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.

Modern collaborative manipulators operate in unknown environments and share the work space with human coworkers. To ensure flexibility, their kinematic design is redundant which increases the solution space of the inverse kinematics (IK). We propose a real-time capable Predictive Kinematics Controller (PKC) that tracks task space trajectories as a first priority and computes optimal joint trajectories w.r.t. secondary objectives based on model predictive control (MPC). Therefor, the PKC solves a MPC problem in the nullspace of the task space trajectory. We benchmark a direct shooting, a direct collocation and an indirect gradient method in simulation and we identify the direct shooting method as the most efficient. We demonstrate the superior performance of the PKC compared to state-of-the-art local redundancy resolution approaches. In experiments, we show the real-time capability of our implementation.

Collaborating robots face rising challenges with respect to autonomy and safety as they are deployed in flexible automation applications. The ability to perform the required tasks in the presence of humans and obstacles is key for the integration of these machines in industry. In this work we introduce a framework for motion planning of manipulators that builds upon the most promising existing approaches by combining them in an advantageous way. It includes a new Obstacle-related Sampling Rejection Probabilistic Roadmap planner (ORSR-PRM) that represents the free workspace in an efficient way. Using this representation, dynamic obstacles can be avoided in real-time using an attractor-based online trajectory generation. The resulting motions satisfy kinematic and dynamic joint limits, ensuring a safe human-robot interaction. We validate the functionality and performance of the presented framework in simulations and experiments.