The main objective of this paper is to find a path for the robot arm from its given start point to its desired goal point in an automated manner without collision with the obstacles. This paper investigates the problem of path planning for a 5 axis robot, operating in environment with obstacles whose boundaries are enveloped by cubic shape. The path planning approach presented is developed in t...

Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arb...

Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arb...

This paper aims to design and generate a loft surface using three distinct curves (Hermitee cubic curve, straight line, quadratic Bezier curve) analyze its characteristics in isotropic space type-2-Bishop. Moreover, the surface's 1st 2nd - fundamental forms were investigated. In addition, their Gaussian, mean, second Gaussian curvatures I3 computed first type-2-Bishop curvatures. Furthermore, r...

Curve fitting with piecewise splines for rapidly varying data has been a difficult problem. Often, the curve exhibits unwanted “wiggles” around those data points whose locations change rapidly in comparison to their neighboring data points. Many methods were proposed to solve this problem using non-homogeneous tension spline or fairing process. In this paper, a new approach using the concept of...

Parametric spline models are used extensively in representing and coding planar curves. For many applications, it is desirable to be able to derive the spline representation from a set of sample points of the planar shape. The problem we address in this paper is to nd a cubic spline model to optimally approximate a given planar shape. We solve this problem by treating the control points which d...

A personal account of the author's encounters with multivariate splines during their early history. 1 Tensor product spline interpolation My first contact with multivariate splines occurred in August 1960. In my first year at the Harvard Graduate School, working as an RA for Garrett Birkhoff, I had not done too well but, nevertheless, had gotten married and so needed a better income than the RA...

In this paper, we propose two Maple procedures and some related utilities to determine the maximum curvature of a cubic Bézier-spline curve that interpolates an ordered set points in R2 or R3. The are designed from closed-form formulas for such open closed curves.

This paper presents a path planning method considering physical limits for two-wheeled mobile robots (TMRs). A convolution operator is used to generate the center velocity trajectory to travel the distance along predefined Bezier curve while considering the physical limits. The trajectory gained through convolution does not consider the rotating angle of TMR, so we present a transformational me...