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A global pattern search method for the optimal control problem of a two-degree-of-freedom manipulator

An optimal control and global mode technology, applied in the direction of manipulators, program-controlled manipulators, manufacturing tools, etc., can solve the problems that mode search can only find local solutions and slow search, and achieve the effect of improving practicability and rapid iteration

Active Publication Date: 2022-06-21
GUANGDONG UNIV OF TECH
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Problems solved by technology

[0006] The purpose of the present invention is to overcome the slow search shortcoming of the traditional global search method, and at the same time solve the shortcoming that the pattern search can only find local solutions, and provide a global model for the optimal control problem of the two-degree-of-freedom manipulator for the two-degree-of-freedom manipulator system Search method for solving the optimization problem of system controllability with respect to the parameters of the state correlation matrix

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  • A global pattern search method for the optimal control problem of a two-degree-of-freedom manipulator
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  • A global pattern search method for the optimal control problem of a two-degree-of-freedom manipulator

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Embodiment Construction

[0026] Before explaining the embodiment, the nonlinear optimal control problem of the two-degree-of-freedom manipulator is explained, such as figure 2 shown, as follows:

[0027]

[0028]

[0029] In formula (1), x(t)∈R 2 is the system state quantity, u(t)∈R is the control quantity, f(x,t)∈R 2 is the system nonlinear function vector, B∈R 2×1 is a constant matrix; J∈R is the performance index to be optimized by the system, L(x,u,t)∈R is the performance function, t i ∈R, t f ∈R are the start time and end time of the problem, respectively; among them, the nonlinear vector f(x, u, t) uses four different state correlation matrices A i (x,t)∈R 2×2 , i=1,2,3,4 is expressed in the following form:

[0030] f(x,u,t)=A(α,x,t)x(t) (2)

[0031] A(α,x,t)=(1-α 1 )(1-α 2 )(1-α 3 )A 1 (x,t)+α 1 (1-α 2 )(1-α 3 )A 2 (x,t)+α 2 (1-α 3 )A 3 (x,t)+α 3 A 4 (x,t) (3)

[0032] In formula (2) and formula (3), α=[α 1 ,α 2 ,α 3 ] T ∈R 3 is the corresponding state correlation ...

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Abstract

The invention discloses a global mode search method for the optimal control problem of a two-degree-of-freedom manipulator. First, several points evenly distributed are calculated in the search space, and iterative search is carried out near the point with the minimum function value. This search method not only has the fast iterative characteristics of the traditional pattern search method, but also makes the obtained optimal point globally optimal in the entire search space, which improves the practicability of the search method. In addition, the present invention uses the existing point set to calculate the simplex gradient after each iterative search, and designs a new search vector set according to the simplex gradient, so that the search vector of each iteration can more accurately reflect the gradient descent of the objective function direction, thereby further reducing the search cost and increasing the search rate.

Description

technical field [0001] The invention relates to the technical field of robot control, in particular to a global pattern search method for the optimal control problem of a two-degree-of-freedom mechanical arm. Background technique [0002] The robotic arm is one of the most common mechanical working devices, consisting of several rigid arms and several rotating joint axes. The manipulator is flexible in operation and has a wide range of applications in the industrial field. But the manipulator is also a kind of complex system with highly nonlinear characteristics. Therefore, the control problem of manipulator has always been the focus of research in the field of control. [0003] State-dependent control is a nonlinear optimal control method suitable for manipulators. Its main operation flow is as follows: figure 2 shown. Such methods have been proposed by Francesco Topputo et al in "Optimal Selection of the Coefficient Matrixin State-Dependent Control Methods". This metho...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): B25J9/16
CPCB25J9/1602
Inventor 陈学松孙剑峰蔡述庭辜方清张丽丽何燕
Owner GUANGDONG UNIV OF TECH
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