Orientation Motion Planning Using Cubic Spline Interpolation Based on Euler Parameters

Many engineering applications require smooth orientation planning, i.e., interpolating the orientation of a rigid body so that its motion is smooth through intermediate poses. This smooth motion ensures for instance the continuity of the control torques. There are several ways to represent the orientation of a rigid body, so there are also different ways to plan motion for orientation. Each way has its advantages and disadvantages. In general, the problem of motion planning for the orientation has been less studied due to its complexity compared to motion planning for the endpoint. This paper presents the motion planning for the orientation using Euler parameters when the initial and final directions, and a set of intermediate directions are known. First, the Euler parameters are interpolated using cubic splines, and then they are normalized. Numerical simulations are carried out to validate the effectiveness of the proposed method. The proposed algorithms presented here preserve the fundamental properties of the interpolated rotation. The algorithms presented in this paper provide interpolation tools for rotation that are accurate, easy to implement.