Robot learning empowers the robot system with human brain-like intelligence to autonomously acquire and adapt skills through experience, enhancing flexibility and adaptability in various environments. Aimed at achieving a similar level of capability in large language models (LLMs) for embodied intelligence, data quality plays a crucial role in training a foundational model with diverse robot skills. In this study, we investigate the collection of data for manipulation tasks using teleoperation devices. Different devices yield varying effects when paired with corresponding controller strategies, including position-based inverse kinematics (IK) control, torque-based inverse dynamics (ID) control, and optimization-based compliance control. In this paper, we develop a teleoperation pipeline that is compatible with different teleoperation devices and manipulator controllers. Within the pipeline, we construct the optimal QP formulation with the dynamic nullspace and the impedance tracking as the novel optimal controller to achieve compliant pose tracking and singularity avoidance. Regarding the optimal controller, it adaptively adjusts the weights assignment depending on the robot joint manipulability that reflects the state of joint configuration for the pose tracking in the form of impedance control and singularity avoidance with nullspace tracking. Analysis of quantitative experimental results suggests the quality of the teleoperated trajectory data, including tracking error, occurrence of singularity, and the smoothness of the joints' trajectory, with different combinations of teleoperation interface and the motion controller.

Manipulability maximization for inverse kinematics is done, e.g., in Dufour and Suleiman (2017). Several important tasks in robotics require compliance in A potential function on the torque level, as an additive the robot's end-effector including handling tasks, such as impedance, based on the manipulability measure is proposed the peg-in-hole task, see, e.g., Park et al. (2017) and Song in Ott (2008) for singularity avoidance. Due to the et al. (2021), or more recently tasks in physical humanrobot complexity introduced by maximizing the manipulability interaction (pHRI), see, e.g., Sharifi et al. (2022) measure, an optimization approach using a dynamic neural and Li et al. (2018). To this end, control concepts enabling network is introduced in Jin et al. (2017) for tracking compliance in the end-effector, e.g., prescribing a specific control including the consideration of joint velocity limits.

Articulated robots such as manipulators increasingly must operate in uncertain and dynamic environments where interaction (with human coworkers, for example) is necessary. In these situations, the capacity to quickly adapt to unexpected changes in operational space constraints is essential. At certain points in a manipulator's configuration space, termed singularities, the robot loses one or more degrees of freedom (DoF) and is unable to move in specific operational space directions. The inability to move in arbitrary directions in operational space compromises adaptivity and, potentially, safety. We introduce a geometry-aware singularity index, defined using a Riemannian metric on the manifold of symmetric positive definite matrices, to provide a measure of proximity to singular configurations. We demonstrate that our index avoids some of the failure modes and difficulties inherent to other common indices. Further, we show that this index can be differentiated easily, making it compatible with local optimization approaches used for operational space control. Our experimental results establish that, for reaching and path following tasks, optimization based on our index outperforms a common manipulability maximization technique and ensures singularity-robust motions.