Orientation planning in task space using quaternion polynomials

This paper introduces a computationally fast method for orientation trajectory planning in point-to-point motion tasks when the angular velocity and acceleration at the endpoints are constrained. Addressing such a problem with existing spherical-interpolation-based methods (in the context of unit quaternion) is not straightforward, since the inherent complexities of spherical curves necessitate task-specific tunings for satisfying all the boundary conditions. To tackle such a difficulty, we propound an interpolation function on the basis of standard polynomials in time with quaternion coefficients. We introduce a novel algorithm to determine varying polynomial coefficients in a way that the unit length of interpolated quaternion can be guaranteed. The performance of the developed planning algorithms is illustrated through a functional analysis and via simulation experiments on an anthropomorphic robotic arm. The results corroborate the merits of the presented approach especially in respecting arbitrary boundary conditions.