Modern collaborative robotic applications require robot motions that are predictable for human coworkers. Therefore, trajectories often need to be planned in task space rather than configuration space ($\mathcal{C}$-space). While the interpolation of translations in Euclidean space is straightforward, the interpolation of rotations in$SO(3)$is more complex. Most approaches originating from computer graphics do not exhibit the often desired$\mathcal{C}^{2}$-continuity in robotics. Our main contribution is a$\mathcal{C}^{2}$-continuous, zero-clamped interpolation scheme for quaternions that computes a fast synchronized motion given a set of waypoints. As a second contribution, we present modifications to two state-of-the-art quaternion interpolation schemes, Spherical Quadrangle Interpolation (SQUAD) and Spherical Parabolic Blends (SPB), to enable them to compute$\mathcal{C}^{2}$-continuous, zero-clamped trajectories. In experiments, we demonstrate that for the time optimization of trajectories, our approach is computationally efficient and at the same time computes smooth trajectory profiles.

This paper presents a system for cooperatively manipulating large objects between a human and a robot. This physical interaction system is designed to handle, transport, or manipulate large objects of different shapes in cooperation with a human. Unique points are the bi-manual physical cooperation, the sequential characteristic of the cooperation including contact changes, and a novel architecture combining force interaction cues, interactive search-based planning, and online trajectory and motion generation. The resulting system implements a mixed initiative collaboration strategy, deferring to the human when his intentions are unclear, and driving the task once understood. This results in an easy and intuitive human-robot interaction. It is evaluated in simulations and on a bi-manual mobile robot with 32 degrees of freedom.