Lagrangian Methods and Robot Dynamics

The flexible manipulato is widely used in the aerospace industry and various other special fields. Control accuracy is affected by the flexibility, joint friction, and terminal load. Therefore, this paper establishes a robot dynamics model under the coupling effect of flexibility, friction, and terminal load, and analyzes and studies its control. First of all, taking the structure of the central rigid body, the flexible beam, and load as the research object, the dynamic model of a flexible manipulator with terminal load is established by using the hypothesis mode and the Lagrange method. Based on the balance principle of the force and moment, the friction under the influence of flexibility and load is recalculated, and the dynamic model of the manipulator is further improved. Secondly, the coupled dynamic system is decomposed and the controller is designed by the multivariable feedback controller. Finally, using MATLAB as the simulation platform, the feasibility of dynamic simulation is verified through simulation comparison. The results show that the vibration amplitude can be reduced with the increase of friction coefficient. As the load increases, the vibration can increase further. The trajectory tracking and vibration suppression of the manipulator are effective under the control method of multi-feedback moment calculation. The research is of great significance to the control of flexible robots under the influence of multiple factors.

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A Survey on Brachiation Robots: An Energy-Based Review

Robotica ◽

10.1017/s026357472000137x ◽

2021 ◽

pp. 1-13

Author(s):

Sibyla Andreuchetti ◽

Vinícius M. Oliveira ◽

Toshio Fukuda

Keyword(s):

Special Class ◽

Control Strategies ◽

Underactuated Systems ◽

Decision Variable ◽

Robot Dynamics ◽

Technical Literature ◽

Control Schemes

SUMMARY Many different control schemes have been proposed in the technical literature to control the special class of underactuated systems, the- so-called brachiation robots. However, most of these schemes are limited with regard to the method by which the robot executes the brachiation movement. Moreover, many of these control strategies do not take into account the energy of the system as a decision variable. To observe the behavior of the system’s, energy is very important for a better understanding of the robot dynamics while performing the motion. This paper discusses a variety of energy-based strategies to better understand how the system’s energy may influence the type of motion (under-swing or overhand) the robot should perform.

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Augmented Lagrangian Methods for Convex Matrix Optimization Problems

Journal of the Operations Research Society of China ◽

10.1007/s40305-021-00346-9 ◽

2021 ◽

Author(s):

Ying Cui ◽

Chao Ding ◽

Xu-Dong Li ◽

Xin-Yuan Zhao

Keyword(s):

Augmented Lagrangian ◽

Optimization Problems ◽

Augmented Lagrangian Methods ◽

Matrix Optimization ◽

Lagrangian Methods

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Parallel Processing of Robot Dynamics Simulation Using Optimal Multiprocessor Scheduling Algorithms

Systems and Computers in Japan ◽

10.1002/scj.4690191005 ◽

1988 ◽

Vol 19 (10) ◽

pp. 45-54

Author(s):

Hironori Kasahara ◽

Masahiko Iwata ◽

Seinosuke Narita ◽

Hirofumi Fujii

Keyword(s):

Parallel Processing ◽

Scheduling Algorithms ◽

Multiprocessor Scheduling ◽

Dynamics Simulation ◽

Robot Dynamics

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On Augmented Lagrangian Methods with General Lower-Level Constraints

SIAM Journal on Optimization ◽

10.1137/060654797 ◽

2008 ◽

Vol 18 (4) ◽

pp. 1286-1309 ◽

Cited By ~ 187

Author(s):

R. Andreani ◽

E. G. Birgin ◽

J. M. Martínez ◽

M. L. Schuverdt

Keyword(s):

Augmented Lagrangian ◽

Augmented Lagrangian Methods ◽

Lagrangian Methods

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Multiobjective Trajectory Optimization and Adaptive Backstepping Control for Rubber Unstacking Robot Based on RFWNN Method

Mathematical Problems in Engineering ◽

10.1155/2018/7974325 ◽

2018 ◽

Vol 2018 ◽

pp. 1-19

Author(s):

Le Liang ◽

Yanjie Liu ◽

Hao Xu

Keyword(s):

Trajectory Optimization ◽

Control Method ◽

External Disturbance ◽

Backstepping Control ◽

Adaptive Robust Control ◽

Robot Dynamics ◽

Adaptive Backstepping ◽

Recycling Process ◽

Adaptive Backstepping Control ◽

Modeling Uncertainties

Multiobjective trajectory optimization and adaptive backstepping control method based on recursive fuzzy wavelet neural network (RFWNN) are proposed to solve the problem of dynamic modeling uncertainties and strong external disturbance of the rubber unstacking robot during recycling process. First, according to the rubber viscoelastic properties, the Hunt-Crossley nonlinear model is used to construct the robot dynamics model. Then, combined with the dynamic model and the recycling process characteristics, the multiobjective trajectory optimization of the rubber unstacking robot is carried out for the operational efficiency, the running trajectory smoothness, and the energy consumption. Based on the trajectory optimization results, the adaptive backstepping control method based on RFWNN is adopted. The RFWNN method is applied in the main controller to cope with time-varying uncertainties of the robot dynamic system. Simultaneously, an adaptive robust control law is developed to eliminate inevitable approximation errors and unknown disturbances and relax the requirement for prior knowledge of the controlled system. Finally, the validity of the proposed control strategy is verified by experiment.

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