Stabilization of Biped Walking Robot Using the Energy Shaping Method

The biped walking robot demonstrates a stable limit cycle on shallow slopes. In previous researches, this passive gait was shown to be sensitive to ground slope and initial conditions. In this paper, we discuss the feedback stabilization of a biped robot by the “energy shaping” technique. Two designs are proposed to reduce the sensitivity of the biped walking robot to slope and initial conditions. In the first design, a moving mass actuator is located on each link of the robot. The actuators are used to shape the potential energy of the biped robot so that it tracks the potential energy of a known passive gait of a similar biped robot on a different slope. Although the method is applied to a simple kneeless planar biped, our results are completely generalizable and may be applied to general $n$-link bipeds. The second design uses a momentum wheel, which is placed on the hip of the robot to shape the energy of the biped. We use the controlled Lagrangian method to design the controller, and the simulation is carried out to show its performance. In the controlled Lagrangian method, either the total energy or the Lagrangian of the uncontrolled system is modified so that the Euler–Lagrange equations derived from this modified expression, called the controlled Lagrangian function, describe the closed loop equations of the system.