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NURBS (Non-Uniform Rational B-Spline) curve velocity interpolation method based on parameter encryption

A parametric and interpolation technology, applied in manipulators, program-controlled manipulators, manufacturing tools, etc., can solve the problems of low efficiency of second-order derivation calculations, and achieve the effects of avoiding complex numerical calculation methods, high calculation efficiency, and reducing vibration

Pending Publication Date: 2021-08-24
NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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AI Technical Summary

Problems solved by technology

[0004] Purpose of the invention: The purpose of the invention is to provide a speed interpolation method for NURBS curves based on parameter densification to solve the problem of low efficiency of the second-order derivation calculation of NURBS curves in view of the prior art

Method used

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  • NURBS (Non-Uniform Rational B-Spline) curve velocity interpolation method based on parameter encryption
  • NURBS (Non-Uniform Rational B-Spline) curve velocity interpolation method based on parameter encryption
  • NURBS (Non-Uniform Rational B-Spline) curve velocity interpolation method based on parameter encryption

Examples

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Embodiment 1

[0114] Embodiment 1: Randomly take ten discrete points as type value points, and the coordinates of type value points are as attached drawings figure 1 ;

[0115] Carry out cumulative chord length parameterization to solve the node vector of the cubic NURBS curve, and set the repetition degree of the first and last nodes to 4, and obtain the node vector as follows:

[0116]

[0117] Select the first tangent vector condition {-1,0,0} to inversely calculate the control vertices, and obtain the control vertices as shown in the attached figure figure 2 ;

[0118] A complete NURBS fitting curve can be obtained by substituting the uniform parameterization between any two node vectors into the De-Boor recursive formula (see attached figure image 3 ).

[0119] Use the chord length between any two points on the NURBS fitting curve to approximate the arc length (see the attached figure for the arc length data Figure 4 ), the arc length is cumulatively parameterized to obtain t...

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Abstract

The invention discloses an NURBS (Non-Uniform Rational B-Spline) curve velocity interpolation method based on parameter encryption, and belongs to the technical field of robot motion control. The NURBS curve velocity interpolation method comprises the steps of: calculating a node vector in an accumulated chord length parameterization manner, inversely calculating a control vertex through a type value point, positively calculating a parameter track through a control vertex, establishing a relation between a curve track parameter and an arc length parameter through a least square method, and performing track point selection in combination with a parameterization model and a T-shaped velocity interpolation model to realize T-shaped acceleration and deceleration variable motion control. The NURBS curve velocity interpolation method is scientific and reasonable. The parameterization model is used in parameter encryption of the NURBS curve, direct second-order derivation operation on the NURBS spline function is avoided, a complex numerical calculation method is avoided, and only basic arithmetic operation is used. The algorithm is simple and convenient, and the operation efficiency is high. The T-shaped velocity interpolation model with self-defined acceleration and deceleration is used, variable-speed motion control over the tail end of a mechanical arm on a cubic NURBS curve is achieved, the velocity is continuously controllable, and vibration generated by an industrial robot is greatly reduced.

Description

technical field [0001] The invention relates to the technical field of robot motion control, in particular to a NURBS curve speed interpolation method based on parameter densification. Background technique [0002] The trajectory planning of industrial robots in the Cartesian task space includes the planning of position, attitude interpolation and velocity, acceleration and jerk curves. Ordinary industrial robot trajectory planning and control systems often only have linear and arc trajectory planning and interpolation, and this system has limited ability to interpolate free curves for complex parts, which will cause large errors, and due to the particularity of free curves It will cause the speed and acceleration of the actuator to be discontinuous at the adjacent positions of the interpolation period, thus causing the industrial robot to vibrate. [0003] Facing the movement of complex trajectory curves in the robot task space, many scholars at home and abroad have carrie...

Claims

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Application Information

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IPC IPC(8): B25J9/16
CPCB25J9/16
Inventor 段晋军俞宙航戴振东刘正权郭策宾一鸣李炳锐
Owner NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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