Jumping motion control for 4-link robot based on virtual constraint on underactuated joint

This paper proposes a control strategy for an underactuated planar robot to achieve jumping motion by toe kicking. The model in this work consists of 4 links and is controlled by input-output linearization and output zeroing. One of the output functions is designed based on a virtual constraint on the unactuated joint. This makes the remaining zero dynamics unstable when output zeroing is achieved. Vertical jumping motion is then accomplished by designing the other output functions to synchronize the joint angles with the zero dynamics. The present scheme is verified through simulations.