In this paper, the sling load dynamics of an aerial vehicle carrying a payload are investigated by employing three formulations of the governing equations. They are the hybrid formulation where the system exists in either a taut cable or slack cable configuration, with appropriate treatment of the transition between the two; the linear complementarity problem (LCP) formulation where the cable constraints are imposed as linear complementarity conditions and finally, the lumped parameter formulation where the cable is modelled with a series of spring-mass elements. The hybrid and LCP formulations neglect the elasticity of the cable while the lumped parameter model explicitly accounts for the elastic properties of the cable, albeit in a discrete way. The importance of the incorporation of elastic properties of the cable on the system is investigated for the variation in solution space of the payload. The three formulations are compared numerically, for information on the computational cost, motion of the payload, and tension profile, for several aerial maneuvers, including an aggressive obstacle avoidance with a window clearance flight.

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