We present an algorithm to solve for local Nash Equilibrium trajectories in the multi-agent motion planning problem for self-interested agents. Our method models the problem as a concurrent game where each agent's action consists of choosing a cubic ...

We present a simple degree reduction technique for piecewise cubic polynomial splines, converting them into piecewise quadratic splines that maintain the parameterization and C1 continuity. Our method forms identical tangent directions at the ...

This work is a further development and the culmination along our research line of interface tracking in two dimensions [Zhang and Liu, J. Comput. Phys., 27 (2008), pp. 4063--4088; Zhang, SIAM J. Numer. Anal., 51 (2013), pp. 2822--2850; Zhang and Fogelson, ...

In this paper we present a particle filter-based lane marker tracking approach using a cubic spline model. The system can detect the two main lane markers (i.e. Lane strips) of marked roads from a monocular camera mounted on the top of a vehicle. ...

A new approach based on fuzzy genetic algorithm is developed to find the time-jerk synthetic optimal trajectory of robot with a joint space scheme using cubic splines. In order to get the optimal trajectory, cubic splines are employed and derived under ...

We present a second order numerical method based on cubic spline on a non-uniform mesh for the singularly perturbed two-point boundary value problems having interior layer in the turning point region. As opposed to our previous work dealing with the ...

For the approximation of gradients from data values at vertices of a uniform grid, we compare two methods based on cubic spline interpolation with a classical method based on finite differences. For univariate cubic splines, we use the so-called de Boor'...

We present a new modified nodal cubic spline collocation scheme for solving the Dirichlet problem for Poisson's equation on the unit square. We prove existence and uniqueness of a solution of the scheme and show how the solution can be computed on an $(...

In this paper, we propose a second–order parameter–uniform convergent hybrid scheme for self–adjoint singular perturbation problems (SPPs) subject to mixed (Robin) type conditions. The cubic spline baesd difference scheme is combined with the classical ...

A number of methods based on nonparametric regression have been developed in the last few years which are capable of approximating highly nonlinear class boundaries in classification problems. Bose (Comput. Statist. Data Anal. 22 (1996) 505) used ...

In this paper, we describe a numerical method for solving the shallow water equations (SWEs) in spherical coordinates. The most popular spatial discretization method used in global atmospheric models is currently the spectral transform method, which ...

A numerical method based on cubic splines with nonuniform grid is given for singularly-perturbed nonlinear two-point boundary-value problems, The original nonlinear equation is linearized using quasilinearization. Difference schemes are derived for the ...

Spatial discretization schemes commonly used in global meteorological applications are currently limited to spectral methods or low-order finite-difference/finite-element methods. The spectral transform method, which yields high-order approximations, ...

We examine the De Casteljau algorithm in the context of Riemannian symmetric spaces. This algorithm, whose classical form is used to generate interpolating polynomials in {\Bbb R}^n , was also generalized to arbitrary Riemannian manifolds by others. ...

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 $C^2$ continuity, a property that permits them to satisfy a ...

The paper presents a novel global path planning approach for mobile robot navigation in two dimensional workspace cluttered by polygonal obstacles. The core of the planning method introduced is based on the approximate cell decomposition method. The ...

A constructive approach has been adopted to build interpolatory and B-spline like cubic spline curves with a more general continuity than /spl beta/-continuity. This method provides not only a large variety of very interesting shape controls like biased,...