scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

scholarly journals Stability of rigid body motion through an extended intermediate axis theorem: application to rockfall simulation

2021 ◽  
Author(s):  
Remco I. Leine ◽  
Giuseppe Capobianco ◽  
Perry Bartelt ◽  
Marc Christen ◽  
Andrin Caviezel
Keyword(s):  
Rigid Body ◽  
Direct Method ◽  
Lateral Spreading ◽  
The Body ◽  
Body Motion ◽  
Numerical Schemes ◽  
Stability Properties ◽  
Principal Axes ◽  
Rockfall Simulation ◽  
The Stability

AbstractThe stability properties of a freely rotating rigid body are governed by the intermediate axis theorem, i.e., rotation around the major and minor principal axes is stable whereas rotation around the intermediate axis is unstable. The stability of the principal axes is of importance for the prediction of rockfall. Current numerical schemes for 3D rockfall simulation, however, are not able to correctly represent these stability properties. In this paper an extended intermediate axis theorem is presented, which not only involves the angular momentum equations but also the orientation of the body, and we prove the theorem using Lyapunov’s direct method. Based on the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints. In particular, we show how this scheme is incorporated in an existing 3D rockfall simulation code. Simulations results reveal that the stability properties of rotating rocks play an essential role in the run-out length and lateral spreading of rocks.

scholarly journals On the Analysis of Damped Gyroscopic Systems Using Lyapunov Direct Method

2021 ◽  
pp. 63-74
Author(s):  
Ubong D. Akpan
Keyword(s):  
Direct Method ◽  
Stability Conditions ◽  
Lyapunov Direct Method ◽  
Gyroscopic Effect ◽  
Stability Properties ◽  
The Stability ◽  
Gyroscopic Systems

In this work, the stability properties of damped gyroscopic systems have been studied using Lyapunov direct method. These systems are generally stable because of the presence of gyroscopic effect. Conditions for determining the stability of the damped gyroscopic systems have been developed. Solution bounds of amplitude and velocity have been obtained for both homogeneous and inhomogeneous cases. An example is given to show how the stability conditions are applied to systems to determine its stability status.

Stability Properties and Optimization of Multi-Cutter Turning Operations

2013 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Removal Rate ◽  
Operational Parameters ◽  
Turning Operations ◽  
Stability Properties ◽  
Chatter Vibrations ◽  
Cylindrical Parts ◽  
Important Quality ◽  
The Stability

Multi-cutter turning systems offer huge potential to raise productivity in the manufacturing process of cylindrical parts. The application of a multi-cutter turning head increases cutting performance, material removal rate, since the advance rate is multiplied by the number of cutters involved. Another reason to apply the multi-cutter turning technology is to ensure high feasible accuracy, which is one of the most important quality measures of cutting operations. Furthermore, adverse chatter vibrations caused by the regenerative effect can also be eliminated through the application of optimized multi-cutters. The aim of this study is to investigate the stability properties of multi-cutter turning operations. It is shown that the application of dynamically uncoupled cutters with identical dynamic properties will not improve the stability properties of the system, however, the usage of cutters with different modal parameters — especially finding the optimal ratio of stiffness values of different cutters — will expand stable area in the stability charts, thus ensuring more flexibility and a wider range of stable operational parameters available for the machinist. This study proves that the stability properties of a multi-cutter turning system using dynamically uncoupled cutters are equal to the stability properties of a system using a single cutter with many degrees of freedom.

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

scholarly journals A New Approach of Soft Joint Based on a Cable-Driven Parallel Mechanism for Robotic Applications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1468
Author(s):  
Luis Nagua ◽  
Carlos Relaño ◽  
Concepción A. Monje ◽  
Carlos Balaguer
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Humanoid Robots ◽  
Inverse Kinematic ◽  
Element Analysis ◽  
New Approach ◽  
Flexible Polymer ◽  
The Mathematical Model

A soft joint has been designed and modeled to perform as a robotic joint with 2 Degrees of Freedom (DOF) (inclination and orientation). The joint actuation is based on a Cable-Driven Parallel Mechanism (CDPM). To study its performance in more detail, a test platform has been developed using components that can be manufactured in a 3D printer using a flexible polymer. The mathematical model of the kinematics of the soft joint is developed, which includes a blocking mechanism and the morphology workspace. The model is validated using Finite Element Analysis (FEA) (CAD software). Experimental tests are performed to validate the inverse kinematic model and to show the potential use of the prototype in robotic platforms such as manipulators and humanoid robots.

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Samuel F. Asokanthan ◽  
Soroush Arghavan ◽  
Mohamed Bognash
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Operating Conditions ◽  
System Stability ◽  
System Response ◽  
Ring Type ◽  
Mems Gyroscopes ◽  
The Stability

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

scholarly journals Motion Planning for a Mobile Humanoid Manipulator Working in an Industrial Environment

2021 ◽  
Vol 11 (13) ◽  
pp. 6209
Author(s):  
Iwona Pajak ◽  
Grzegorz Pajak
Keyword(s):  
Kinetic Energy ◽  
Collision Avoidance ◽  
Industry 4.0 ◽  
Degrees Of Freedom ◽  
Industrial Environment ◽  
Acceleration Level ◽  
Different Types ◽  
Manipulability Measure ◽  
Robotic Tasks ◽  
Primary Problem

This paper presents the usage of holonomic mobile humanoid manipulators to carry out autonomous tasks in industrial environments, according to the smart factory concept and the Industry 4.0 philosophy. The problem of transporting lengthy objects, taking into account mechanical limitations, the conditions for avoiding collisions, as well as the dexterity of the manipulator arms was considered. The primary problem was divided into three phases, leading to three different types of robotic tasks. In the proposed approach, the pseudoinverse Jacobian method at the acceleration level to solve each of the tasks was used. The redundant degrees of freedom were used to satisfy secondary objectives such as robot kinetic energy, the maximization of the manipulability measure, and the fulfillment mechanical and collision-avoidance limitations. A computer example involving a mobile humanoid manipulator, operating in an industrial environment, illustrated the effectiveness of the proposed method.

scholarly journals Formation Control of Unmanned Vessels with Saturation Constraint and Extended State Observation

2021 ◽  
Vol 9 (7) ◽  
pp. 772
Author(s):  
Huixuan Fu ◽  
Shichuan Wang ◽  
Yan Ji ◽  
Yuchao Wang
Keyword(s):  
Formation Control ◽  
Control Method ◽  
Tracking Error ◽  
External Environment ◽  
Control Force ◽  
Extended State ◽  
Parameter Perturbation ◽  
State Observation ◽  
Saturation Constraint ◽  
The Stability

This paper addressed the formation control problem of surface unmanned vessels with model uncertainty, parameter perturbation, and unknown environmental disturbances. A formation control method based on the control force saturation constraint and the extended state observer (ESO) was proposed. Compared with the control methods which only consider the disturbances from external environment, the method proposed in this paper took model uncertainties, parameter perturbation, and external environment disturbances as the compound disturbances, and the ESO was used to estimate and compensate for the disturbances, which improved the anti-disturbance performance of the controller. The formation controller was designed with the virtual leader strategy, and backstepping technique was designed with saturation constraint (SC) function to avoid the lack of force of the actuator. The stability of the closed-loop system was analyzed with the Lyapunov method, and it was proved that the whole system is uniformly and ultimately bounded. The tracking error can converge to arbitrarily small by choosing reasonable controller parameters. The comparison and analysis of simulation experiments showed that the controller designed in this paper had strong anti-disturbance and anti-saturation performance to the compound disturbances of vessels and can effectively complete the formation control.

scholarly journals Galloping Stability and Wind Tunnel Test of Iced Quad Bundled Conductors considering Wake Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xiaohui Liu ◽  
Ming Zou ◽  
Chuan Wu ◽  
Mengqi Cai ◽  
Guangyun Min ◽  
...  
Keyword(s):  
Wind Tunnel ◽  
Transmission Lines ◽  
Degrees Of Freedom ◽  
Wind Tunnel Test ◽  
Aerodynamic Coefficients ◽  
Wake Effect ◽  
Aerodynamic Coefficient ◽  
Set Up ◽  
The Stability ◽  
Three Degrees Of Freedom

A new quad bundle conductor galloping model considering wake effect is proposed to solve the problem of different aerodynamic coefficients of each subconductor of iced quad bundle conductor. Based on the quasistatic theory, a new 3-DOF (three degrees of freedom) galloping model of iced quad bundle conductors is established, which can accurately reflect the energy transfer and galloping of quad bundle conductor in three directions. After a series of formula derivations, the conductor stability judgment formula is obtained. In the wind tunnel test, according to the actual engineering situation, different variables are set up to accurately simulate the galloping of iced quad bundle conductor under the wind, and the aerodynamic coefficient is obtained. Finally, according to the stability judgment formula of this paper, calculate the critical wind speed of conductor galloping through programming. The dates of wind tunnel test and calculation in this paper can be used in the antigalloping design of transmission lines.

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