Analytical Model and Experimental Testing of the SoftFoot: an Adaptive Robot Foot for Walking over Obstacles and Irregular Terrains

TL;DR

The paper introduces SoftFoot, a passive, biomimetic robot foot whose shape and stiffness adapt through a pulley–tendon–spring network to walking on obstacles and irregular terrains. A linearized mathematical model links foot configuration $q$ to external loads, enabling closed-form design insights under a small-angle assumption, while experiments compare SoftFoot to rigid and compliant feet, showing an expanded equivalent support surface and competitive impact absorption. Experimental validation—including stability tests and obstacle drops—demonstrates reduced ankle compensation and improved load rejection, supporting SoftFoot as a robust alternative for unstructured environments. Real-world demonstrations on humanoid and quadruped platforms, plus discussion of prosthetic applications, suggest broad relevance for improved safety and efficiency in diverse robotic and assistive technologies.

Abstract

Robot feet are crucial for maintaining dynamic stability and propelling the body during walking, especially on uneven terrains. Traditionally, robot feet were mostly designed as flat and stiff pieces of metal, which meets its limitations when the robot is required to step on irregular grounds, e.g. stones. While one could think that adding compliance under such feet would solve the problem, this is not the case. To address this problem, we introduced the SoftFoot, an adaptive foot design that can enhance walking performance over irregular grounds. The proposed design is completely passive and varies its shape and stiffness based on the exerted forces, through a system of pulley, tendons, and springs opportunely placed in the structure. This paper outlines the motivation behind the SoftFoot and describes the theoretical model which led to its final design. The proposed system has been experimentally tested and compared with two analogous conventional feet, a rigid one and a compliant one, with similar footprints and soles. The experimental validation focuses on the analysis of the standing performance, measured in terms of the equivalent support surface extension and the compensatory ankle angle, and the rejection of impulsive forces, which is important in events such as stepping on unforeseen obstacles. Results show that the SoftFoot has the largest equivalent support surface when standing on obstacles, and absorbs impulsive loads in a way almost as good as a compliant foot.

Figures (13)

• Figure 1: Pictures show a comparison between a human foot (a-b) and the SoftFoot (c-d), while walking on irregular ground. The SoftFoot is designed with a compliant structure that allows it to adapt to uncertain environments and increase the device robustness towards impact. Pictures a-b adapted from Shutterstock.
• Figure 2: Two surfaces in contact (a): $S$ is the eventually non--convex contact area, $C(S)$ is the convex hull of $S$. In (b) we report the traction $P(r)$ exerted in a generic contact point $r \in S$.
• Figure 3: Schematic representation of different feet models described in Section \ref{['sec:comparison']} and \ref{['sec:adaptive']}: rigid flat foot (a-b), compliant flat foot (c-e), and adaptive foot (f-g). It is possible to observe different behaviors according to the foot design characteristics and the shape of the terrain encountered. COM = center of mass; ZMP = Zero Moment Point; P = traction force; H = leg height; L = contact surface; $\theta$ = ankle motion angle; $\alpha$ = rotation of the foot ankle due to the obstacle; $k$ = sole stiffness; $T_{\mathrm{h}}$ = contact force at the heel of the foot; $T_{\mathrm{o}}$ = contact force at the obstacle; $T_{\mathrm{t}}$ = contact force at the tip of the foot.
• Figure 4: Schematic architecture of the human foot, bones, phalanges and representation of the longitudinal arch and windlass mechanism $(a)$. Prototype of the robotic foot, with components adopted for the implementation of the artificial longitudinal arch and windlass mechanism $(b)$.
• Figure 5: Architecture of the SoftFoot, simplified kinematic with the main parts underlined. $F_1,F_2,F_3$ are the are the three considered contact forces, $F_P$ is the load applied by the robot, which is connected to body (2) through the ankle. (6-7) represent the phalanxes. The plantar fascia is implemented by the set of links (3-4-5) and the tendon (green in figure) which is connected from the calcaneous to the tip of the toe. Bodies (3-4-5-6-7) are connected each other through a spring of stiffness $e$. Bodies (2-3) are also connected through a spring of stiffness $e_0$.

Theorems & Definitions (2)

• Theorem 1
• Lemma 1