Abstract
Controlling the exact Cartesian stiffness values of a robot end-effector (EE) is troublesome because of difficulties associated with estimating the stiffness and controllability of a full Cartesian stiffness matrix. However, most practical applications require only quantitative (high/low) stiffness values in the EE motion direction (or perpendicular direction). Full control of the stiffness matrix requiring too many control inputs which is hardly possible in practical applications. To ensure the efficiency of execution for a range of redundant robots, we present an algorithm for shaping a robot’s Cartesian stiffness ellipsoid, a more intuitive and visual stiffness representation, using a nonlinear sequential least square programming optimization. The algorithm is designed to optimize the joint stiffness values and the trajectory of the robot’s joints, using null-space exploration, for a given task. Using eigenvalue decomposition of the stiffness matrix, the algorithm minimizes the orientation difference between the major axis of the current and the desired stiffness ellipsoid and specify a scaling factor between the major and the minor axis. The presented approach allows the user to better understand and control of a robot, regardless of the user’s knowledge of the achievable stiffness range and the interdependencies of the Cartesian stiffness matrix elements.
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Acknowledgements
This research was supported by the Science Fund of the Republic Serbia, #6784, Modular and versatile collaborative intelligent waste management robotic system for circular economy - CircuBot and Slovenian Research Agency grant N2-0269.
Funding
This research was supported by the Science Fund of the Republic Serbia, #6784, CircuBot and Slovenian Research Agency grant N2-0269.
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All authors contributed to the study conception and design. Conceptualisation, resources and funding acquisition were done by Kosta Jovanović and Tadej Petrič. Material preparation, data collection and analysis were performed by Nikola Knežević and Branko Lukić. The first draft of the manuscript was written by Nikola Knezevic and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Knežević, N., Lukić, B., Petrič, T. et al. A Geometric Approach to Task-Specific Cartesian Stiffness Shaping. J Intell Robot Syst 110, 14 (2024). https://doi.org/10.1007/s10846-023-02035-6
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DOI: https://doi.org/10.1007/s10846-023-02035-6