Whole-Body Impedance Coordinative Control of Wheel-Legged Robot on Uncertain Terrain

Abstract

This article propose a whole-body impedance coordinative control framework for a wheel-legged humanoid robot to achieve adaptability on complex terrains while maintaining robot upper body stability. The framework contains a bi-level control strategy. The outer level is a variable damping impedance controller, which optimizes the damping parameters to ensure the stability of the upper body while holding an object. The inner level employs Whole-Body Control (WBC) optimization that integrates real-time terrain estimation based on wheel-foot position and force data. It generates motor torques while accounting for dynamic constraints, joint limits,friction cones, real-time terrain updates, and a model-free friction compensation strategy. The proposed whole-body coordinative control method has been tested on a recently developed quadruped humanoid robot. The results demonstrate that the proposed algorithm effectively controls the robot, maintaining upper body stability to successfully complete a water-carrying task while adapting to varying terrains.

Figures (10)

• Figure 1: The newly developed wheel-legged robot, X-Man, with its 80 kg mass, introduces significant inertial challenges. Despite this, our work enables it to achieve upper-limb passive stability and demonstrate adaptability across varied uncertain terrains while maintaining balance.
• Figure 2: Schematic diagram of X-Man. Robot control tasks including: base position task(height, forward), base orientation task, wheel-Centroid task, Centroid task, arm task. In addition, we define the head orientation as the front, and according to the configuration characteristics of the robot, it can be divided into front legs and hind legs, front wheels and rear wheels, front hip and rear hip. The robot's legs are mobile joints, and other parts are rotational joints.
• Figure 3: The overview controller framework of X-Man. Denote $\boldsymbol{q}$ and $\boldsymbol{x}$ are the joint value and point state of robot. $\boldsymbol{\dot q},\boldsymbol{\ddot q}$ are the angular velocity and acceleration. $\boldsymbol{\tau}$ is joint torque. $\{ \boldsymbol{n}_x,\boldsymbol{n}_y,\boldsymbol{n}_z\}$ is the terrain frame. And $\boldsymbol{n}_{z}$ is unit normal vector, and $\boldsymbol{\boldsymbol{n}}_{x},\boldsymbol{n}_{y}$ are two orthonormal tangent vectors described with respect to the object frame.
• Figure 4: The dual-arm variable damping-based impedance coordinative controller, where $t_1$ represents the instant of zero relative motion between the load and the robot body, and $t_2$ is the instant when the variation in robot leg length reaches a steady state. The coefficients $\boldsymbol{K}_b$, $\boldsymbol{K}_L$, and $\boldsymbol{K}_R$ are the stiffness matrices, and $\boldsymbol{D}_b$, $\boldsymbol{D}_L$, and $\boldsymbol{D}_R$ are the damping matrices. These matrices are diagonal, representing stiffness and damping properties in the $x$, $y$, and $z$ directions for the body and loads. $M$ represents the body mass, while $m_L$ and $m_R$ represent the masses of the left and right loads. And $m_L$, $m_R$, and $M$ are the components in $\boldsymbol{M}$ of (\ref{['imped']}).
• Figure 5: Terrain frame estimation. $\{ \boldsymbol{n}_{x,i},\boldsymbol{n}_{y,i},\boldsymbol{n}_{z,i}\}$ is the terrain frame of $i$-th contact point. $\boldsymbol{f}_{C,i}$ is the ground contact force of $i$-th contact point.

Theorems & Definitions (2)

• Remark 1
• Remark 2