Computed Torque Control of an aerospace craft using nonlinear inverse model and rotation matrix

This paper newly presents how to apply the Computed Torque Control scheme to the flight control of a 4-DOF controllable aerospace craft, such as a multicopter and a rocket, by using a nonlinear inverse model to track a reference trajectory arbitrarily given in the 3D space of gravity condition and it shows the simulation results for some cases. Aerodynamics is neglected for the clarity of the explanation of the subject. The nonlinear inverse model of the rigid body are used to calculate and feedforward the ideally desired torque and force in the scheme without linearizing the nonlinear model of the craft. The analytic formula of the nonlinear inverse kinematics is newly presented for a 4-DOF controllable rigid body in the 3D space of gravity condition. The rotation matrix is used to represent the attitude of the craft. The attitude error is represented by using the rotation vector (the product of a rotation angle and a rotation unit vector) from the current attitude to the desired attitude and its calculation method is newly presented. The stability of the system is indirectly checked by the simulations for a reference trajectory with various deviated initial positions. It shows by simulations that the computed torque improves steady state errors and the PID control in the scheme compensates modeling errors and copes with incorrect initial conditions and abrupt changes of input commands.