Walking motion generation with online foot position adaptation based on ℓ1- and ℓ℞-norm penalty formulations

The article presents an improved formulation of an existing model predictive control scheme used to generate online "stable" walking motions for a humanoid robot. We introduce: (i) a change of variable that simplifies the optimiza tion problem to be solved; (ii) a simply bounded formulation in the case when the positions of the feet are predetermined; (iii) a formulation allowing foot repositioning (when the system is perturbed) based on ℓ
₁
- and ℓ
_∞
-norm minimization; (iv) a formulation that accounts for (approximate) double support constraints when foot repositioning occurs.