Ball juggling with an under-actuated flying robot

This paper presents a trajectory tracking control strategy based on the subspace stabilization approach to accurately manipulate an under-actuated flying robot from a known initial state to the desired terminal state. To facilitate the development of this tracking strategy, the dynamical model of the quadrotor is firstly proposed. Subsequently, an optimal trajectory generation algorithm is adopted to generate dynamically consistent trajectories regarding the initial and terminal state constraints in specific missions. Then, a trajectory tracking control strategy based on the subspace stabilization approach is developed considering the lumped disturbances and time delays. The developed control strategy is applied for ball juggling of a highly under-actuated quadrotor, which is a popular flying robot in recent years. Real-time experimental results show that the quadrotor can be accurately manipulated from a known initial state to the desired terminal state within a given time horizon. In the consecutive juggling tasks, the quadrotor with a racket of radius 0.065 m can consecutively juggle the ball for averagely 4 hits in each rally, and a longest rally achieved by the developed control strategy is 14 hits. The feasibility of the developed control strategy is also preliminarily verified through the cooperative juggling between two quadrotors. All of these results demonstrate the effectiveness of the developed control strategy.