Schooling for Multiple Underactuated AUVs
Jihong Li, Pan-Mook Lee · InTech eBooks · 2009
Underwater Vehicles 296 tracking methods were all case-by-case that strongly depended on the ship's specifically simplified dynamics.Therefore, these tracking methods also cannot be directly applicable to the case of underwater vehicles.Since the sway and heave forces are unavailable, the most challenge in the tracking control is how to properly handle the vehicles' sway and heave dynamics in the position tracking.To deal with this problem, in this chapter, we introduce a certain polar coordinates transformation for the vehicle's velocities in the body-fixed frame.Through this coordinates transformation, each vehicle's dynamics can be transformed to a certain two inputs nonlinear strict-feedback form, according to which the proposed schooling scheme is derived.For the torpedo-type underwater flying vehicles considered in this chapter, the pitch and yaw moments are proportional to the square of the vehicle's forward speed.From this point of view, the pitch and yaw moments are not exactly independent with the surge force.If the vehicle's forward speed is taken small value, then the pitch and yaw moments are also have to take small values, therefore, in this case we cannot fully excite the vehicle's pitch and yaw dynamics.To appropriately taking these three only available control inputs -surge force, pitch and yaw moments as independent ones, the vehicle's forward speed has to be guaranteed to take considerable magnitude.For this reason, in this chapter, firstly we assume that the vehicle's forward speed satisfies the above consideration.And the proposed schooling scheme, which is derived under this assumption, reversely can guarantee the assumption always to be fulfilled under certain initial conditions.The common method of formation among the schemes presented so far is to apply certain potential function to conduct the agents' group behaviour.The potential function initially used in the robotics for mobile robot's motion planning (Latombe, 1991;Rimon & Koditschek, 1992), and recently widely applied in the formation of multiple agents systems (Leonard & Fiorelli, 2001;Olfati-Saber, 2006;Do, 2007).Aforementioned Reynolds's three heuristic rules of flock centring, collision avoidance, and velocity matching, which are also known as cohesion, separation, and alignment, are usually embodied by suitably selected potential functions.In Leonard & Fiorelli (2001), only 1 time differentiable function was used as potential for group formation, while How to referenceIn order to correctly reference this scholarly work, feel free to copy and paste the following: