A Novel Paradigm for Controlling Navigation and Walk in Biped Robotics

Classically the walk in biped robotics was obtained controlling balance during the whole step, i.e. guaranteeing that the pressure point under the soles always stayed in the polygon of the supporting feet. However, this assumed that the feet were able to transfer torque to the ground during the whole gait cycle. In spite of the fact that the amount of transferrable torque in the feet-ground contact is limited, it is possible only during some phases of the step, and the overall process is energetically inefficient. On the other side, starting from the passive motion of the rimless wheel falling on an inclined surface, and ending to the inverted pendulum with a compass, balance in the whole was proven in spite of dynamical instability inside each step. Along this line results of Foot Placement Estimation (FPE) in 2-D and 3-D showed how energy efficient walk was possible, emulating the human walk with a free fall on the swing foot and energy restitution at the foot collision with the ground for the next step. This model assumes pointy feet, so without torque transfer to the ground. In the realm of FPE, in previous papers the present author adopted the 3-D inverted pendulum in polar coordinates (Spherical Inverted Pendulum - SIP) to introduce omnidirectional walks with arbitrarily changing characteristics. No torque control was used during the step, i.e the pendulum was always in free fall at each step, the only control actions were at the beginning of the next step. These actions are: the change of angular velocities at the start of a new step, with respect to those given after the collision (emulating the torque action in the brief double stance period), to recover for the losses, and the preparation of the position in the frontal and sagittal planes of the swing foot for the next collision. The present paper improves this paradigm, proposing a general model to account for all characteristics of the biped and of the gait, with adding a minimum of dynamical complexity with respect to the SIP. This model allows, not only to walk omnidirectionally on a flat surface, but also to go up and down staircases.