Trajectory linearization control on SO(3) with application to aerial manipulation

The dynamics of multi-DOF aerial manipulators is complex system evolving in non-Euclidean Lie group, making design and tuning of the control of such systems challenge. In this paper we consider the nonlinear geometric control for aerial manipulation system. The linearized tracking error kinematic equation of motion on SO(3) is obtained from the variation on SO(3). Based on the linearized tracking error kinematic equation of motion on SO(3), the trajectory linearization control for the kinematics on SO(3) is investigated. The decoupled dynamics of multi-DOF aerial manipulator enables us to apply the results of trajectory linearization control for the kinematics on SO(3). We then design the entire controller for aerial manipulation system by composing different trajectory linearization control loops. Such controller structure eases the controller implementation and tuning procedure. The stability of the proposed controlled system is analyzed using Lyapunov's method. The proof is finished from inner loop to outer loop. It is proven that the closed loop shape system is exponentially stable. The attraction basin of the configuration error for the shape system can almost cover the whole SO(3)×Rⁿ. The stability of the system considering the actuator dynamics and perturbations is also discussed in this paper. From the stability of the shape system, the stability of the entire system is proven. The stability analysis results are further verified through several numerical simulations.