Orthogonal Transformation Operation Theorem Of The Spatial Universal Rotating Magnetic Field Based On Independent Variables

Spatial universal rotating magnetic field(SURMF)can provide the energy for the drivingof the wireless capsule endoscopy,which is used as the driving source for the active control of the robotic position and posture,and then the efficient,painless and noninvasive diagnosis can be realized in the human gastrointestinal tract.Therefore,the SURMF has the widespread clinical application prospect and high scientific research value.Our group has proposed the anti-phase sine current superposition theorem to adjust the orientation,the magnetic flux density,the angular speed and the rotational direction of the SURMF.Nevertheless,three coupling direction angles of the normal vector of the SURMF in the Descartes coordinate system is employed as control variables,which cannot be separately controlled,thus the adjustment of the orientation of the SURMF is difficult and the control flexibility of the robotic posture and position is restricted.For the dimension reduction and the decoupling of control variables,the orthogonal transformation operation theorem of the SURMF is proposed based on the lower dimensional and independent variables in this paper.Firstly,the structure features and two locomotion modes of the dual hemisphere capsule robot with active and passive modes are introduced,as well as the manipulation system of the SURMF.The three-phase sine current superposition formula is derived by the orthogonal rotation inverse transformation,which employs the azimuth and altitude angles of the normal vector of the SURMF as two control variables.Then,the unique control rules of the orientation of the SURMF are generalized as well as the method to change the rotational direction in each spatial quadrant according to the relationship among the current phase angles,the orientation,and the rotational direction.And the three-phase sine current superposition formula for the robotic steering rolling locomotion is derived based on the orthogonal transformation operation theorem of the SURMF.The resistance and the inductance of the tri-axial orthogonal square Helmholtz coils cause the error of the SURMF(including orientation error and the uniformity error),which have an effect on the control accuracy of the robotic posture and rolling direction,and the stability of the magnetic torque by the SURMF.To adjust the orientation of the SURMF accurately and improve its uniformity,the cause of the error is analyzed,and then thethree-phase sine current superposition formula for the practical application is derived.And the linear polarization of the electromagnetic wave is proposed to correct the error.To validate the feasibility and maneuverability of the orthogonal transformation operation theorem of the SURMF,the prototype of the dual hemisphere capsule robot with active and passive modes and the SURMF manipulation system have been manufactured.And the experiments of the robotic posture adjustment and steering rolling locomotion are conducted in the simulated intestine and the pig colon,respectively.It is demonstrated that the posture adjustment and the steering rolling locomotion of the robot can be realized through single variable control,thus the orthogonal transformation operation theorem makes the control of the orientation of the SURMF convenient and flexible significantly.This breakthrough will lay a foundation for the human-machine interaction control of the SURMF.