tailieunhanh - Autonomous Underwater Vehicles Part 2

Tham khảo tài liệu 'autonomous underwater vehicles part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Development of a Vectored Water-Jet-Based Spherical Underwater Vehicle 9 So a general transform matrix can be obtained pPb bp pPp C 4 where pPb is the position vector of propeller-fixed coordinate expressed in vehicle-fixed coordinate p p1 p2 p3 T is the transform matrix from propeller-fixed coordinate to vehicle-fixed coordinate p Pp is the position vector in propeller-fixed coordinate and the C is a constant vector. Now let us take a look at three motions surge heave and yaw. The definition of these three motions can be found in Fossen 1995 . Before that we define two angles which will be used for orientation of propellers. gives the definition of a and ft. gives a demonstration of surge heave and yaw. a Rotation in X-Y Plane b Rotation in X-Z Plane Fig. 10. Orientation of Propellers a Surge b Heave c Yaw Fig. 11. Propulsion Forces for Surge Heave and Yaw The first case is surge. In this case two of the water-jet propellers will work together and the other one could be used for brake. So from a two water-jet propellers in the left will be used for propulsion and if we want to stop the vehicle from moving the third propeller can act as a braking propeller. From Equation 4 the resultant force for surge can be expressed in vehicle-fixed coordinate as pFxb bJ1 i p Fip e1Q 0 I pFyb 0 I pFzb 0 5 10 Autonomous Underwater Vehicles where ei 1 0 0 T. Then for the heave case all the three water-jet propellers will work and the side servo motor will rotate to an angle that Ỉ n 2. Therefore in this case the resultant force for heave can be expressed in vehicle-fixed coordinate as pFxb 0 I pFyb 0 3 3 f pFp esC 0 i 1 6 where es 0 0 1 T. The third case is yaw which is rotating on z-axis. By denoting in propeller-fixed coordinates a should have the same orientation clockwise or counterclockwise that means Xj 0 or a 0. So in yaw rotation moment will take effect. We can write the equation for yaw in vehicle-fixed coordinate as r T 3 pFxb pi f pFp eiC 0 pFyb p f