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.

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.......

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