The sharing of skills over the Internet enables professionals to democratize their expertise and skills without exhausting their availability, e.g., through excessive traveling. To enable this Internet of Skills, we present a novel Digital Twin (DT) platform for the remote control of machines with human-in-the-loop. The DT of a remotely controlled machine acts effectively as an inter-layer between the operator and the controlled machine, e.g., robot arm. The DT can be optimized for a particular application to interact with the operator with an intuitive low-latency interface and, on other side, to control and monitor the quality of the remote task. Essentially, the human operator controls the DT, while the DT controls the remote robot. This paper introduces the DT framework for the remote control. The human-machine-human control loop is split into Virtual Reality (VR), remote control, and robot control loops. The proposed framework achieves low latency visual feedback and very short system reaction times for unexpected changes with arbitrary distances between operator and robot. Within the DT framework, this paper proposes a robot control algorithm for controlling time-critical robot applications over networks with considerable delays and jitter. The proposed framework has been implemented in a demonstrator with a robot arm and its DT in VR.

Remote Robot Control with Human-in-the-Loop over Long Distances Using Digital Twins

The article presents analysis on construction of two-stage remote control for space robots. This control ensures efficiency of the robot control system at large delays in transmission of control signals from the ground control center to the local control system of the space robot. The conditions for control stability of and high transparency are found.

Dynamic Analysis of Space Robot Remote Control System

In the paper the authors propose a method of bilateral control for space robotic manipulators construction with large delays in transmissions of control signals from the Earth to the local space manipulator’s control system.

Bilateral remote control over space manipulators

In this paper the stabilization problems of program motion of objects with elastically connected elements are considered. The conditions for stabilizing a program motion ×=0 of the control object are given.

Stabilization of the program motion of control object with elastically connected elements

About stability of selector linear differential inclusions

In the paper a method of remote bilateral control of space robots operating in a non-deterministic environment with a large delay in control signals transmission is presented. The method provides adaptation of space robot behavior to possible changes in its external environment. Compared to the known approaches this method reduces influence of external environment variation on the control process.

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Remote Control of Space Robots Change-Adaptive in its External Environment

In this article the modeling of robot motion for the case of transferring a robot to a given point in the phase space and for transferring it to a program trajectory is under study. The equations of motion of the robot in the form of Lagrange’s equations of the 2nd kind were derived. The positional control in the form of feedbacks is constructed. The graphs of changes in the components of the deviation vector and the components of the control vector for its translation onto the program trajectory are given.

Modeling the motion of a space manipulation robot using position control

In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered.

https://www.mdpi.com/2227-7390/7/8/677/pdf

A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis

Approaches to estimate the number of almost periodic solutions of ordinary differential equations are considered. Conditions that allow determination for both upper and lower bounds for these solutions are found. The existence and stability of almost periodic problems are studied. The novelty of this paper lies in the fact that the use of apparatus derivatives allows for the reduction of restrictions on the degree of smoothness of the right parts. In our work, regarding the number of periodic solutions of equations first order, we don’t require a high degree of smoothness and no restriction on the smoothness of the second derivative of the Schwartz equation. We have all of these restrictions lifted. Our new form presented also emphasizes this novelty.

https://www.mdpi.com/2227-7390/6/9/171/pdf

Almost Periodic Solutions of First-Order Ordinary Differential Equations

The Fermat, Roll and Lagrange theorems are generalized into the class of nondifferentiable functions, the necessary and sufficient conditions for monotonicity and convexity of one variable functions are given.

Gennady Alferov

Papers

Remote Control of Space Robots Change-Adaptive in its External Environment

Modeling the motion of a space manipulation robot using position control

A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis

Almost Periodic Solutions of First-Order Ordinary Differential Equations

Application of derived numbers theory in convex analysis