## Friday, 26 July 2013

### Translator Between Torque controller and thrusters

As the AUV have four thrusters that can rotate in any direction its generates a vector U of possible Torque direction where T1,T2,T3 is the component x,y,z of  thruster number 1.However the PD tracking controller generates a force vector Tb of the way  where X,Y,Z are the forces and K,M,N are the moments over the gravitational center in the AUV.

$\bg_black&space;U=\left(&space;\begin{array}{c}&space;T_1&space;\\&space;T_2&space;\\&space;T_3&space;\\&space;T_4&space;\\&space;T_5&space;\\&space;T_6&space;\\&space;T_7&space;\\&space;T_8&space;\\&space;T_9&space;\\&space;T_{10}&space;\\&space;T_{11}&space;\\&space;T_{12}&space;\\&space;\end{array}&space;\right)$ $\bg_black&space;T_B=\left(&space;\begin{array}{c}&space;X&space;\\&space;Y&space;\\&space;Z&space;\\&space;K&space;\\&space;M&space;\\&space;N&space;\\&space;\end{array}&space;\right)$ $\bg_black&space;L=\left(&space;\begin{array}{cccccccccccc}&space;1&space;&&space;0&space;&&space;0&space;&&space;1&space;&&space;0&space;&&space;0&space;&&space;1&space;&&space;0&space;&&space;0&space;&&space;1&space;&&space;0&space;&&space;0&space;\\&space;0&space;&&space;1&space;&&space;0&space;&&space;0&space;&&space;1&space;&&space;0&space;&&space;0&space;&&space;1&space;&&space;0&space;&&space;0&space;&&space;1&space;&&space;0&space;\\&space;0&space;&&space;0&space;&&space;1&space;&&space;0&space;&&space;0&space;&&space;1&space;&&space;0&space;&&space;0&space;&&space;1&space;&0&space;&&space;0&space;&&space;1\\&space;-0.3&space;&&space;0&space;&&space;0&space;&&space;0.3&space;&&space;0&space;&&space;0&space;&&space;0.3&space;&&space;0&space;&&space;0&space;&&space;0.3&space;&&space;0&space;&&space;0&space;\\&space;0&space;&&space;0.3&space;&&space;0&space;&&space;0&space;&&space;0.3&space;&&space;0&space;&&space;0&space;&&space;0.3&space;&&space;0&space;&&space;0&space;&&space;0.3&space;&&space;0\\&space;0&space;&&space;0&space;&&space;0.3&space;&&space;0&space;&&space;0&space;&&space;0.3&space;&&space;0&space;&&space;0&space;&&space;0.3&space;&&space;0&space;&&space;0&space;&&space;0.3&space;\\&space;\end{array}&space;\right)$
However L can not be inverse and to solve the system it has to be applied and advanced algorithm to solve the system with a seed data .In the case of Matlab this can be made with fsolve(@myfun,x0) where x0 is the seed data .In this case seed data is a vector where each data is X/4,Y/4,Z/4,K/4,M/4 and N/4

Work in progress.......