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.
Learning-based control has revolutionized dynamic locomotion, yet navigating unstructured terrain remains limited by a robot's incomplete awareness of imminent ground contact. While global perception systems such as LiDARs and depth cameras provide environmental context, they are frequently plagued by latencies, occlusions, and the high computational cost of dense geometric reconstruction. On the other hand, proprioceptive feedback is purely reactive, initiating corrections only after impact has occurred. This work explores embedding a minimal suite of low-cost, high-frequency infrared proximity sensors directly into the feet of a quadrupedal robot. These sensors provide "pre-contact" feedback that is robust to self-occlusions and significantly less computationally demanding than conventional vision-based pipelines. By integrating these localized signals into a reinforcement learning framework, we enable the robot to anticipate terrain discontinuities such as gaps and stepping stones that are problematic for traditional perception stacks due to occlusions or state estimation drift. We demonstrate that such sparse, near-field sensing can be reliably modeled in simulation and transferred to the real world with high fidelity. Experimental results show that local proximity sensing substantially improves traversal robustness over discrete terrain and offers a low-power, low-latency alternative or complement to complex global perception suites in unpredictable environments. For more information about results and methods, please see the project website: https://sites.google.com/view/foot-tof/home.
Jiale Fan, Connor Flynn, Tianao Xu +4
All authors are with the Robotic Systems Lab, ETH Zurich.
Reliable odometry for legged robots without cameras or LiDAR remains challenging due to IMU drift and noisy joint velocity sensing. This paper presents a purely proprioceptive state estimator that uses only IMU and motor measurements to estimate body pose and velocity, with a unified formulation applicable to quadruped and wheel-legged robots and extensible to other legged morphologies. The key idea is to treat each reliable contact as a kinematic anchor: joint-torque--based foot wrench estimation selects stance contacts, and the corresponding footfall records provide intermittent world-frame constraints that suppress long-term drift. To prevent elevation drift during extended traversal, we introduce a lightweight height clustering and time-decay correction that snaps newly recorded footfall heights to previously observed support planes. For wheel-legged platforms, the recorded contact is further propagated by effective wheel rolling displacement with shank-motion compensation and a slope-aware rolling direction. To improve foot velocity observations under encoder quantization, we retain an inverse-kinematics cubature Kalman filter as an optional velocity-enhancement module that filters foot-end velocities from joint angles and velocities. The implementation further mitigates yaw drift through multi-contact geometric consistency, which is injected as a soft heading prior rather than as a hard reset of the attitude state. The method is evaluated on four quadruped platforms.
Minxing Sun, Yao Mao
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.
Deformable granular terrains introduce significant locomotion and immobilization risks in planetary exploration and are difficult to detect via remote sensing (e.g., vision). Legged robots can sense terrain properties through leg-terrain interactions during locomotion, offering a direct means to assess traversability in deformable environments. How to systematically exploit this interaction-derived information for navigation planning, however, remains underexplored. We address this gap by presenting PSANE, a Proprioceptive Safe Active Navigation and Exploration framework that leverages leg-terrain interaction measurements for safe navigation and exploration in unknown deformable environments. PSANE learns a traversability model via Gaussian Process regression to estimate and certify safe regions and identify exploration frontiers online, and integrates these estimates with a reactive controller for real-time navigation. Frontier selection is formulated as a multi-objective optimization that balances safe-set expansion probability and goal-directed cost, with subgoals selected via scalarization over the Pareto-optimal frontier set. PSANE safely explores unknown granular terrain and reaches specified goals using only proprioceptively estimated traversability, while achieving performance improvements over baseline methods.
Matthew Y. Jiang, Feifei Qian, Shipeng Liu
Georgia Institute of Technology, Atlanta, GA 30332, USA · University of Southern California, Los Angeles, CA 90089, USA