We present a novel trajectory computation algorithm to smooth jerky collision-free paths computed by samplebased motion planners. Our approach uses cubic B-splines to generate G or curvature continuous trajectories. The algorithm performs local spline refinement to compute smooth, collision-free paths in narrow passages and satisfy velocity and acceleration constraints. We also present a fast a...

We present a novel trajectory computation algorithm to smooth piecewise linear collision-free trajectories computed by samplebased motion planners. Our approach uses cubic B-splines to generate trajectories which are C almost everywhere, except on a few isolated points. The algorithm performs local spline refinement to compute smooth, collision-free trajectories and it works well even in enviro...

Taylor B-spline collocation method (TCM) is proposed to obtain the numerical solution of the nonlinear Schrödinger(NLS) equation with appropriate initial and boundary conditions. Time discretization is carried out with Taylor series expansion and resulting system of equation is fully-integrated using cubic B-spline collocation method. Test problems concerning single soliton motion, interaction ...

We consider the efficient estimation of the semiparametric additive transformation model with current status data. A wide range of survival models and econometric models can be incorporated into this general transformation framework. We apply the B-spline approach to simultaneously estimate the linear regression vector, the nondecreasing transformation function, and a set of nonparametric regre...

Three different spline-based approaches for solving Bratu and Bratu-type equations are presented. The classical cubic spline collocation method, an adaptive spline collocation on nonuniform partitions, and an optimal collocation method are derived for solving Bratu-type equations. Numerical examples are presented to verify the efficiency and accuracy of these methods when compared to other nume...

A new method using the cubic B-spline curves with nominal uniform knot set to parameterize the geometry is proposed to deal with shape optimization problems. In the method, the control points of the B-spline curves are set to be the design variables in the optimization scheme. A knot insertion algorithm has been introduced in order to keep the geometry unchanged whilst increasing the number of ...

Bivariate cubic L1 smoothing splines are introduced. The coefficients of a cubic L1 smoothing spline are calculated by minimizing the weighted sum of the L1 norms of second derivatives of the spline and the 1 norm of the residuals of the data-fitting equations. Cubic L1 smoothing splines are compared with conventional cubic smoothing splines based on the L2 and 2 norms. Computational results fo...

Inertial navigation is the problem of estimating the flight path of a moving object based on only acceleration measurements. This paper describes and compares two approaches for intertial navigation. Both approaches estimate the flght path of the moving object using cubic spline interpolation, but they find the coefficients of the cubic spline pieces by different methods. The first approach use...

This paper describes the use of cubic splines for interpolating monotonic data sets. Interpolating cubic splines are popular for fitting data because they use low-order polynomials and have C2 continuity, a property that permits them to satisfy a desirable smoothness constraint. Unfortunately, that same constraint often violates another desirable property: monotonicity. The goal of this work is...

The appropriateness of various numerical procedures for obtaining valid time-derivative data recently reported in the literature (Zernicke et a/., 1976: McLaughlin er al., 1977; Pezzack et u/., 1977) is discussed. A case for the use of quintic natural splines is presented. based on the smoothness of higher derivatives and flexibility in application. \‘ES; /\ . _J”P JGTc, SE=5 :;yz,s’sy = z7 ___...