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A limit optimization method for a seven-degree-of-freedom manipulator based on position-level inverse kinematics

A technology of inverse kinematics and optimization methods, which is applied to manipulators, program-controlled manipulators, and manufacturing tools. Dynamic self-motion, ensuring consistency, and optimizing the joint range of motion

Active Publication Date: 2021-11-19
HARBIN INST OF TECH
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  • Abstract
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  • Claims
  • Application Information

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Problems solved by technology

[0004] The purpose of the present invention is to solve the problem that the existing numerical solution cannot obtain a closed solution, and there will be self-motion in the final state; the analytical solution cannot address the offset configuration, and the possibility of understanding the solution with the reduced degree of freedom is limited. Fixing a joint is equivalent to The flexibility of the robotic arm is limited, and there is a problem that it is impossible to optimize the motion

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  • A limit optimization method for a seven-degree-of-freedom manipulator based on position-level inverse kinematics
  • A limit optimization method for a seven-degree-of-freedom manipulator based on position-level inverse kinematics
  • A limit optimization method for a seven-degree-of-freedom manipulator based on position-level inverse kinematics

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specific Embodiment approach 1

[0054] Specific Embodiment 1: A position-level inverse kinematics-based seven-degree-of-freedom mechanical arm limit optimization method in this embodiment includes the following steps:

[0055] Step 1: Obtain the analytical solution of the inverse kinematics of the seven-degree-of-freedom manipulator based on the parametric solution of a fixed joint angle;

[0056] Step 2: take the fixed joint angle parameter as input, and the joint limit as an optimization index, and establish an optimal control problem;

[0057] Step 3: Transform the constrained problem into an unconstrained problem based on the Lagrange multiplier method;

[0058] Step 4: Realize the solution to the optimal joint angle parameters based on the Newton iterative method;

[0059] Step 5: By giving the initial configuration, expected end pose and Cartesian path planning, seven joint space trajectories considering joint limit optimization are obtained.

[0060] The present invention aims at optimizing the para...

specific Embodiment approach 2

[0061] Specific implementation mode two: step one of this embodiment mode comprises the following steps:

[0062] Step 11: For the 7DOF manipulator joint θ i (i=1, 2...7), fix a certain joint u, and regard it as a six-degree-of-freedom robotic arm. The positive kinematic relationship of the robotic arm can be expressed as:

[0063] f(x,u)=T (1)

[0064] Among them, x is the remaining joints except the joint u, T is the desired pose, which is a constant value when solving;

[0065] Step 1 and 2: Based on the joint angle parameterization method, the analytical solution of inverse kinematics is solved, and the corresponding position-level inverse kinematics is expressed as:

[0066] x=ikine(u, T, x 0 ) (2)

[0067] where x 0 is the initial configuration of the robot arm. In the motion space of the manipulator, regardless of the singular position of the manipulator, each corresponding to a fixed joint angle u and the corresponding end pose T, there is a set of corresponding ...

specific Embodiment approach 3

[0068] Specific implementation mode 3: Step 2 of this implementation mode considers the joint limit optimization criterion when establishing the optimal control problem. For each joint angle θ, the objective function that needs to be satisfied is:

[0069]

[0070] Among them, θ imax and θ imin are the upper and lower limits of the motion range of the i-th joint, respectively, formula (1) and formula (3) form the inverse kinematics solution problem of the seven-degree-of-freedom manipulator considering the joint limit optimization. The goal of optimization is to minimize H, and this optimization index keeps the joint motion of the manipulator away from the limit position. Other compositions and connections are the same as those in Embodiment 1 or Embodiment 2.

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Abstract

A limit optimization method for a seven-degree-of-freedom manipulator based on position-level inverse kinematics, which relates to a limit optimization method for a seven-degree-of-freedom manipulator. The present invention solves the problem that the existing numerical solution cannot obtain a closed solution, and there is self-motion of the final state; the analytical solution cannot target the offset configuration, and there is a problem that the motion optimization cannot be realized. The present invention first obtains the analytical solution of the inverse kinematics of the 7-DOF manipulator based on the parametric solution method of fixing a certain joint angle; then takes the fixed joint angle parameter as input and the joint limit as the optimization index to establish the optimal control problem; then based on the Lagrange multiplier method, the constrained problem is transformed into an unconstrained problem; finally, based on the Newton iterative method, the optimal joint angle parameter is solved, by giving the initial configuration, the expected end pose and Cartesian path planning obtains 7 joint space trajectories considering joint limit optimization. The invention is used for the limit optimization of a seven-degree-of-freedom mechanical arm.

Description

technical field [0001] The invention relates to a limit optimization method for a seven-degree-of-freedom mechanical arm, in particular to a limit optimization method for a seven-degree-of-freedom mechanical arm based on position-level inverse kinematics, and belongs to the field of robot inverse kinematics. Background technique [0002] In order to meet the flexibility of the manipulator's movement, the manipulator often has redundant degrees of freedom (such as 7 degrees of freedom) and different configurations, which brings challenges to the inverse kinematics solution. The speed-level inverse kinematics solution method based on the Jacobian null space is a numerical solution. Due to the redundant mechanical arm, its inverse kinematics is a numerical solution, so an analytical solution cannot be obtained, and it will fall into the final state of self-motion. Based on the Jacobian The general solution of the inverse kinematics of the manipulator is that the manipulator rea...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): B25J9/16
CPCB25J9/1664
Inventor 刘业超张耀文谢宗武刘宏
Owner HARBIN INST OF TECH
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