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We propose a linear MPC scheme for online computation of reactive walking motions, necessary for fast interactions such as physical collaboration with humans or collision avoidance in crowds. Unlike other existing schemes, it provides fully adaptable height, adaptable step placement and complete kinematic and dynamic feasibility guarantees, making it possible to walk perfectly safely on a piecewise horizontal ground such as stairs. A linear formulation is proposed, based on efficiently boundingdoi:10.1109/icra.2019.8794117 dblp:conf/icra/PajonW19 fatcat:kv4zqpujujdqzeqvtjsg5pt7fi