Towards Terrain-Aware Safe Locomotion for Quadrupedal Robots Using Proprioceptive Sensing

TL;DR

This work presents an estimation framework that generates a 2.5-D terrain map and extracts support plane parameters, which are then integrated into contact and state estimation, which reduces the mean absolute error of base position estimation, decreases the estimation variance, and improves the robustness of contact estimation compared to a decoupled framework.

Abstract

Achieving safe quadrupedal locomotion in real-world environments has attracted much attention in recent years. When walking over uneven terrain, achieving reliable estimation and realising safety-critical control based on the obtained information is still an open question. To address this challenge, especially for low-cost robots equipped solely with proprioceptive sensors (e.g., IMUs, joint encoders, and contact force sensors), this work first presents an estimation framework that generates a 2.5-D terrain map and extracts support plane parameters, which are then integrated into contact and state estimation. Then, we integrate this estimation framework into a safety-critical control pipeline by formulating control barrier functions that provide rigorous safety guarantees. Experiments demonstrate that the proposed terrain estimation method provides smooth terrain representations. Moreover, the coupled estimation framework of terrain, state, and contact reduces the mean absolute error of base position estimation by 64.8%, decreases the estimation variance by 47.2%, and improves the robustness of contact estimation compared to a decoupled framework. The terrain-informed CBFs integrate historical terrain information and current proprioceptive measurements to ensure global safety by keeping the robot out of hazardous areas and local safety by preventing body-terrain collision, relying solely on proprioceptive sensing.

Figures (10)

• Figure 1: An example of the scenario we deal with in this work. A quadruped is capable of walking on uneven terrain without any prior knowledge of the environment or any exteroceptive sensors, using the proposed method.
• Figure 2: The block diagram of the proposed control system. The blue shading zone shows the terrain-aware estimation system, and the yellow shading zone presents the CBF-MPC. In the figure, KF stands for the Kalman filter.
• Figure 3: Global safety CBF design. (a) Side view. (b) Top view. The gray point cloud represents previously recorded terrain points during locomotion. The green dotted line denotes the critical safety boundary. $\theta_{thr}$ is the angle relative to the horizontal plane and represents the maximum traversable slope of the robot.
• Figure 4: Constrained body rotation for local safety in side and front views.
• Figure 5: The comparative experimental results of terrain estimation. For the 2.5-D map, we compare our method with the point updating method yang2023proprioception when generating terrain maps with varying accuracy levels (low, medium, and high from left to right), corresponding to pixel lengths of 0.2m, 0.1m, and 0.05m, respectively. For the support plane, we compare our method with the local slope approximation strategy wang2023estimation. The experiments are implemented in an environment with slopes and a platform.