An inverse simulation algorithm based on an integration method is applied to a system formed by a submerged vehicle towed by a single main rotor helicopter by means of a massive, elastic cable. The problem is split into two phases: at each discretization time-step of the inverse simulation, the trajectory of the cable suspension point is derived first, which results into the submerged vehicle following the desired pattern in water; then the control variables for the helicopter are determined, which make the suspension point follow the trajectory obtained at the previous step, including cable tension as an additional load. The control action is then integrated forward in time for a fully coupled complete helicopter-cable-vehicle system model. Discrepancies in the results between the inverse solution and the forward simulation at the end of the time-step are compensated by (ⅰ) introducing a guidance term, which slightly modifies the desired variables at the following step, in order to maintain the towed vehicle on the desired trajectory, and (ⅱ) by an attitude control logic for the helicopter, which manages the variation of moments generated by cable tension. The method is demonstrated for a towed vehicle representative of a realistic sonar system.
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