Abstract
Aerial towed-cable-body systems consisting of helicopters with payloads suspended by cables have been widely used to transport payloads to environments inaccessible by other means. This chapter addresses the kinematics of cooperative transport with multiple aerial robots. Given the desired position and orientation of the payload suspended by cables from aerial robots, we want to determine the positions of the aerial robots to which the cables are attached. This is the inverse kinematics problem. The inverse kinematics problem has, in general, no solutions for the case with one or two aerial robots, and infinitely many solutions for three or more aerial robots. However, in the case with three robots, when the tensions of the cables are given, the inverse kinematics problem is shown to have a finite number of solutions. The problem of determining the position and orientation of the suspended payload for given positions of the aerial robots is the direct kinematics problem. This problem has multiple solutions regardless of the number of cables and robots and is harder than the inverse kinematics problem, as is generally the case with parallel mechanisms. For symmetric geometries, the motion of the system restricted to vertical planes of symmetry can be studied by analyzing equivalent planar four-bar linkages allowing the derivation of closed form solutions. In addition to the direct and inverse kinematics, we briefly discuss the stability analysis that allows us to limit the number of solutions for the direct kinematics to those that are stable.
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Acknowledgements
The authors gratefully acknowledge the support from NSF grants IIS-0413138, IIS-0427313 and IIP-0742304, ARO Grant W911NF-05-1-0219, ONR Grant N00014-08-1-0696, and ARL Grant W911NF-08-2-0004. The first author was supported in part by the PDF fellowship from the Natural Sciences and Engineering Research Council of Canada (NSERC).
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Jiang, Q., Kumar, V. (2013). The Kinematics of 3-D Cable-Towing Systems. In: McCarthy, J. (eds) 21st Century Kinematics. Springer, London. https://doi.org/10.1007/978-1-4471-4510-3_6
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DOI: https://doi.org/10.1007/978-1-4471-4510-3_6
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