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We present a multi-contact walking pattern generator based on preview-controlof the 3D acceleration of the center of mass (COM). A key point in the designof our algorithm is the calculation of contact-stability constraints. Thanks toa mathematical observation on the algebraic nature of the frictional wrenchcone, we show that the 3D volume of feasible COM accelerations is a always adownward-pointing cone. We reduce its computation to a convex hull of (dual) 2Dpoints, for which optimal O(n log n) algorithms are readily available. Thisreformulation brings a significant speedup compared to previous methods, whichallows us to compute time-varying contact-stability criteria fast enough forthe control loop. Next, we propose a conservative trajectory-widecontact-stability criterion, which can be derived from COM-acceleration volumesat marginal cost and directly applied in a model-predictive controller. Wefinally implement this pipeline and exemplify it with the HRP-4 humanoid modelin multi-contact dynamically walking scenarios.

Multi-contact Walking Pattern Generation based on Model Preview Control of 3D COM Accelerations