Reference shaping of periodic trajectory for systems having constraints

2004 ◽  
Author(s):  
T. Sugie ◽  
H. Suzuki
Keyword(s):  
Periodic Trajectory

On stability loss delay for a periodic trajectory

1996 ◽  
pp. 253-278 ◽  
Author(s):  
A. I. Neishtadt ◽  
C. Simó ◽  
D. V. Treschev
Keyword(s):  
Stability Loss ◽  
Periodic Trajectory

Robustness Analysis of a Simple and Augmented Proportional Plus Derivative Controller in Trajectory Following Robots Using the Floquet Theory

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
B. Sandeep Reddy ◽  
Ashitava Ghosal
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Floquet Theory ◽  
Robustness Analysis ◽  
Periodic Trajectory ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Pd Controller ◽  
Simulation Results ◽  
Trajectory Following

This paper deals with the issue of robustness in control of robots using the proportional plus derivative (PD) controller and the augmented PD controller. In the literature, a variety of PD and model-based controllers for multilink serial manipulator have been claimed to be asymptotically stable for trajectory tracking, in the sense of Lyapunov, as long as the controller gains are positive. In this paper, we first establish that for simple PD controllers, the criteria of positive controller gains are insufficient to establish asymptotic stability, and second that for the augmented PD controller the criteria of positive controller gains are valid only when there is no uncertainty in the model parameters. We show both these results for a simple planar two-degrees-of-freedom (2DOFs) robot with two rotary (R) joints, following a desired periodic trajectory, using the Floquet theory. We provide numerical simulation results which conclusively demonstrate the same.

Non-Attractive Periodic Trajectory Formation Mechanism on Random and Chaotic Time Series

2020 ◽  
Author(s):  
Hitoaki Yoshida ◽  
Takeshi Murakami
Keyword(s):  
Time Series ◽  
Formation Mechanism ◽  
Random Number ◽  
Periodic Trajectory ◽  
Closed Trajectory ◽  
Number Series ◽  
Pseudo Random Number ◽  
Trajectory Formation ◽  
Random Neural Network ◽  
Iot Devices

Pseudo-random number series extracted from chaotic and random time series from the chaotic and random neural network (CRNN) with fixed-point arithmetic has been the focus of attention for protecting the information security of IoT devices. Pseudo-random number series generated by a computer is eventually periodic, practically. The produced closed trajectory is not a limit cycle, because which does not divide the phase space into 2 regions. The closed trajectory in this work is called a non-attractive periodic trajectory (NPT) because it hardly attracts trajectories within the neighborhood. The method of preventing the closed trajectory formation has been proposed on the basis of the NPT formation mechanism in this paper. The method has extended the period of NPT considerably. It is expected to apply security applications for IoT devices.

scholarly journals Global asymptotic stability of a passive juggling strategy: A possible parts-feeding method

1995 ◽  
Vol 1 (3) ◽  
pp. 193-224 ◽  
Author(s):  
P. J. Swanson ◽  
R. R. Burridge ◽  
D. E. Koditschek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Initial Conditions ◽  
Periodic Trajectory ◽  
Degree Of Freedom ◽  
Feeding Method ◽  
Feeding Problem ◽  
Simulation Results ◽  
Parts Feeding

In this paper we demonstrate that a passive vibration strategy can bring a one-degree-of-freedom ball to a specified periodic trajectory from all initial conditions. We draw motivation from the problem of parts feeding in sensorless assembly. We provide simulation results suggesting the relevance of our analysis to the parts feeding problem.

Dynamic Servo Control for Underactuated Mechanical Systems

2012 ◽  
Author(s):  
Hongtai Cheng ◽  
Heping Chen ◽  
Xiaohua Zhang ◽  
Hongjun Chen
Keyword(s):  
Periodic Trajectory ◽  
Servo Control ◽  
Underactuated Mechanical Systems ◽  
Dynamic Tracking ◽  
Generating Method ◽  
Lack Of Control ◽  
Tracking Controller ◽  
State Point ◽  
Planning Procedure ◽  
Motion Range

Due to the lack of control inputs, the motion range and application areas of underactuated mechanical system are greatly limited. To overcome such difficulties, the arbitrary state point dynamic tracking problem named dynamical servo control is discussed in this paper. Considering simplicity and repeatability, periodic trajectory is the best way leading to the desired point. Virtual constraints concept is employed and a target oriented trajectory planning procedure is proposed, which can generate periodic dynamic compatible and desired point crossing trajectory. A Lyapunov based tracking controller is proposed to avoid the strict conditions for using a traditional LQR based method. Experiments are performed on an Acrobot prototype and verify the correctness of the proposed periodic trajectory generating method and the effectiveness of the tracking controller.

Cislunar Navigation Constellation by Displaced Solar Sails

2017 ◽  
Vol 70 (5) ◽  
pp. 963-982 ◽  
Author(s):  
Xiao Pan ◽  
Ming Xu
Keyword(s):  
Stability Boundary ◽  
Differential Evolution Algorithm ◽  
Periodic Trajectory ◽  
Trajectory Design ◽  
Regular Tetrahedron ◽  
Solar Sails ◽  
Lagrangian Points ◽  
Out Of Plane ◽  
Number Variation ◽  
Navigation Constellation

Increasing lunar exploration activities are giving rise to higher demands for a navigation constellation system in cislunar space. A novel constellation of solar sails around the Sun-Earth Artificial Lagrangian Points (ALPs) is proposed for cislunar navigation in this paper, which benefits from the numberless and out-of-plane advantages of ALPs compared with the classical Lagrangian points. To relieve the technical pressure on sail equipment, a two-layer optimisation strategy including the navigation constellation architecture and trajectory design is developed to reduce the desired lightness number of the sail's motion. The constellation architecture is constructed in the shape of a regular tetrahedron, whose size and orientation are derived from the realisable lightness number at the ALPs. The powerful Hamiltonian structure-preserving controller and differential evolution algorithm are adopted to propagate the bounded quasi-periodic trajectory with minimum lightness number variation. With the premise of the sail's high feasibility in the mechanism, the numerical navigation simulations for a typical trans-lunar weak stability boundary trajectory indicate that the proposed navigation constellation has a low geometric dilution of precision factor and a good navigation performance.

THE COMPUTATION OF LYAPUNOV EXPONENTS FOR PERIODIC TRAJECTORIES

2005 ◽  
Vol 15 (12) ◽  
pp. 4075-4080 ◽  
Author(s):  
JIALIN HONG
Keyword(s):  
Lyapunov Exponents ◽  
Lorenz System ◽  
Periodic Trajectory ◽  
Computational Time ◽  
Periodic Trajectories ◽  
Linear Differential Systems ◽  
Periodic Linear ◽  
Group Methods ◽  
Linear Differential ◽  
The Lorenz System

We present a new method for the numerical computation of Lyapunov exponents of periodic trajectories which is crucial in the investigation of dynamics. The computational time of this method is merely a period of the periodic trajectory considered, when Lyapunov exponents can be approximated as precise as one wants. Our method stems from a combination between Floquet theory on periodic linear differential systems and Lie group methods in structure preserving algorithms on manifolds. The Lyapunov exponents of a periodic trajectory of the Lorenz system and a periodic solitary wave of the nonlinear Schrödinger equation with periodic coefficients are investigated by using the method.

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