This issue encompasses the collection of articles, which highlight emerging, novel meth- ods in control theory crucial for applications in robotics and mechanics, with a focus on both theoretical advancements and practical engineering solutions. The papers of the issue can be roughly divided into two groups, where the first one is focused the elaborating new tools and analytical arguments of control theory for solving motion planning and motion control assignments in new settings. Meanwhile, the second group of the papers provides an anal- ysis of specific control engineering problems and reflects various contributions of technical nature.

Motivated by problems in robotic interaction control, we present a model-based method for robust orbital stabilization. Our objective is to design a time-invariant feedback law for a model of a nonlinear system, or for its digital twin, that makes the distance between its solutions and a planned periodic trajectory decay exponentially. The method uses transverse coordinates, which are functions that vanish on the orbit and remain independent in the firstorder approximation. We regulate the linearized dynamics of transverse coordinates to zero. The novelty of the method is that it replaces the projection-based modification of a stabilizing time-periodic controller with a combination of a time-invariant control law for a subsystem and a discontinuous sliding-mode term. The sliding-mode part forces the state to a switching manifold in finite time and provides robustness to matched uncertainties. We develop a stepby- step procedure and demonstrate its use by an academic example that consists of two masses coupled by a spring and actuated by an external control force. Although the procedure usually requires numerical approximations, this example allows all steps to be carried out analytically. We also discuss the corresponding design for the velocity-controlled case.

This paper addresses the problem of orbital stabilization of a periodic walking gait for a model or a digital twin of a three-link planar biped robot with a single actuator. A Lyapunov equation-based approach is proposed for the synthesis of a stabilizing controller for the corresponding impulsive mechanical system. The method ensures exponential vanishing of transverse coordinates, defining deviations from the nominal periodic trajectory, by solving Lyapunov matrix inequalities, which provide sufficient conditions for orbital stability of the closed-loop dynamics in the nominal case of no disturbances. The proposed approach allows systematic feedback controller design for impulsive systems, taking into account the discontinuities associated with a simplified model of the impact phase of walking.
To ensure robustness against matched disturbances, an additional integral sliding mode (ISM) control law is introduced. The ISM component guarantees exact disturbance compensation (for a solution understood in the Filippov’s sense) from the initial moment of motion, ensuring that the perturbed system behaves identically to the nominal model from the very start. Theoretical results are validated through numerical simulations on a model of a three-link biped robot. The obtained results demonstrate that the proposed control law ensures stable periodic walking and significant reduction of deviations from the nominal gait, even under external perturbations.

This paper addresses the problem of orbital stabilization of periodic trajectories in underactuated mechanical systems. We focus on cases where the desired trajectory arises from a nonregular virtual holonomic constraint, leading to reduced dynamics with isolated singularities. Existing stabilization methods are generally inapplicable or ineffective in such cases.
We propose an alternative approach based on the approximate linearization of the transverse dynamics, which yields a linear time-varying system that remains regular at singular points and is typically controllable. A stabilizing LQR-based feedback is then designed for this linear system, and we show that it ensures local orbital asymptotic stability of the original nonlinear system’s trajectory.
The effectiveness of the proposed approach is illustrated through the stabilization of a periodic trajectory in the Pendubot system, where the second link oscillates around the horizontal position.

In this paper, the stability problem of trivial equilibrium positions is addressed for two classes of nonlinear mechanical systems with unbounded delays. It should be noticed that the delaydependent terms in the equations considered can be interpreted as integral parts of proportionalintegral- differential (PID) controllers. It is known that such terms can improve the characteristics of transient processes and provide the damping of undesirable vibrations. First, assuming that strongly nonlinear dissipative and positional forces acting on the system are homogeneous of different homogeneity degrees, an original approach to the Lyapunov – Krasovskii functional construction is proposed. With the aid of this functional, it is proved that the asymptotic stability of the auxiliary delay-free system implies the asymptotic stability for the original time-delay system. Next, we study a mechanical system that is subject to linear gyroscopic forces in addition to nonlinear homogeneous dissipative and positional forces. To derive asymptotic stability conditions for such a system, a special technique to the application of the decomposition method is developed. The investigated system composed of the second-order equations is represented as a complex system describing interaction of two isolated subsystems consisting of the first-order equations. This form of the decomposition is an extension of the classical one for delay-free linear gyroscopic systems. However, in the linear case, the asymptotic stability was guaranteed only under an additional restriction on the system. It was assumed that there is a large positive parameter at the vector of the gyroscopic forces. In the present contribution, it is proved that, for systems with strongly nonlinear dissipative and positional forces, such a constraint is not required. The effectiveness of the obtained results is demonstrated on the problem of nonlinear PID controller design providing the triaxial stabilization of a rigid body.

In this paper we examine the controlled motion of a three-link wheeled mobile robot on a horizontal plane. The motion of the system is induced by periodic oscillations of the outermost links relative to the central link in the horizontal plane. The dynamics of the robot is analyzed using two theoretical models. The first is a model of nonholonomic rolling which assumes motion without slipping at the points of contact. The second is a hybrid dynamical model which takes into account the possibility of alternation between nonholonomic rolling and motion with slipping along the axis of a wheel pair. An experimental investigation of the dynamics of the developed prototype with different controls is carried out. A comparative analysis is made of the data obtained in the course of a full-scale experiment and the results of numerical simulation based on both models considered. This comparative analysis is used to identify the limits of applicability of the nonholonomic model. It is shown that within these limits the nonholonomic model describes the real motion with good accuracy.

This study investigates the dynamics of a nonholonomic mechanical system consisting of two rigid spherical bodies. The primary configuration involves the base sphere rolling without slipping on the horizontal plane which is fixed or moves uniformly and in a straight line. Another sphere rolls, also without slipping, along the external or internal surface of the base sphere. A system of equations of motion is constructed. A complete set of first integrals and an invariant measure are identified. It is demonstrated that the system of equations of motion is integrable by virtue of the Euler – Jacobi theorem and is therefore reducible to quadratures. To analyze the stability of the system’s stationary motions, a reduced potential energy function is derived. It is shown that, when the sphere moves along the internal surface of the base sphere, the stationary motions are orbitally stable with respect to perturbations that preserve the values of the first integrals. The conditions for orbital stability are established for motion along the external surface of the base sphere. To prove stability with respect to arbitrary perturbations, other methods are required.

Sliding mode control (SMC) provides strong robustness against matched disturbances. Among SMC schemes, the super-twisting algorithm (STA) provides continuous control action and finite-time convergence for systems of relative degree one. However, in real applications, actuator imperfections and unmodeled dynamics prevent true finite-time convergence and cause high-frequency oscillations called chattering. The chattering effect can be mitigated by tuning control parameters, for instance, through frequency-domain analysis. Yet, most existing methods rely on simplified system models, limiting their applicability to complex systems. This work proposes a generalized frequency-domain framework for STA gain tuning based on a first-order plus dead time (FOPDT) model. The method identifies FOPDT parameters from the reaction curve and employs describing function and harmonic balance analysis to predict analytically the chattering amplitude, average energy, and frequency. The resulting relations provide explicit guidelines for tuning STA gains to minimize chattering while maintaining robust performance. Validation through both simulations and experiments on a DC motor position control system confirms that the proposed approach achieves improved robustness and accuracy compared with standard STA and PI tuning methods.

Cable-driven parallel robots (CDPR) represent an emerging field of research that has vast applications across different fields of science and engineering, such as medical, aerospace, construction, etc. Dynamic modeling plays an important role in understanding the behavior of these complex systems as well as in enhancing their performances. The state of the art in cable-driven parallel robots (CDPRs) is thoroughly summarized in this review, which covers both basic ideas and cutting-edge advancements in a variety of design modeling control and application domains. The study starts with a thorough examination of the geometric layout and essential elements of CDPR systems describing how the special arrangement of flexible cables allows for better workspace scalability and dynamic performance. It also looks at the complex kinematic and dynamic models that portray the nonlinear behaviors that are essential for attaining accurate motion control like cable sagging elasticity and friction. The optimization of workspace and tension distribution is prioritized in order to preserve system stability and energy efficiency. Furthermore, the review looks at a number of control and planning strategies such as motion planning methods and advanced algorithms like reinforcement learning which guarantee reliable trajectory tracking and operational safety. The wide-ranging effects of CDPR technology are demonstrated through a variety of case studies in the fields of construction entertainment, medical care, agriculture, disaster response, material handling, and space research. Lastly, new developments that promise to improve the capabilities and uptake of CDPRs in next-generation robotic systems are explored, including the incorporation of artificial intelligence machine learning and innovative materials.

This study introduces an approach for open-loop geometric calibration of industrial manipulators that integrates three widely used kinematic formulations: Denavit – Hartenberg (DH), Product of Exponentials (POE), and Complete Parametric Continuous (CPC) models. The proposed method focuses on identifying optimal measurement configurations within a local, spatially narrow workspace, which is a common operational scenario in industrial robotic applications. To achieve high calibration efficiency, a linear approximation model was employed, and the measurement configurations were selected using the D-optimality criterion to maximize parameter identifiability. Experimental validation was performed on an ABB IRB 1600 (10/1.45) manipulator equipped with an API Radian Laser Tracker EMSD3 measurement system, providing a linear accuracy of 0.7 $\mu$m per meter. The system was equipped with a Smart Track Sensor offering an orientation accuracy of 0.005 degrees. Independent measurement sets were used for experiments for each model in several variations to identify the best parameter estimates that can be used in the future for this robot. The results demonstrate a substantial enhancement in calibration accuracy. Specifically, applying the POE-based identification procedure within the narrow workspace region reduced the average error in the Tool Center Point (TCP) position by a factor of 22 when compared to the uncalibrated nominal parameters, with the mean error decreasing from 2.852 mm to 0.13 mm. Additionally, the repeatability analysis showed that the standard deviation of TCP position errors across repeated measurements did not exceed 0.007 mm. These results confirm that the proposed approach ensures high calibration precision and robustness suitable for high-accuracy industrial robotic tasks.

This article presents the results of a study exploring sensorimotor integration in upperlimb prostheses through the development of a prototype noninvasive adaptive control system for a bionic hand prosthesis. The study focuses on creating sensory feedback that replicates the properties of biofeedback with a focus on signals from the fingertips, unlike most studies that focus on recognizing patterns in electromyogramm (EMG) signals. The prototype integrates a twocomponent sensor system into a bionic hand prosthesis model with five independent servomotors. This system consists of a surface EMG sensor, which detects muscle activation intent, and thinfilm resistive pressure sensors embedded in the fingertips. The algorithm processes normalized EMG and pressure data in real time using a programmable microcontroller, implementing closedloop grip force adjustment. Key developments include dynamic calibration using the RMS signal envelope, multi-input PID controllers (tuned using the Ziegler – Nichols method) to minimize overshoot, and low-latency force adaptation for objects with variable compliance. The study also included numerical simulations using the Kelvin – Voigt contact model to simulate fingertip contact with soft and rigid materials. A series of experiments using the proposed prototype were conducted for comparison with the numerical simulations. The experimental results are consistent with the numerical simulations, with a smoother increase in force observed when interacting with the soft material. However, the experimental data differ from the model data for a given force setpoint and also have a dead zone associated with the characteristics of the force sensors used in the prototype. This research lays the foundation for accessible adaptive prosthetics and has direct applications in robotic systems.

The paper handles the problem of automatic path tracking by an autonomous off-road eightwheeled robotic vehicle subject to uncertain longitudinal and lateral wheel slips. A sliding mode guidance law is proposed that solves this problem, explicitly takes into account the constraints on the control inputs, and ensures tracking of any path whose contortion lies within given bounds. Necessary conditions for the mission feasibility are first established. Under slight and partly inevitable enhancement of them, nonlocal convergence and robust stability of the proposed guidance law are theoretically justified. In doing so, the slipping effects are treated as bounded uncertainties. Simulation results confirm the applicability and performance of the control law.

This paper deals with the problem of autonomously driving a mobile robot to the source of an unknown planar scalar environmental field based on pointwise measurement of its value at the current location of the robot. An underactuated nonholonomic Dubins car-like robot with a bounded control range is handled. A novel bioinspired algorithm based on hybrid control paradigm is proposed and justified via mathematically rigorous results on nonlocal convergence. This algorithm assumes the use of only two field sensors and does not require measuring or estimating the field gradient. It is also shown that, in the case of an extended source represented by a curve, the proposed algorithm endows the robot with the ability to track this curve, thereby exhibiting its layout. Theoretical results are confirmed with computer simulation experiments. The proposed control law is efficient both computationally and in terms of the resulting motion.