Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bipedal Robust Walking on Uneven Footholds: Piecewise Slope LIPM with Discrete Model Predictive Control

Yapeng Shi, Sishu Li, Yongqiang Wu, Junjie Liu, Xiaokun Leng, Xizhe Zang, Songhao Piao

Abstract

This study presents an enhanced theoretical formulation for bipedal hierarchical control frameworks under uneven terrain conditions. Specifically, owing to the inherent limitations of the Linear Inverted Pendulum Model (LIPM) in handling terrain elevation variations, we develop a Piecewise Slope LIPM (PS-LIPM). This innovative model enables dynamic adjustment of the Center of Mass (CoM) height to align with topographical undulations during single-step cycles. Another contribution is proposed a generalized Angular Momentum-based LIPM (G-ALIP) for CoM velocity compensation using Centroidal Angular Momentum (CAM) regulation. Building upon these advancements, we derive the DCM step-to-step dynamics for Model Predictive Control MPC formulation, enabling simultaneous optimization of step position and step duration. A hierarchical control framework integrating MPC with a Whole-Body Controller (WBC) is implemented for bipedal locomotion across uneven stepping stones. The results validate the efficacy of the proposed hierarchical control framework and the theoretical formulation.

Bipedal Robust Walking on Uneven Footholds: Piecewise Slope LIPM with Discrete Model Predictive Control

Abstract

This study presents an enhanced theoretical formulation for bipedal hierarchical control frameworks under uneven terrain conditions. Specifically, owing to the inherent limitations of the Linear Inverted Pendulum Model (LIPM) in handling terrain elevation variations, we develop a Piecewise Slope LIPM (PS-LIPM). This innovative model enables dynamic adjustment of the Center of Mass (CoM) height to align with topographical undulations during single-step cycles. Another contribution is proposed a generalized Angular Momentum-based LIPM (G-ALIP) for CoM velocity compensation using Centroidal Angular Momentum (CAM) regulation. Building upon these advancements, we derive the DCM step-to-step dynamics for Model Predictive Control MPC formulation, enabling simultaneous optimization of step position and step duration. A hierarchical control framework integrating MPC with a Whole-Body Controller (WBC) is implemented for bipedal locomotion across uneven stepping stones. The results validate the efficacy of the proposed hierarchical control framework and the theoretical formulation.

Paper Structure

This paper contains 8 sections, 31 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Model Formulation
  3. PS-LIPM Hybrid Dynamics
  4. G-ALIP Model
  5. DCM Step-to-Step Dynamics
  6. Hierarchical Control Framework Based on DCM Step-to-Step Dynamics
  7. Results
  8. Conclusions

Figures (11)

  • Figure 1: Humanoid robot KUAVO with its MuJoCo simulation walking on uneven stepping stones.
  • Figure 2: As the contact point lands on the new virtual support plane (yellow dashed line), the CoM transitions from the old slope to the new slope (yellow solid line), with the velocity undergoing a sudden change at their intersection, noting that the two transitions do not occur simultaneously.
  • Figure 3: Step positions of the robot during periodic motion without lateral offset. The blue dots are the step positions and the gray rectangles represent the stepping stones.
  • Figure 4: Segmented slope virtual constraint generation. The blue dots are the desired step positions and black dots are adjusted step positions used to generate virtual slope considering the fixed step width $W$.
  • Figure 5: KUAVO traverses over the stepping stones with periodic elevation.
  • ...and 6 more figures