Abstract
This paper presents an ellipsoidal set-membership uncertainty model for wire-based tracking systems with wire length uncertainties and joint clearances. Although the proposed model is valid for any number of wires and configurations, including singularities, it has been particularized to a 3-2-1 parallel wire mechanism. The Euler’s tetrahedron formula has been used to obtain a numerically stable solution to the direct kinematics of this particular tracking system as well as a compact characterization of its singularities directly expressed in terms of the wire lengths. It is also shown that these singularities, when expressed in the configuration space of the moving element, can be identified as C-surfaces associated with the three basic contacts between polyhedra, which have been widely studied in the context of path planning.
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Thomas, F., Ottaviano, E., Ros, L., Ceccarelli, M. (2002). Uncertainty Model and Singularities of 3-2-1 Wire-Based Tracking Systems. In: Lenarčič, J., Thomas, F. (eds) Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0657-5_12
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DOI: https://doi.org/10.1007/978-94-017-0657-5_12
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