This paper presents an improved modelling method for a water jet-based multi-propeller propulsion system. In our previous work, the modelling experiments were only carried out in 2D planes, whose experimental results had poor agreement when we wanted to control the propulsive forces in 3D space directly. This research extends the 2D modelling described in the authors' previous work into 3D space. By doing this, the model could include 3D space information, which is more useful than that of 2D space. The effective propulsive forces and moments in 3D space can be obtained directly by synthesizing the propulsive vectors of propellers. For this purpose, a novel experimental mechanism was developed to achieve the proposed 3D modelling. This mechanism was designed with the mass distribution centred for the robot. By installing a six-axis load-cell sensor at the equivalent mass centre, we obtained the direct propulsive effect of the system for the robot. Also, in this paper, the orientation surface and propulsiv...
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