In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a spacelike curve in Minkowski space. In this case, the derivative of the tangent vector of the spacelike curve at a point s is taken as timelike. A method is propose...

In this paper, the stationary acceleration of the spherical general helix in a 3-dimensional Lie group is studied by using a bi-invariant metric. The relationship between the Frenet elements of the stationary acceleration curve in 4-dimensional Euclidean space and the intrinsic Frenet elements of the Lie group is outlined. As a consequence, the corresponding curvature and torsion of these curve...

This paper presents a path learning method through physical human-robot interaction (pHRI) based on stretch-compression iterative control (ILC) scheme and contouring impedance control. The robot learns task desired by the human user kinaesthetic interface provides assistance to in repetitive interactions. Due uncertainty of user’s force motion, time duration each iteration may be different, so ...

This paper defines a symplectic form on the infinite dimensional Fréchet manifold of framed curves of fixed length over a three dimensional simply connected Riemannian manifold of constant curvature. The framed curves are anchored at the initial point and are further constrained by the condition that the tangent vector of the projected curve coincides with the first leg of the orthonormal frame...

A simple measure of overall walking effort would be valuable to patients and clinicians to select suitable treatment interventions and to monitor progress. In this paper, the reproducibility and responsiveness of seven potentially useful clinical measures of walking effort are presented. These walking effort outcomes were derived from a compass gait model and space curve displacement, accelerat...

Asymptote is widely used in astronomy, mechanics, architecture and relevant subjects. In this paper, by analyzing the Frenet frame and the Darboux frame of a curve on the surface, the necessary and sufficient conditions for a quadrilateral boundary being asymptotic of a surface are derived. This quadrilateral is called asymptotic quadrilateral. Given corner data including positions, tangents an...