Dynamic Walking over Rough Terrains by Nonlinear Predictive Control of the Floating-base Inverted Pendulum

Stéphane Caron, Abderrahmane Kheddar. Submitted 1 March 2017.

Abstract

We present a real-time rough-terrain dynamic walking pattern generator. Our method automatically finds step durations, which is a critical issue over rough terrains where they depend on terrain topology. To achieve this level of generality, we introduce the Floating-base Inverted Pendulum (FIP) model where the center of mass can translate freely and the zero-tilting moment point is allowed to leave the contact surface. We show that this model is equivalent to the linear-inverted pendulum mode with variable center of mass height, aside from the fact that its equations of motion remain linear. Our design then follows three steps: (i) we characterize the FIP contact-stability condition; (ii) we compute feedforward controls by solving a nonlinear optimization over receding-horizon FIP trajectories. Despite running at 30 Hz in a model-predictive fashion, simulations show that the latter is too slow to stabilize dynamic motions. To remedy this, we (iii) linearize FIP feedback control computations into a quadratic program, resulting in a constrained linear-quadratic regulator that runs at 300 Hz. We finally demonstrate our solution in simulations with a model of the HRP-4 humanoid robot, including noise and delays over both state estimation and foot force control.

HRP-4 walking down an elliptic staircase using our dynamic walking pattern generator

Cite

@unpublished{caron2017dynamic,
  title = {Dynamic Walking over Rough Terrains by Nonlinear Predictive Control of the Floating-base Inverted Pendulum},
  author = {Caron, St{\'e}phane and Kheddar, Abderrahmane},
  year = {2017},
  month = {March},
  note = {working paper or preprint},
  hal_id = {hal-01481052},
  hal_version = {v1},
  url = {https://hal.archives-ouvertes.fr/hal-01481052},
}

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