Exponentially stabilizing an one-legged hopping robot with non-SLIP model in flight phase

The nonlinear dynamic control for a novel one-legged hopping robot in flight phase is investigated. The proposed planar hopping robot is composed of single leg, a body, and a tail. The leg of the robot is structured by two links connected by an elastically passive joint with articulated form. The body of the robot is designed as an inertia wheel that the mass center is coincident to the hip joint. Though there are an articulated type leg and a tail such that the suggested one-legged hopping robot cannot be effectively approximated by the famous Spring Loaded Inverted Pendulum (SLIP) model system, the dynamics of the robot is considerably simplified since the novel design for the body. Considering the nonholonomic constraints of the hopping robot in flight phase due to angular momentum conservation, the problem of stabilizing the posture of the hopping robot in flight phase is investigated. By converting the dynamics to a chained form, an exponentially stabilizable control is proposed based on the integrator backstepping procedure. Some numerical simulations show the performance of the control.