An Optimal Feed Interpolator Based on G2 Continuous Bézier Curves for High-Speed Machining of Linear Tool Path

Jin, Yongqiao; Zhao, Shengfeng; Wang, Yuhan

doi:10.1186/s10033-019-0360-8

Cited by 10 publications

(3 citation statements)

References 26 publications

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“…For example, in the cubic spline, if we change only two interpolating points, then we need to redetermine the cubic spline function, but in Bezier functions, one can find a new Bezier function from the old one. Bezier functions are used in computer-aided design (CAD) (see [21]), computer graphics to draw shapes, solving the various control problems such as switching control systems (see [22]), and many different applications (see [23,24,25,26,27,28,29]).…”

Section: Preliminariesmentioning

confidence: 99%

A Novel Method to Solve a Class of Non-local Diffusion Optimal Control Problems by using Bernstein Polynomials

Ketabdari¹,

Farahi²

2020

IJISA

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The aim of this paper is solving optimal control problems governed by non-local diffusion equations via a mesh-less method. The diffusion equation and in particular, the heat conduction equation is essential in sciences. This equation appears in many fields, such as engineering, electrostatic, and mathematics. For solving the mentioned optimal control problems, the method is established upon expanding of variables by the basis of Bezier functions. We apply, for the first time, the Bernstein approximation in solving an optimal control problem governed by the diffusion equation. A direct algorithm is given for solving this problem. Bernstein polynomials expand the trajectories and control functions with unknown control points. Then the optimal control problem is converted to a mathematical programming problem. By solving the mathematical programming problem, the approximated solution of trajectories and control are driven. The convergence of the method in approximating of the optimal control problem is proved. Some numerical examples for demonstrating the effectiveness of the method are included.

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Section: Preliminariesmentioning

confidence: 99%

A Novel Method to Solve a Class of Non-local Diffusion Optimal Control Problems by using Bernstein Polynomials

Ketabdari¹,

Farahi²

2020

IJISA

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“…The polynomial curve, Akima spline curve, Bezier curve, and B-spline curve are commonly used to realize the high-order continuity [11][12][13][14][15][16][17]. While the fitted toolpath is CNC-friendly, this method requires a large amount of calculation [18].…”

Section: Introductionmentioning

confidence: 99%

A Symmetrical Arrangement Strategy based Real-time Toolpath Planning Method for A 5-DoF Fully Parallel Machining Robot

Wang,

Xie,

Xie

et al. 2023

Preprint

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A 5-DoF fully parallel machining robot (PMR) with attitude coupling motion property has the potential to realize the high-efficiency and high-quality machining of complex parts with curved surfaces. From the perspective of mechanism, this kind of 5-DoF fully PMR can achieve no singularity in the workspace after optimum design, so the mobile platform can be adjusted to an arbitrary orientation directly and flexibly. In order to give full play to the above mechanical characteristics, the idea of planning orientation path in unit spherical coordinate system was proposed in our previous work, and then the orientation adjustment efficiency was improved. But the toolpath continuity and calculation simplicity remain to be solved. In light of this concern, the constraint equations to ensure the continuity between two adjacent B-splines are established, and the configuration of control points that can ensure the controllable curvature is derived. On this basis, a symmetrical arrangement strategy that generates shape limits for fitted B-splines to achieve high-order continuity is proposed, and a toolpath planning method is established accordingly. To reduce computational complexity in the feedrate scheduling stage, a linear constraints system is adopted to calculate the feedrate of each point, and the feedrate calculation and interpolation are conducted simultaneously to generate the motion trajectory in real-time. The trajectory planning of S-shaped toolpaths is conducted using the proposed method and the commercial ISG CNC kernel respectively. The comparison results show that the proposed method can effectively improve the motion efficiency, the complexity of calculation, and the fluctuation of feedrate and acceleration. This study provides a more efficient and effective trajectory planning method and is of great significance to the further development of the 5-DoF PMR.

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“…The curve transition technique has been proposed for constructing the G 2 continuous path. The theory of this technique is that sharp corners between adjacent line segments are replaced with a spline curve, and the adjacent lines and curves have G 2 continuity, which has already been adopted in the robot domain [10,11]. Jouaneh et al [12] inserted a circular arc between the adjacent line segments for rapid cornering.…”

Section: Introductionmentioning

confidence: 99%

A Real-time Look-ahead Trajectory Planning Methodology for Multi Small Line Segments Path

Zhang

Liu

Yan³

et al. 2023

Chin. J. Mech. Eng.

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When a robot is required to machine a complex curved workpiece with high precision and speed, the tool path is typically dispersed into a series of points and transmitted to the robot. The conventional trajectory planning method requires frequent starts and stops at each dispersed point to complete the task. This method not only reduces precision but also causes damage to the motors and robot. A real-time look-ahead algorithm is proposed in this paper to improve precision and minimize damage. The proposed algorithm includes a path-smoothing algorithm, a trajectory planning method, and a bidirectional scanning module. The path-smoothing method inserts a quintic Bezier curve between small adjacent line segments to achieve $$G^{2}$$ G 2 continuity at the junctions. The trajectory planning method utilizes a quartic polynomial and a double-quartic polynomial that can achieve a constant velocity at the velocity limitation. The bidirectional scanning module calculates the velocity at each trajectory planning segment point, simplifying calculation complexity and can be run in real time. The feasibility of the proposed algorithm is verified through simulations and experiments, which can be run in real time. In addition, high machining precision can be achieved by adjusting the relevant parameters.

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An Optimal Feed Interpolator Based on G2 Continuous Bézier Curves for High-Speed Machining of Linear Tool Path

Cited by 10 publications

References 26 publications

A Novel Method to Solve a Class of Non-local Diffusion Optimal Control Problems by using Bernstein Polynomials

A Novel Method to Solve a Class of Non-local Diffusion Optimal Control Problems by using Bernstein Polynomials

A Symmetrical Arrangement Strategy based Real-time Toolpath Planning Method for A 5-DoF Fully Parallel Machining Robot

A Real-time Look-ahead Trajectory Planning Methodology for Multi Small Line Segments Path

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