Robust backstepping control of an underactuated one-legged hopping robot in stance phase

Exponentially stabilizing a non-Spring Loaded Inverted Pendulum (SLIP) model-based one-legged hopping robot in stance phase is studied. Differing from the SLIP model systems, the hopping robot with non-SLIP model considered in this paper does not restrict the center of mass of the robot coinciding to the hip joint. A specific underactuated one-legged hopping robot with two actuated arms are selected to investigate the dynamics and control problem. It is shown that the system holds the essential nonlinear prosperities of general systems and belongs to a class of second-order nonholonomic mechanical systems, which cannot be stabilized by any smooth time-invariant state feedback. By using a coordinates transform based on the so-called normalized momentum, a robust backstepping control method is presented for the specific hopping robot system. Both theoretical analysis and numerical simulations show that the robust backstepping controller can stabilize the underactuated one-legged hopping robot to its balance configuration as well as a periodic motion trajectory near to the balance configuration. These results are significative for designing a new non-SLIP model based hopping robot systems with more biological characteristics.