This paper presents a cubic spline trajectory generation algorithm that produces continuous position, velocity, and acceleration profiles for 3-axis CNC machines with confined axis jerk and tracking error. A series of reference knots are connected using cubic spline functions in time t for constructing axis trajectories. They are generated in such a way that continuity up to the second derivati...

This paper presents a new method to generate curves, which allows the designer to produce a curve in combinational way allowing him to get the shape that he had in his imagination with keeping the four control point for the curve design. Basing on the modified BEZIER curve, the upgraded algorithm used de Casteljau algorithm on interval [r, s] as a mathematical base to upgrade the suggested meth...

The algorithms and programs in this handy book deal almost exclusively with cubic splines. A short introduction stresses the maximum "smoothness" of "natural" splines. The next chapter reviews the numerical solution of tridiagonal linear systems by Gauss elimination and of block tridiagonal linear systems by relaxation. Chapter 3 offers programs for cubic spline interpolation with various (sepa...

In this paper, we propose a cubic spline interpolation method to generate desired curve path and present an integral line of sight (ILOS) control strategy for course tracking based on nonsingular terminal sliding mode enable underwater snake-like robot (USR) move towards follow the generated by parametric cubic-spline (PCSI) path-planning method, while considering disturbances caused ocean curr...

Bezier curves (BC) have become fundamental tools in many challenging and varied applications, ranging from computer aided geometric design to generic object shape descriptors. A major limitation of the classical Bezier curve however, is that only global information about its control points (CP) is considered, so there can often be a large gap between the curve and its control polygon, leading t...

Parametric curves and surfaces have b e en with us for a long time, and their use for object mode ling in Computer Graphics (as opposed to designing in CAD a pplica tions ) is still growing. There is sometimes. however, a r elucta nce t o use them because i t seems that the added power they give is more than otIse t by the complexity of their formulations and their computat.ions. The purpose of...

The distance between a Be-....ier segment and its control polygon is bounded in terms of the second differences of the control point sequence and a constant that depends only on the degree of the polynomial. The constant derived here is the smallest possible and is sharp for the Hausdorff distance between control polygon and curve segment. The bound provides a straightforward proof of quadratic...

The research status of industrial robot trajectory planning is discussed in detail, and the applicable occasions cubic polynomial interpolation, quintic B-spline curve, mixed interpolation other methods commonly used basic are comprehensively analyzed. At same time, various optimal for robots reviewed. advantages disadvantages compared important direction prospected.

This paper presents cubic spline interpolation based trajectory planning method which is aiming to achieve smooth biped robot walking trajectory. We first characterize the bipedal walking cycle and point out some major issues that need to be addressed to plan a continuous swing leg trajectory by using the concept of cubic polynomial and cubic spline interpolation. By applying these interpolatio...

in the present article, a numerical method is proposed for the numerical solution of thekdv equation by using a new approach by combining cubic b-spline functions. in this paper we convert the kdv equation to system of two equations. the method is shown to be unconditionally stable using von-neumann technique. to test accuracy the error norms2l, ∞l are computed. three invariants of motion are p...