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This paper addresses the kinematics of cooperative transport of payloads suspended by multiple aerial robots with cables. In such problems, it is important to determine the positions of the aerial robots to achieve a specified position and orientation of the payload. In general, this inverse kinematics problem has no solutions for the case with one or two robots and infinitely many solutions for three or more robots. However, in the case with three robots, when the tensions of the cables are also specified, this inverse kinematics problem is shown to have a finite number of solutions. In order to obtain all possible solutions, an efficient analytic algorithm based on dialytic elimination is presented in this paper. Case studies with an equilateral triangle payload and a general payload are used for demonstration. In addition, a numerical procedure is developed to determine the set of allowable tensions. Finally, an approach for stability analysis is developed, and the stability of all equilibrium configurations is analyzed.
Date of Publication: Feb. 2013