Organizations: Dynamic Legged Systems, Istituto Italiano di Tecnologia (IIT), Italy · Department of Industrial Engineering, University of Trento, Italy · Department of Computer Science, University of Manchester, UK · Cognitive Robotics, Delft University of Technology, The Netherlands · Institute of Robotics and Mechatronics, German Aerospace Center (DLR), Germany
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 & tables
Fig. 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.
Fig. 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.
Fig. 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. θthr is the angle relative to the horizontal plane and represents the maximum traversable slope of the robot.
Fig. 4: Constrained body rotation for local safety in side and front views.
Fig. 5: The comparative experimental results of terrain estimation. For the 2.5-D map, we compare our method with the point updating method [ 20 ] 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 [ 19 ] . The experiments are implemented in an environment with slopes and a platform.
Parameter
Value
Parameter
Value
hthr
0.5 m
γ
0.15 m
Lmax
1.2 m
Δϕ
10∘
Lmin
0.5 m
Δψ
10∘
θthr
60∘
αglobal
1.5
αlocal
0.5
TABLE I: List of parameters used in safety guarantees
Parameter
Value
Parameter
Value
kpos
0.40
kforce
0.60
σpos
1.28
Pmid
0.01
σforce
0.78
Fmid
5.00
TABLE II: List of parameters for contact estimation.
Fig. 6: Terrain estimation on unstructured terrain. (a) Motion trajectory; (b) top view of the 2.5-D map; (c) oblique side view of the terrain; (d) oblique side view of the 2.5-D map. (b) and (d) share the same colorbar.
Fig. 7: Hardware experiments for terrain estimation when walking across a slope (top panel) and a flat ground (bottom panel).
Fig. 8: Contact estimation with and without terrain information. Pseudo-contact refers to instances where contact occurs, but the measured force remains below the sensor threshold. For clarity, the contact judgment from (a) is overlaid in (b) as a dashed curve for direct comparison.
Fig. 9: Estimated CoM height profiles, with and without incorporating terrain information.
Fig. 10: An illustration of CBF constraints for avoidance in hazardous areas. The blue arrow represents the terrain collection route, the red arrow indicates the command direction, and the blue point marks the corrected hazard points. Upon approaching the hazardous boundary (highlighted by the red segment), the robot executes a stop-approaching maneuver. The continuous behavior is demonstrated in the supplementary video.
Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, China · Institute for Infocomm Research (I2R), Agency for Science, Technology and Research, Singapore. · Shenzhen Astralldynamics Technology.