bench with an adjustable inclination angle and a pneumatic system enabling controlled variation of vacuum pressure and detection of the critical onset of motion is developed. An algorithm for determining the critical vacuum level based on pressure and platform rotation angle measurements is proposed. А comparison of theoretical and experimental Δ P values for several configurations ( β , γ ) is performed. The discrepancy is shown to remain within a few percent; the mean absolute percentage error for absolute pressure is 2.26 %, while the mean absolute error in vacuum pressure is about 2.2 kPa. The results confirm the adequacy of the proposed model and its applicability to the design of vacuum holding systems, selection of gripper geometry, and synthesis of control algorithms for robot operation near the boundaries of static stability. The proposed approach provides a unified analytical expression for analyzing various robot configurations and can be extended to multi-gripper systems and optimization of center-of-mass placement and vacuum system parameters.

This paper presents a robust quadrotor attitude control method that combines feedback linearization with an enhanced highorder sliding mode disturbance observer to address issues such as channel cross-coupling, model uncertainties, and both matched and mismatched disturbances. The proposed method with a prescribed bandwidth is proposed to estimate model uncertainties and disturbances along with their derivatives of arbitrary order. It is constructed by integrating a high-order sliding mode differentiator with an extended state observer. The particle swarm optimization algorithm is used to determine the optimal observer gain coefficients. Stability of system with proposed controller is proven using the input-to-state stability criterion, while stability of system with proposed method is established through Lyapunov analysis. Effectiveness of the proposed controller is demonstrated through comparisons with uncertainty and disturbance estimators, active disturbance rejection control, and cascaded PID controllers.

Proposed method comprises plotting phase portraits of aircraft angular motion by digital processing of its optical image sequence. As an application, the problem of recognition by the formed phase portraits of the model of angular motion of the aircraft is considered. The decision on the aircraft model belonging to a certain class is made by the criterion of conjugacy of the vector representing the observed object with the reference subspace of the class. Vectors are formed by scanning images of phase portraits built from calculated values of angle and angular velocity of aircraft at intervals of aircraft proper motion. Current readings of angular position are calculated from coordinates of projections of given marker points of aircraft in the image, and angular velocity is estimated using the formula of the first central difference. Reference subspaces of classes are formed b y marked vectors representing the corresponding class. Calculated processes of aircraft angle and angular velocity used to form reference vectors are subjected to preliminary processing by Kalman-Bucy filter. An algorithm for calculating coordinates of projections of marker points on images has been developed, which makes it possible to form reference subspaces by modeling. An example of construction of phase portraits and recognition of aircraft angular motion models in pitch channel with different values of state equation parameters is given

The paper investigated the effectiveness of using direct side-force control (DSFC) to improve the quality and accuracy of automatic lateral control of non-maneuverable aircraft during approach and landing. It is hypothesized that, on advanced aircraft, aerodynamic shields capable of generating transverse aerodynamic forces will be installed on engine pylons or nacelles, or alternatively, jet engines will be equipped with devices for thrust vector control. Control systems incorporating DSFC alongside conventional control elements belong to the class of two-channel systems, characterized by the presence of slow and fast subsystems, with the latter exerting significantly less control influence. Consequently, there is a need to optimize the integrated utilization of traditional control mechanisms and DSFC. The control system design employed a hierarchical architecture. The inner control loop that performs executive functions is comprised of: stabilization system the roll angle during maneuvering by means of coordinated lateral control, or stabilization system the prescribed lateral overload during control without roll. In both configurations, a unified two-channel stabilization scheme was implemented to counteract wind disturbances, specifically designed for regulating the prescribed lateral overload. To account for the limited actuation resource of DSFC, a cascade control scheme was adopted, combining an autonomous yaw control loop (slow subsystem) with the DSFC loop (fast subsystem with resource constraints).The proposed methodology facilitates the integration of DSFC with standard trajectory control systems. А schematic of an astatic stabilization system for the prescribed lateral overload incorporating DSFC is presented. Transient response characteristics and simulation results illustrating the system’s reaction to lateral wind gusts are provided. The research findings demonstrate that an aircraft control system equipped with DSFC significantly improves the accuracy of flight path stabilization under wind disturbance conditions.