Trajectory generation and dynamic control of planar biped robots with curved soles

This paper proposes a locomotion pattern and a control method for biped robots with curved soles. First, since the contact point of a supporting leg may arbitrarily move back and forth on the ground, we derived the desired trajectory from a model called the Moving Inverted Pendulum Model (MIPM) where the Zero Moment Point (ZMP) exists at the supporting point and can be moved intentionally. Secondly, a biped robot with curved soles is an under-actuated system since the supporting point contacting with a point on the ground has no actuator during the single supporting phase. Therefore, this paper proposes a computed-torque control for this under-actuated system using decoupled dynamic equations. A series of computer simulations with a 7-DOF biped robot with curved soles shows that the proposed walking pattern and control method are effective and allow the biped robot to walk fast and stably, and move more like human beings. Also, it is shown that the curved sole shape has superior energy consumption compared to flat soles, and greater efficiency in ascending and descending the stairs.