Let f : Mn [right arrow] [R.sup.n+1] be a frontal with a unit normal vector field
Let V be a vector field
along [alpha] such that it is a curve's infinitesimal variation.
In this paper we present a novel motion planning method for a differential drive mobile robot using two-dimensional vector fields
. This method requires that the given path for a mobile robot control system must be specified as a set of the reference points that we will call here the "nodal" points.
(1) Let [??](m, [epsilon]) be the mean curvature vector field
of [[phi].sub.[epsilon]] at m [member of] S, then
If v and w are two vector fields
defined in a neighborhood of S, then the covariant derivative [[nabla].sup.S.sub.v]w is equal, at x [member of] S, to the orthogonal projection of [D.sub.v]w, projected orthogonally to the tangent space [T.sub.x]S (cf.
For a vectorial case, if we have a vector field
H(r), then it can be treated as a dual 1-cochain H on the dual mesh as:
The system is described by a switched nonlinear differential equation with piecewise smooth vector fields
. Reconstructed image pixels were obtained by using the initial value problem of differential equations describing the dynamical system, for example, a continuous-time image reconstruction (CIR) system.
It is well known that a cooperative vector field
satisfies the following Kamke condition (see [22, Remark 1.1, pp.
Therefore, since both the Einstein and energy-momentum tensors are diagonal, only one component of the Lyra displacement vector field
may be nonzero and its other components should be zero.
The key of MA-R algorithm is how to compute the motion vector field
of each non-key frame, which is described as follows.
A vector field
V on a semi-Riemannian manifold ([bar.M], [bar.g]) is an ACV ifand only if