On the Suitability of Different Online Gait Generation Methods for Pre-Defined Footsteps

Detailed dynamical modeling is the basis for simulation and model based control. In this contribution the Projection Equation is used for the modeling of a biped walking machine, resulting in the equations of motion which are needed for gait generation and verification of its stability. For biped robots one main issue is the generation of stable trajectories for the center of mass (CoM). Several different approaches based on the Zero Moment Point (ZMP) scheme have been presented in the past. Due to the complex dynamic structure of bipedal robots most of the considered algorithms use a linear inverted pendulum as a simplified model. This results in a decoupling of the ZMP equations in lateral and forward direction, but limits the trajectories to a constant height of the CoM. An extension of the well known LQR theory by future reference values has been proposed. This model based approach seems to perform quite well, but does not allow the consideration of constraints on the position of the ZMP. This limitation is removed by the use of Model Predictive Control (MPC) with inequality constraints. By extending this approach to a time invariant one the restriction to a constant height of the CoM is no longer necessary. Both methods as well as the time invariant approach for variable CoM heights have been evaluated in simulations and will be experimentally verified on a real robot soon.