Failure Mechanisms and Risk Estimation for Legged Robot Locomotion on Granular Slopes

Abstract

Locomotion on granular slopes such as sand dunes remains a fundamental challenge for legged robots due to reduced shear strength and gravity-induced anisotropic yielding of granular media. Using a hexapedal robot on a tiltable granular bed, we systematically measure locomotion speed together with slope-dependent normal and shear granular resistive forces. While normal penetration resistance remains nearly unchanged with inclination, shear resistance decreases substantially as slope angle increases. Guided by these measurements, we develop a simple robot-terrain interaction model that predicts anchoring timing, step length, and resulting robot speed, as functions of terrain strength and slope angle. The model reveals that slope-induced performance loss is primarily governed by delayed anchoring and increased backward slip rather than excessive sinkage. By extending the model to generalized terrain conditions, we construct failure phase diagrams that identify sinkage- and slippage-induced failure regimes, enabling quantitative risk estimation for locomotion on granular slopes. This physics-informed framework provides predictive insight into terrain-dependent failure mechanisms and offers guidance for safer and more robust robot operation on deformable inclines.

Figures (6)

• Figure 1: Importance and challenges of legged locomotion on sand slopes. (a) Sand slopes widely present in natural environments (White Sands National Park, NM). (b) Hexapedal robot ascending a dune slope. (c) Quadruped robot traversing a relatively mild sand slope at White Sands. (d) Example ascent paths on a sand slope, illustrating the tradeoff between shorter routes (yellow) and longer but potentially less risky path (red, cyan).
• Figure 2: Robot and experimental setup for studying locomotion on granular slopes. (a) Hexapedal robot used in this study. (b) Diagram illustrating the key parameters of robot leg. Here $R$ denotes robot leg radius, $d$ denotes the leg penetration depth, $\omega$ denotes the leg angular velocity, and $h$ denotes the hip height, measured as the distance from the leg axle to the bottom of the robot body. (c)Schematic of the tiltable granular trackway for testing robot locomotion on sand. In b and c, $\theta$ denotes the slope angle of the granular incline.
• Figure 3: Robot locomotion on sand slopes of varying inclinations. (a) Average robot up-slope speed as a function of slope angle. (b) Experimentally-measured robot speed vs. time over one stride period $T$. Purple, red, orange, green, and blue curves represent 0, 10, 15, 20, 24 degree inclinations, respectively. (c) Experimental image sequences showing the side view of the robot traveling on a 15-degree slope. Corresponding critical moments, $t_0$,$t_1$, $t_2$, $t_3$ are also labeled on the orange (15-deg) curve in (b). (d) Schematic of the leg-ground interaction during each phases. In c and d, images from up to bottom correspond to the critical timings, $t_0$, $t_1$, $t_2$, and $t_3$, labeled in b.
• Figure 4: Sand resistive force measurements on inclined granular surfaces. (a, e) Experimental setups for penetration and shear force measurements. (b, f) Schematics illustrating the penetration and shear plate motion. (c, g) Measured penetration and shear resistive forces, as functions of penetration and shear displacements. Red to blue colors represent inclination angle from 0$\degree$ to 24$\degree$. (d, h) Measured sand penetration and shear resistance per unit area as functions of slope angles.
• Figure 5: Predictive model to link anchoring timing to robot step length. (a) Comparison of robot speed vs. time on 0$\degree$ and 24$\degree$ sand slope in one representative step. Red and blue vertical dashed lines denote the anchoring timing $t_1$ for 0$^\circ$ and 24$^\circ$, respectively. The yellow shaded region indicates the backward slippage $s_1$ on the 24$^\circ$ slope. The purple and blue shaded regions (net positive area under the velocity curve) denote the propulsion displacement $s_2$ for 0$^\circ$ and 24$^\circ$, respectively. (b) Experimentally-measured (black asterisks) and model-predicted (red dashed line) $t_1$ as a function of slope angle. (c) Experimentally-measured (black asterisks) and model-predicted (red dashed line) robot net step length $s$ as a function of sand slope angle.