Smooth Orientation Path Planning with Quaternions Using B-Splines

Many robotics applications require smooth orientation planning, i.e. interpolation or approximation of a frame orientation through prescribed configurations such that the angular velocity and its time derivatives are smooth. This for instance ensures the continuity of the motor torques of robotic manipulator. Yet no satisfactory solution to this problem has been presented. This paper presents a solution using a B-spline parameterization of rotations. The method allows for a continuous interpolation and approximation through a given set of quaternions up to a specified order. The algorithm resembles the well-known B-spline interpolation in the sense that it boils down to solving a system of linear equations. The method is demonstrated for a polishing application (car fender) with an industrial robot.