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Summary With the increasing demand for humans and robots to collaborate in a joint workspace, it is essential that robots react and adapt instantaneously to unforeseen events to ensure safety. Constraining robot dynamics directly on SE(3), that is, the group of 3D translation and rotation, is essential to comply with the emerging Human–Robot Collaboration (HRC) safety standard ISO/TS 15066. We argue that limiting coordinate-independent magnitudes of physical dynamic quantities at the same time allows more intuitive constraint definitions. We present the first real-time capable online trajectory generator that constrains translational and rotational magnitude values of 3D translation and 3D rotation dynamics in a singularity-free formulation. Simulations as well as experiments on a hardware platform show the utility in HRC contexts.

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With the increasing demand for robots to react and adapt to unforeseen events, it is essential that a robot preserves agility at all times. While manipulability is a common measure to quantify agility at a given joint configuration, an efficient direct evaluation in task space is usually not possible with conventional methods, especially for redundant robots with an infinite number of Inverse Kinematic solutions. Yet, this is essential for global online optimization of a robot posture. In this work, we derive analytical expressions for a conventional 7-degrees of freedom (7-DOF) serial robot structure, which enable the direct evaluation of manipulability from a reduced task space parametrization. The resulting expressions allow array operation and thus achieve very high computational efficiency with vector-optimized programming languages. This direct and simultaneous calculation of the task space manipulability for large numbers of poses benefits many optimization problems in robotic applications. We show applications in global optimization of robot mounting poses, as well as redundancy resolution with global online optimization w.r.t. manipulability.