A universal approach to interpolation on reductive homogeneous spaces

A method for computing a [Formula: see text]-curve with given initial and final velocities interpolating a finite number of points on a reductive homogeneous space is presented. Here the reductive homogeneous space is assumed to be embedded into some manifold in a suitable way making the proposed approach very general. Building on the notion of intrinsic rolling, the method presented here offers a solution of the interpolation problem in closed form. This is illustrated on the example of matrix Lie groups. Moreover, this method is applied to the (compact) Stiefel manifold, where an efficient algorithm for solving the interpolation problem is also obtained.