Proprioceptive External Torque Learning for Floating Base Robot and its Applications to Humanoid Locomotion

TL;DR

This paper tackles the challenge of estimating external joint torque for floating-base humanoids without force-torque sensors by proposing a GRU-based learning approach that uses only proprioceptive inputs. By training on diverse, randomly walking data, the method accurately estimates external torques and reconstructs foot contact wrenches, enabling ZMP-based walking control with comparable stability to FTS-based feedback. The method demonstrates robustness to inertia and minor geometric changes, and a calibration framework supports foot-size variations when replacing FTS hardware. Overall, the work shows the practicality of sensor reduction in humanoid locomotion without sacrificing stability or performance, with potential for safer, cheaper, and more reliable robots.

Abstract

The estimation of external joint torque and contact wrench is essential for achieving stable locomotion of humanoids and safety-oriented robots. Although the contact wrench on the foot of humanoids can be measured using a force-torque sensor (FTS), FTS increases the cost, inertia, complexity, and failure possibility of the system. This paper introduces a method for learning external joint torque solely using proprioceptive sensors (encoders and IMUs) for a floating base robot. For learning, the GRU network is used and random walking data is collected. Real robot experiments demonstrate that the network can estimate the external torque and contact wrench with significantly smaller errors compared to the model-based method, momentum observer (MOB) with friction modeling. The study also validates that the estimated contact wrench can be utilized for zero moment point (ZMP) feedback control, enabling stable walking. Moreover, even when the robot's feet and the inertia of the upper body are changed, the trained network shows consistent performance with a model-based calibration. This result demonstrates the possibility of removing FTS on the robot, which reduces the disadvantages of hardware sensors. The summary video is available at https://youtu.be/gT1D4tOiKpo.

Figures (7)

• Figure 1: The unfolded graph of GRU and a linear output layer. This GRU network takes the two vectors; current sensor data $\mathbf{x}(k)$, a hidden state vector $\mathbf{h}_{k-1}$ from the previous time step, and outputs $\mathbf{h}_{k}$. The linear output layer calculates the estimated external torque $\bm{\tau}_{e,leg}(k)$ from $\mathbf{h}_{k}$.
• Figure 2: Overall walking control framework and the estimated external torque feedback of the proposed GRU network to the ZMP controller. $\mathbf{S}^{ref}$ is the reference footsteps. $\bm{\xi}^{ref}$ is the reference CP trajectory. $\mathbf{P}_{d}$ is the desired ZMP. $\Delta\mathbf{e}_{f}$, $\mathbf{e}_{f}^{ref}$, and $\mathbf{e}_{f,d}$ are the modified, reference, and desired transformation of both legs, respectively. $\mathbf{R}_p$ and $\mathbf{R}_d$ are the current and desired rotation of the pelvis link, respectively. $\mathbf{c}_{d}$ is the desired center of mass position. $\mathbf{q}_{d}$ is the desired joint position. $\bm{\tau}_{q}$, $\bm{\tau}_{g}$, and $\bm{\tau}_{d}$ are the joint PD control torque, gravity compensation torque, and the desired joint torque, respectively.
• Figure 3: (a) The estimated external joint torque of the left leg by the proposed GRU network (red), the measured external torque by FTS (blue), and the estimated external torque by MOB with friction model (gray). (b) The estimated contact wrench by projecting the estimated external torque from the network (red), and the measured contact wrench by FTS (blue).
• Figure 4: ZMP and CP trajectories when the humanoid is walking forward according to the contact wrench feedback methods.
• Figure 5: Comparison of ZMP and CP tracking errors in x and y directions according to the contact force sensing method.