Tham khảo tài liệu 'new approaches in automation and robotics part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Models for Simulation and Control of Underwater Vehicles 203 pressure of the vehicle and are a function of the vehicles shape and of the square of its velocity. The center of pressure is also strongly dependent on vehicle s shape. For a more indepth analysis of this subject see for instance Hoerner 1992 . With the exception of the gravity and buoyancy forces these effects are best described in the Body-Fixed Frame. Therefore the remaining equations of motion describing the vehicle s kinetics can be presented in the following compact form MV c v v d v v g n Tact 11 M is the constant inertia and added mass matrix of the vehicle c v is the Coriolis and centripetal matrix D v is the Damping matrix g n is the vector of restoring forces and moments and Tact is the vector of body-fixed forces from the actuators. We follow the common formulation where the lift and drag terms are both accounted in the damping matrix. For vehicles with a streamlined shape theoretical and empirical formulas may be used. However it must be remarked that in practice these vehicles are not quite as regular as assumed in the formulas usually employed for added mass drag and lift they have antennas transducers and other protuberances that affect those effects with special incidence on the drag terms. Therefore we should look at the formulas as giving underestimates of the true values of the coefficients. In certain situations it may be useful to consider the following simplifications if the vehicle s weight equals its buoyancy and the center of gravity is coincident with the center of buoyancy g n is null for an AUV with port starboard top bottom and fore aft symmetries M and D v Di v D2 v are diagonal. In the later case the damping matrix has the following form D1 V diag Xu Yv Zw Kp Mq Mq 12 D2 v diag Xu u I ul Yv v lvl Zw w w Kp p lpl Mq q q Nr r r 13 For low velocities the quadratic terms on Eq. 13 such as Yv v v may be considered negligible. However in practice the fore aft symmetry is rarely
