Abstract
Bipedal robot control techniques implementing self clocking properties, as presented in Westervelt et al. (Feedback control of dynamic bipedal robot locomotion, Taylor & Francis LLC, Milton Park, 2007) and Novaes et al. (IFAC 19th world congress, 4843–4848, 2014), have desirable properties, like the ability to drive the robot step with respect to its own geometry. In this control technique, one of the possible angular coordinates of the robot is made monotonic during the step execution. The other angular coordinates will track reference functions of the former. One difficulty with this approach is to determine the region around the nominal step for which the stability is assured. In this paper, we propose an algorithm to estimate this stability region by computing numerically an interval matrix related to a Poincare return map. In conjunction with the algorithm proposed in Ahn and Chen (IEEE Trans Autom Control 52(3):510–514, 2007), we are able to determine the maximum singular value of this interval matrix and so determine a guaranteed stability region.
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