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Design and Control of a Bio-inspired Wheeled Bipedal Robot

Haizhou Zhao, Lei Yu, Siying Qin, Gumin Jin, Yuqing Chen

Abstract

Wheeled bipedal robots (WBRs) have the capability to execute agile and versatile locomotion tasks. This paper focuses on improving the dynamic performance of WBRs through innovations in both hardware and software development. Inspired by the human barbell squat, a bionic mechanical design is proposed and implemented as shown in Fig. 1. It distributes the weight onto its hip and knee joints to improve the effectiveness of joint motors while maintaining a relatively large workspace of the base link. Meanwhile, a novel model-based controller is devised, synthesizing height-variable wheeled linear inverted pendulum (HV-wLIP) model, Control Lyapunov Function (CLF) and whole-body dynamics for theoretically guaranteed stability and efficient computation. Compared with other alternatives, as a more accurate approximation of the WBR dynamics, the HV-wLIP can enable more agile response and provide theory basis for WBR controller design. Experimental results demonstrate that the robot could perform human-like deep squat, and is capable of maintaining tracking CoM velocity while manipulating base states. Furthermore, it exhibited robustness against external disturbances and unknown terrains even in the wild.

Design and Control of a Bio-inspired Wheeled Bipedal Robot

Abstract

Wheeled bipedal robots (WBRs) have the capability to execute agile and versatile locomotion tasks. This paper focuses on improving the dynamic performance of WBRs through innovations in both hardware and software development. Inspired by the human barbell squat, a bionic mechanical design is proposed and implemented as shown in Fig. 1. It distributes the weight onto its hip and knee joints to improve the effectiveness of joint motors while maintaining a relatively large workspace of the base link. Meanwhile, a novel model-based controller is devised, synthesizing height-variable wheeled linear inverted pendulum (HV-wLIP) model, Control Lyapunov Function (CLF) and whole-body dynamics for theoretically guaranteed stability and efficient computation. Compared with other alternatives, as a more accurate approximation of the WBR dynamics, the HV-wLIP can enable more agile response and provide theory basis for WBR controller design. Experimental results demonstrate that the robot could perform human-like deep squat, and is capable of maintaining tracking CoM velocity while manipulating base states. Furthermore, it exhibited robustness against external disturbances and unknown terrains even in the wild.
Paper Structure (26 sections, 2 theorems, 41 equations, 10 figures, 3 tables)

This paper contains 26 sections, 2 theorems, 41 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Mechanical Design
  3. Controller Design
  4. Contributions
  5. Mechanical Design
  6. Controller
  7. Bio-inspired Mechanical Design
  8. Link Length Design
  9. Mass & Torque Distribution
  10. Dynamic Model
  11. Reduced-Order Model
  12. The WIP Model
  13. The HV-wLIP Model
  14. HV-wLIP Infinite-Horizon OCP
  15. CLF-based Stability Analysis
  16. ...and 11 more sections

Key Result

Theorem 1

(Load Capacity Improvement) By controlling $r_\tau=1$, the load capacity of the WBR is maximized for $\mathcal{O}=\{\theta_P,\theta_K\in(-\pi/2, 0), \theta_H \in (0, \pi/2):\theta_H < \theta_P + \pi\}$.

Figures (10)

  • Figure 1: Overview of the bio-inspired wheeled bipedal robot.
  • Figure 2: Schematic demonstration of WBRs with 2 DoF legs. (a) Five-bar linkage, (b) planar 2-link serial layout. The dashed line represents the short distance between the CoM and the hip joint, indicating the much longer moment arm of the knee motors.
  • Figure 3: Bionic design of the WBR. (a) Barbell squat illustration of human. (b) The simplified design model imitating human squatting. (c) The hardware implementation of the bionic WBR during human-like squat. $z$ is the body CoM height from the wheel center and $x_c$, $x_w$ are respectively the body CoM and wheel horizontal positions in sagittal plane. $l_p$, $l_h$, $l_k$ are respectively the link length of the base, thigh, and shank. $\boldsymbol{\Theta}=[\theta_P,\theta_H,\theta_K]$, $\theta_P$, $\theta_H$, and $\theta_K$ are respectively base pitch, hip and knee absolute angles.
  • Figure 4: Contact frame illustration of the right wheel. $\{C\}$ has its z-axis normal to the ground, its x-axis opposite the floating-base x-axis, and its origin at the contact point $c$. $\{W\}$ is rotated from $\{C\}$ by clockwise angle $\psi$ w.r.t. $x_C$ and has its origin at the wheel center $o$. The transparent blue cone represents the friction cone constraint of the 3D linear force components $\mathbf{f}_c^{(\cdot)}=[f_x,f_y,f_z]^\top$ where $(\cdot)$ can be left or right.
  • Figure 5: Simplified model illustration. (i) WIP (ii) LIP (iii) HV-wLIP.
  • ...and 5 more figures

Theorems & Definitions (10)

  • Theorem 1
  • proof
  • Remark 1: Model Accuracy of HV-wLIP
  • Remark 2: Dynamic Performance of HV-wLIP
  • Remark 3: Extensibility of HV-wLIP
  • Remark 4
  • Theorem 2
  • proof
  • Remark 5: Relaxed CLF condition
  • Remark 6: Computational efficiency