Control of Powered Ankle-Foot Prostheses on Compliant Terrain: A Quantitative Approach to Stability Enhancement

TL;DR

This work tackles the challenge of maintaining gait stability for powered ankle-foot prostheses on compliant terrain. It introduces a phase-based admittance controller that dynamically modulates ankle quasi-stiffness and compares it against a standard tibia-phase controller across bilaterally compliant surfaces using three healthy subjects. The admittance controller achieves higher quasi-stiffness and, in many cases, improved stability as evidenced by phase portraits, reduced short- and long-term Lyapunov exponents, and favorable margins of stability, though effects are direction- and subject-dependent. These findings support the potential for adaptive, stability-aware prosthesis control to reduce fall risk in real-world environments and guide future real-time, terrain-aware assistance for individuals with lower-limb amputation.

Abstract

Walking on compliant terrain presents a substantial challenge for individuals with lower-limb amputation, further elevating their already high risk of falling. While powered ankle-foot prostheses have demonstrated adaptability across speeds and rigid terrains, control strategies optimized for soft or compliant surfaces remain underexplored. This work experimentally validates an admittance-based control strategy that dynamically adjusts the quasi-stiffness of powered prostheses to enhance gait stability on compliant ground. Human subject experiments were conducted with three healthy individuals walking on two bilaterally compliant surfaces with ground stiffness values of 63 and 25 kN/m, representative of real-world soft environments. Controller performance was quantified using phase portraits and two walking stability metrics, offering a direct assessment of fall risk. Compared to a standard phase-variable controller developed for rigid terrain, the proposed admittance controller consistently improved gait stability across all compliant conditions. These results demonstrate the potential of adaptive, stability-aware prosthesis control to reduce fall risk in real-world environments and advance the robustness of human-prosthesis interaction in rehabilitation robotics.

Figures (10)

• Figure 1: Front and side view of a subject standing on the VST 2, while wearing the powered ankle-foot prosthesis ROA attached to ankle bypass adapter. The magenta circles designate the four markers positioned around the pelvis, specifically, the left and right anterior and posterior superior iliac spine. The yellow circle denotes the marker placed on the left heel (LHEEL) of the prosthetic foot. The red, green, and blue axes correspond to the medial-lateral (ML), anterior-posterior (AP), and vertical (VT) directions, respectively.
• Figure 2: Block diagram illustrating the implementation of the standard TC on the lower-limb prosthesis. The tibia angular velocity $\dot{\theta}_s$, determines the gait percent and stride length, subsequently establishing the reference motor position $x_g$ through a gait LUT. The ankle moment $M$ is estimated based on the motor position $x$ and the ankle angle $q$ through a LUT ($\text{LUT}_{1}$). A moment feedback controller exports the motor command $x_m$ based on the ankle moment $M$ to enhance the reference motor command at low stride lengths. The two motor commands are combined to yield the final motor position command $x_{d}^{tc}$, sent to the low-level motor controller. The low-level motor controller directs the rotation of the prosthesis ankle joint by issuing precise position commands to the motor.
• Figure 3: Block diagram illustrating the implementation of the proposed AC on the lower-limb prosthesis. The desired stiffness $K_d$ is set, and the admittance controller calculates an ankle angle offset based on the applied moment $M$. Again, $M$ is derived from a LUT based on the motor position $x$ and the ankle angle $q$ ($\text{LUT}_{1}$). Simultaneously, the tibia controller calculates a motor position command $x_{d}^{tc}$ based on the ankle moment and the tibia angular velocity $\dot{\theta}_s$. The virtual unloaded reference ankle angle $q_{u}^{tc}$ is calculated through an inverted version of the ankle moment LUT ($\text{LUT}_{2}$), based on $x_{d}^{tc}$ and a virtual zero ankle moment. The ankle angle offset is added to $q_{u}^{tc}$, producing a desired ankle angle $q_d$, which is then fed into the ankle controller. The ankle controller consists of a FF and a proportional FB system, which combined together yield the final motor position command $x_{d}^{ac}$ sent to the low-level motor controller. The low-level motor controller sends position commands to the motor, causing the rotation of the prosthesis ankle joint.
• Figure 4: Representative divergence curve from the ML velocity signal for the trial of the first subject with the TC over rigid terrain. The orange line represents the divergence curve, while the black solid and dashed lines indicate the least-square fits over the intervals of 0-1 and 4-10 strides, respectively. Divergence exponents $\lambda_{S}$ and $\lambda_{L}$ represent the slopes of the least-square fits, expressed as $\left<\ln\{d_{j}(i)\}\right>/\text{stride}$. Inset: Divergence curve over the interval of 0-1 strides.
• Figure 5: Representative example for the calculation of the mediolateral $\text{MOS}_{\text{ML}}$ (top) and anteroposterior $\text{MOS}_{\text{AP}}$ (bottom) margins of stability for the right side (intact limb) during one gait cycle. Blue dashed lines denote the filtered position of the CoM, while solid orange and yellow lines depict the filtered positions of the XcoM and the CoP, respectively. Vertical solid black lines indicate the timings during the stance phase at which the margins of stability were derived; when the distance between the CoP and the XcoM was minimized in the mediolateral (top) and maximized in the anteroposterior (bottom) direction, respectively. For this example, $\text{MOS}_{\text{ML}} = 39.21\;mm$ and $\text{MOS}_{\text{AP}} = 212.06\;mm$. For brevity, only the derivation for the right side (intact limb) is shown in this figure, with the left side (prosthetic limb) following a similar procedure.