D. Dimitrov, A. Paolillo, and P-B. Wieber
Walking motion generation with online foot position adaptation based on L_1- and L_\inf-norm penalty formulations
Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), 2011, pp. 3523-3529

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 optimization 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_\inf-norm minimization; (iv) a formulation that accounts for (approximate) double support constraints when foot repositioning occurs.

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