Introduction

Despite advances in prosthetic technology, the incidence of falls among lower-limb prosthetic users (LLPUs) remains high. Over 50% of LLPUs experience at least one fall annually1, with more than a quarter reporting falls that result in injuries2. These incidents not only adversely affect the quality of life for LLPUs3, but also contribute to increased healthcare costs4.

Uneven terrains pose a considerable risk of falls for prosthetic users1,5. Tripping over obstacles is frequently reported as a major challenge, with the prosthesis often being perceived as a source of instability and a contributing factor to falls1. In a study involving non-vascular transfemoral prosthetic users6, nearly 60% reported an inability to walk on uneven ground. LLPUs must always focus on their movements1, resulting in an increased cognitive load. To navigate uneven terrains, they heavily depend on visual input and employ predictive and compensatory strategies to maintain balance effectively3,7,8,9,10. Spatio-temporal adjustments include reduced speed, larger step width, and longer double support time3. Kinematic compensations comprise increased upper limb motion3, greater hip and knee flexion on the prosthetic side in transtibial users (both at stance onset to lower the body’s centre of mass and during swing to increase foot-ground clearance7), and compensatory movements such as vaulting or hip hiking11.This prudent gait is usually associated with greater and painful socket pressures12 and an overall increased control effort. Moreover, compensatory strategies determine increased metabolic cost13 and gait asymmetries7,9, overloading the contralateral limb with an associated increased long-term risk of osteoarthritis14.

While training can improve LLPUs’ balance in various environments, current commercial passive energy-storage-and-return prosthetic feet, mainly made of carbon fibre laminates, fail to ensure adaptability on uneven grounds (Fig. 1b). Surface adaptation is usually, indeed, tackled through split keels, which offer limited adaptation. Other passive solutions on the market include: the Evanto (Ottobock), which allows multi-planar motion through a pivot axis and foam wedges at the heel; the Triton Side Flex (Ottobock, https://www.ottobock.com/en-gb/product/1C68) and the META® Arc (WillowWood)15, both of which feature ankle units allowing 10° inversion/eversion. Commercial microprocessor-controlled prostheses like the Meridium and the Triton Smart Ankle (both by Ottobock), the Elan (Blatchford), and the Freedom Kinnex 2.0 (Proteor) can adapt to slopes and slightly enhance sagittal ankle joint range of motion (ROM) by actively modulating the ankle joint impedance. The Proprio Foot (Össur) improves swing ground clearance through an electric motor driving ankle rotation. The Meridium also includes a metatarsophalangeal joint axis for improved sagittal motion.

Fig. 1: Biological and artificial feet.
Fig. 1: Biological and artificial feet.
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a Human foot. b A commercial passive energy-storage-and-return prosthetic foot made of carbon fibre in its aesthetic cover. c The SoftFoot Pro, an anthropomorphic and adaptive prosthetic foot, in its aesthetic cover. The stiff and flat sole of prostheses such as (b) prevents ground adaptation. The soft and flexible sole of the SoftFoot Pro (c), instead, conforms to the ground profile, similarly to the human counterpart. Credit: Aron Cserveny.

Over the past two decades, research efforts have predominantly focused on developing active prosthetic ankles capable of generating biomimetic sagittal torque and power profiles across various tasks16,17,18,19,20,21,22,23,24,25, advanced control algorithms for seamless locomotion mode transitions in powered leg prostheses16,26,27, and bidirectional human-prosthesis interfaces enabling active device control26,28,29,30 and sensory feedback restoration29,30,31. About ankle prostheses, semi-active prototypes adjust mechanical properties based on the task and walking speed without directly injecting energy into the gait cycle. These adjustments include modifying ankle stiffness32, altering forefoot stiffness33, or repositioning the ankle joint during swing34. Some recently developed adaptive designs feature two degrees of freedom (DoFs) at the ankle joint – through active or passive solutions – for sagittal and frontal motion22,29,35,36,37,38, while others attempt to emulate the flexibility of the human foot sole by embodying rotational axes at the midfoot or metatarsophalangeal joints (see for instance the powered toe joint of the Utah Bionic Leg24 and other examples in refs. 22,39). A flexible toe joint was, for instance, preferred to a rigid one by LLPUs for navigating uneven terrains40. It reduced the positive hip joint work in the prosthetic side. Adding flexibility in the foot sole can also contribute to lowering the output torque and the energy consumption in the design of new active prosthetic ankles41.

However, these designs still fall short of the human foot functionality and adaptive performance. Comprising 26 bones, 20 muscles, 33 joints, and over 100 ligaments, the human foot evolved from great apes to support bipedal walking and running, with high midfoot motion during stance42. Its longitudinal and transverse arches modulate sagittal foot stiffness, ensuring stability over the gait cycle and on all terrains42,43. The longitudinal arch also provides an energy-recycling behaviour during running42. The connective tissue of the foot base, named plantar fascia, strains for most of the stance phase, contributing to saving energy44. Ankle plantar flexors and plantar intrinsic muscles further strain it during push-off (i.e. at 50–62% of the gait cycle45), enabling the foot to act as a stiff lever, converting ankle power generation into forward body propulsion46. Moreover, the foot’s multiple joints allow it to conform to larger ground irregularities (Fig. 1a), whilst the soft tissues of the sole filter small irregularities47. As a result, the human foot exhibits robustness and adaptability across diverse environments and tasks, with high mobility and versatility. With respect to the human foot, most commercial and research prosthetic feet neglect the complex sole’s dynamics and deformability, embodying flat and rigid components at the sole like carbon fibre laminates (Fig. 1b). These stiff soles prevent ground adaptation and obstacle negotiation7.

Here, we present the SoftFoot Pro: a prosthetic foot that passively provides ground adaptation across all terrains (Figs. 1c and 2). The project stems from an artificial adaptive foot, the SoftFoot48, developed for legged robotic systems, which was designed according to a soft robotics approach49 reminiscent of previous design approaches for artificial hands50. It was developed to overcome the drawbacks of state-of-the-art robotic flat feet in unstructured environments. Bench-testing of the SoftFoot yielded promising results on obstacles in terms of support surface and absorption of impulsive forces, exceeding the performance of completely rigid and compliant artificial feet48. The SoftFoot was also tested with the HRP-4 humanoid robot: it outperformed the robot’s original flat feet when negotiating obstacles, even without controller optimisation51.

Fig. 2: The SoftFoot Pro.
Fig. 2: The SoftFoot Pro.
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a 3D CAD model of the adaptive foot with the pylon and the socket for a transtibial prosthetic user. b Physical prototype. c Exploded view of the prosthesis with its main components.

Therefore, building upon the promising performance of the SoftFoot in legged robotic applications, we developed its prosthetic counterpart, the SoftFoot Pro, which matches the human foot anthropometry and can be interfaced with any prosthetic leg through standard prosthetic adapters (suitable for amputation levels from transtibial to more proximal). It features a flexible and inextensible sole that passively conforms to ground profiles, allowing the foot to intrinsically adapt to various surfaces. We hypothesized that this design could facilitate obstacle negotiation for LLPUs, by mainly reducing gait modifications on uneven terrains and thereby improving gait symmetry. This hypothesis was tested with two unilateral below-knee prosthetic users performing tasks including stepping on obstacles. The performance of the adaptive foot was compared to that of a standard passive carbon fibre prosthetic foot. Results of the experimental activity follow, and a detailed description of the prosthesis design is presented in the Methods.

Results

Overview of the SoftFoot Pro

The anthropomorphic, adaptive prosthetic foot we propose – the SoftFoot Pro – consists of two rigid components replicating the human longitudinal arches, a rigid heel component, and a flexible sole acting as both the human plantar fascia and toes (Figs. 2 and 3a, Supplementary Fig. 1). A revolute joint, representing the ankle joint, connects the frontal arch to the rear arch. The rotation of the frontal arch relative to the rear arch, despite the latter being rigidly connected to the prosthetic shank, allows some plantarflexion and dorsiflexion (in the unloaded configuration, the maximum relative rotation of the frontal arch with respect to the rear arch is approximately 24°, all in plantarflexion). The sole comprises five parallel modules, each consisting of small bodies connected through elastic bands and a wire that exhibits inextensible behaviour under load (detailed design description in the Methods section). This configuration provides compliant interaction with the environment, enlarging the ground contact area and enabling effective obstacle negotiation whilst supporting the user’s body weight (BW). The sole’s behaviour is passively determined by environmental interaction through the combined action of elastic bands and wires responding to the ground profile and the user’s load. As it bends to match the ground profile, the sole exhibits non-linear stress-stiffening behaviour under load48 (with stiffness increasing primarily due to the wire characteristics), before returning to its original shape when unloaded (via elastic band action). This behaviour arises from the wire’s properties: negligible flexural rigidity for easy deformation, thus conformity to ground profiles, as well as negligible elongation under load.

Fig. 3: Parallelism between the human foot and artificial feet.
Fig. 3: Parallelism between the human foot and artificial feet.
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a On the left, the bones constituting the longitudinal arches, the plantar fascia, and the intrinsic muscles in the sole are emphasized in the human foot. On the right, the anthropomorphic adaptive prosthesis SoftFoot Pro. b–d Case study I and e, f case study II: participants stepping on the arch-shaped obstacle with b the contralateral sound limb, and c–f the prosthetic limb, when using c, e their own prosthesis (Triton by Ottobock), and d, f the SoftFoot Pro. The top row displays the participant stepping on the obstacle from a static position, to show the change in shape of the sole of the SoftFoot because of the obstacle, resembling the human foot, contrary to the carbon foot. The bottom row, instead, shows the participant’s performance on the obstacle while walking. Images of the bottom row come from an overlay of the 3D marker data onto 2D videos in the software Vicon Nexus. Coloured links denote the reconstructed body segments based on the 3D markers trajectories from Vicon, with the GRF vector displayed in yellow.

Validation of the SoftFoot Pro with prosthetic users

The SoftFoot Pro was tested with a prosthetic user with knee rotationplasty in collaboration with the Laboratory for Biomechanics and Biomaterials, Hannover Medical School (henceforth Case Study I (CSI)), and with an individual with unilateral transtibial amputation and osseointegration, in collaboration with the Clinical Laboratory for Bionic Extremity Reconstruction, Medical University of Vienna, and Imperial College London (Case Study II (CSII)).

Results from level ground walking and obstacle stepping are presented below for the two case studies, with reference data from unimpaired individuals.

The SoftFoot Pro exhibited ankle joint range of motion (ROM) closer to able-bodied data than the Triton across all tasks in both case studies. On level ground, it was greater than the carbon foot in CSI, or comparable to it in CSII. Obstacles reduced prosthetic ankle ROM, though the reduction was smaller with the SoftFoot (about 10% in CSI and 30% in CSII, the latter closer to the reduction in a sound ankle) compared to the carbon foot (up to 50% in CSI and 70% in CSII) (Fig. 4, Supplementary Tables 1, 2). Stepping on obstacle with the prosthesis led to a slight increase in the ankle ROM of the contralateral limb during the following step on flat ground. However, the contralateral ankle ROM was overall smaller with the SoftFoot than with the Triton and closer to level able-bodied data. In CSI, the SoftFoot outperformed the Triton across all tasks in terms of stance dorsiflexion and push-off plantarflexion; also in CSII it showed about 4° of push-off plantarflexion in all tasks (Supplementary Table 2), unlike the Triton.

Fig. 4: Sagittal ankle angle, torque, and power (from top to bottom) on level ground and obstacles (arch and rectangle).
Fig. 4: Sagittal ankle angle, torque, and power (from top to bottom) on level ground and obstacles (arch and rectangle).
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Mean values across 6 strides in CSI (n = 6) and 5 strides in CSII (n = 5; n = 3 for level walking with the participant’s prosthetic foot) for the prosthetic limb (blue solid line for the carbon foot Triton, red solid line for the SoftFoot Pro), and the contralateral limb (CSII only - blue dotted line when using the Triton, red dotted line for the SoftFoot Pro, ±1 SD for torques). Contralateral data always refer to the stride on flat ground following the prosthetic limb's step on either flat ground or the obstacle. Grey-shaded areas correspond to reference data from unimpaired individuals (±1 SD). Data are displayed normalized to stride duration (i.e. time between two consecutive heel strikes of the same limb). Torque and power values are normalized by the participant’s body mass.

The average stance torque of the prosthetic ankle consistently fell below that of unimpaired subjects in both case studies (except for the SoftFoot on the rectangle in CSII). In CSI, it was smaller for the SoftFoot than for the carbon foot (although the peak values were similar, Fig. 4, Supplementary Tables 3, 4). In CSII, instead, it was greater with the SoftFoot for all tasks and limbs, and closer to able-bodied data for level and the arched obstacle (Supplementary Table 3). Peak values for the contralateral side were smaller with the SoftFoot across all tasks, and when the prosthetic limb stepped on the obstacles they were also closer to the peak value for able-bodied level walking (Supplementary Table 4).

Push-off power generation was deficient in both prostheses in all tasks in both case studies, with peak values (e.g. in CSII, 0.54 W/kg (SoftFoot) and 1.65 W/kg (Triton) for level, 0.42 W/kg (SoftFoot) and 0.51 W/kg (Triton) for the arch, 0.61 W/kg (SoftFoot) and 0.43 W/kg (Triton) for the rectangle) much lower than those of the contralateral limb (respectively 2.45 W/kg and 4.04 W/kg, 3.04 W/kg and 4.75 W/kg, 3.09 W/kg and 4.72 W/kg, Supplementary Table 4) and normative data (3.27 W/kg for flat ground, 1.67 W/kg for the arch, and 1.84 W/kg for the rectangle). The push-off power peaks for the contralateral side were smaller when the adaptive foot was used compared to the carbon foot in all tasks, and on obstacles they were closer to the corresponding peak for able-bodied level walking.

In CSI, a typical double-hump profile characterised the GRF in its three components for both prostheses for the level task (Fig. 5). However, there is a drop in the second peak of the prosthetic-side vertical ground reaction force (vGRF) and the corresponding propulsive peak of the anterior-posterior GRF (apGRF). In CSII, the prosthetic limb exhibited lower vertical mean values across all tasks compared to able-bodied values and the contralateral limb, resulting in uneven joint loading. Prosthetic vGRF peaks were both approximately equal to and lower than body weight for flat ground and obstacle stepping respectively, while the first vGRF peak of the contralateral limb was always much larger than body weight (e.g. just less than 140%BW for level walking, Fig. 5, Supplementary Table 5). The SoftFoot exhibited a second vGRF peak larger than that from using the Triton foot, approaching values closer to the contralateral limb and similar to able-bodied subjects. However, this peak, corresponding to the ankle dorsiflexion peak, occurred earlier than expected (approximately at 35% of the gait cycle), followed by a third smaller peak (also exhibited by the medio-lateral, mlGRF, and antero-posterior, apGRF, GRF components).

Fig. 5: GRF components in the sagittal (vGRF, top row), frontal (mlGRF, middle row), and transverse (apGRF, bottom row) planes, on level ground and obstacles (arch and rectangle).
Fig. 5: GRF components in the sagittal (vGRF, top row), frontal (mlGRF, middle row), and transverse (apGRF, bottom row) planes, on level ground and obstacles (arch and rectangle).
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Mean values across 6 strides in CSI (n = 6) and 5 strides in CSII (n = 5; n = 3 for level walking with the participant’s prosthetic foot) for the prosthetic limb (blue solid line for the carbon fibre foot Triton, red solid line for the SoftFoot Pro), and the contralateral limb (CSII only - blue dotted line when using the Triton, red dotted line for the SoftFoot Pro, ±1 SD for torques). Contralateral data always refer to the stride on flat ground following the prosthetic limb's step on either flat ground or the obstacle. Grey-shaded areas correspond to reference data from unimpaired individuals (±1 SD). Data are displayed normalized to stride duration. GRF data are shown as a percentage of the participant’s body weight (%BW).

Obstacles further reduced the vGRF (closer to BW in CSI and notably lower than BW in CSII) in the prosthetic side and increased the first vGRF peak of the contralateral side during the following step on flat ground – the former lower than the able-bodied counterpart on obstacles, and the latter much larger than normative data for level ground. The SoftFoot mitigated these effects by likely enabling greater load-bearing on the prosthetic limb during the second half of stance in both case studies, and closer to the corresponding able-bodied data. In CSII, this was confirmed by the symmetry index (SI) between limbs (Supplementary Fig. 2, Supplementary Tables 5, 6), which showed higher asymmetry with the Triton (i.e. higher SI) on obstacles, particularly for the peaks of the vGRF, but also for those of the apGRF. The SI for the two peaks of the vGRF of the Triton increased from almost 27% and 12.7% for level walking to almost 70.9% and 27.5% for the arched obstacle, and 62.2% and 27.4% for the rectangular obstacle. Conversely, the SI for the SoftFoot showed a much smaller increase when going from level to obstacle: from 34.7% and −8% for level ground to 54.5% and 12% for the arch, and 45.7% and 18.6% for the rectangle. In CSI, the Triton showed a noticeable further reduction in the second peak of the prosthetic-side vGRF when stepping on obstacle, suggesting increased reliance on the contralateral limb for support, whereas the SoftFoot preserved its double-hump – almost triple-hump – profile in the three GRF components.

In CSI, the knee joint in the prosthetic limb remained extended until push-off for all tasks (Fig. 6, Supplementary Table 7). This resulted in a resistive flexor torque, exacerbated by the obstacles, but noticeably reduced by using the adaptive foot (e.g. stance mean values: −0.01 Nm/kg (SoftFoot) and −0.18 Nm/kg (Triton) for level, −0.17 Nm/kg and −0.32 for the arch, −0.12 Nm/kg and −0.30 Nm/kg for the rectangle), which also allowed torques closer to the able-bodied mainly extensor knee torque (0.02 Nm/kg for level, 0.13 Nm/kg arch, 0.09 Nm/kg rectangle, Supplementary Tables 8, 9). In case of obstacles, the GRF vector exhibited an anterior shift in the prosthetic limb relative to the knee joint centre of rotation, generating knee extension, which was slightly reduced when using the adaptive foot, Fig. 3b–d, Supplementary Movie 1). Unlike normative data, knee power profiles for both prostheses showed no noticeable absorption or generation peaks until push-off.

Fig. 6: Sagittal knee angle, torque, and power (from top to bottom) on level ground and obstacles (arch and rectangle).
Fig. 6: Sagittal knee angle, torque, and power (from top to bottom) on level ground and obstacles (arch and rectangle).
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Mean values across 6 strides in CSI (n = 6) and 5 strides in CSII (n = 5; n = 3 for level walking with the participant’s prosthetic foot) for the prosthetic limb (blue solid line for the carbon fibre foot, red solid line for the SoftFoot Pro), and the contralateral limb (CSII only - blue dotted line when using the Triton, red dotted line for the SoftFoot Pro, ±1 SD for torques). Contralateral data always refer to the stride on flat ground following the prosthetic limb's step on either flat ground or the obstacle. Grey-shaded areas correspond to reference data from unimpaired individuals (±1 SD). Data are displayed normalized to stride duration. Torque and power are normalized by the participant’s body mass.

In CSII, the SoftFoot induced greater knee flexion for the prosthetic side until push-off on flat ground compared to the Triton (mean values of 26.1° vs. 15.9°, Supplementary Table 7), even exceeding the values for the contralateral limb (19.7° (SoftFoot), 23.9° (Triton)) and normative data (7.43°), and resisted by a larger extensor torque (stance mean values: 0.36 Nm/kg (SoftFoot), 0.26 Nm/kg (Triton), 0.02 Nm/kg (normative data), Supplementary Table 8, Fig. 6). Obstacles amplified this trend, inducing increased stance knee flexion in the prosthetic limb with both prostheses (noticeably on the arched obstacle), which was also observed in able-bodied negotiating obstacles. In particular, the SoftFoot determined a more posterior GRF vector relative to the knee joint centre, which promoted increased stance knee flexion (Fig. 3e, f, Fig. 6, Supplementary Movie 2). The stance knee flexion mean values and peaks for the contralateral step on flat ground following the prosthetic step on the obstacle were, instead, lower with the SoftFoot across all tasks. They were closer to able-bodied data, and associated with lower extensor torques (Fig. 6, Supplementary Tables 7–9). For example, with the arched obstacle, mean values were 0.81 Nm/kg (Triton) and 0.53 Nm/kg (SoftFoot), with peaks in the first half of the stance of 2.82 Nm/kg (Triton) and 1.75 Nm/kg (SoftFoot) – able-bodied level peak of 0.41 Nm/kg. Additionally, despite the stance knee power of the contralateral side exceeding normative data across all tasks, the use of the SoftFoot on the obstacle induced half the power peaks compared to the Triton in the contralateral limb.

In CSI, the prosthetic limbs showed an increased extensor hip torque during most of stance of level walking compared to normative data, associated with greater stance energy generation (Fig. 7, Supplementary Table 11). This trend amplified on obstacles. However, unlike the Triton, the SoftFoot mitigated the increase in both the extensor torque (mean values also closer to those of unimpaired subjects) and the energy generation during obstacle negotiation, which were also associated with a greater hip flexion at the gait cycle start. In CSII, the SoftFoot reduced hip joint ROM in both limbs (Fig. 7, Supplementary Table 10) across all tasks compared to the Triton, with values closer to normative data in most cases. This reduction was likely attributable to shorter stride lengths: 1.4 m with the SoftFoot versus 1.7 m with the Triton during level walking. Walking speed also decreased: 1.2 m/s (SoftFoot) versus 1.6 m/s (Triton). Conversely, the Triton induced larger hip extension in the prosthetic side during terminal stance (i.e. at 30–50% of the gait cycle45) and push-off of level walking, resulting in greater extending torque and power peaks, also in the contralateral limb (mean stance torques: 0.02 Nm/kg (SoftFoot) and −0.19 Nm/kg (Triton) in the prosthetic limb, −0.07 Nm/kg (SoftFoot) and −0.16 Nm/kg (Triton) in the contralateral limb, Supplementary Table 11). Obstacles did not exacerbate hip torque and power peaks in the prosthetic limbs but did it in the contralateral limb when using the Triton. Conversely, the SoftFoot almost halved the contralateral extensor peak during load acceptance (i.e. about 3–12% of the gait cycle45), and considerably reduced the hip flexor torque during push-off on both obstacles, with values closer to normative data. Overall, differences in contralateral limb torques between the two prostheses were rarely statistically significant according to a t-test (see Supplementary Note 1 for the results of the statistical analysis).

Fig. 7: Sagittal hip angle, torque, and power (from top to bottom) on level ground and obstacles (arch and rectangle).
Fig. 7: Sagittal hip angle, torque, and power (from top to bottom) on level ground and obstacles (arch and rectangle).
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Mean values across 6 strides in CSI (n = 6) and 5 strides in CSII (n = 5; n = 3 for level walking with the participant’s prosthetic foot) for the prosthetic limb (blue solid line for the carbon fibre foot, red solid line for the SoftFoot Pro), and the contralateral limb (CSII only - blue dotted line when using the Triton, red dotted line for the SoftFoot Pro, ±1 SD for torques). Contralateral data always refer to the stride on flat ground following the prosthetic limb's step on either flat ground or the obstacle. Grey-shaded areas correspond to reference data from unimpaired individuals (±1 SD). Data are displayed normalized to stride duration. Torque and power are normalized by the participant’s body mass.

For completeness, Supplementary Figs. 3–6 show data of the contralateral sound limb stepping on the obstacle in CSI, when using the Triton in the prosthetic side. The joint patterns characterising the prosthetic user’s sound limb during both level walking and obstacles negotiation are close to those of unimpaired subjects, particularly during the second half of the stance and the swing phase. Additionally, Supplementary Figs. 7–11 show joint data in the frontal plane for both case studies (knee data are lacking for CSII due to limitations of the OpenSim model used), with able-bodied reference data for level ground from Bovi et al.52.

Lastly, when mounted under walking boots on an unimpaired individual53 (Supplementary Fig. 12), the adaptive foot showed negligible pressure at the midfoot during level walking due to its soft sole, with pressure peaks under the heel, metatarsal heads, and toes (Fig. 8b, e) resembling those of a sound foot (Fig. 8a, d). In contrast, the carbon foot’s aesthetic cover enabled continuous ground contact throughout stance (Fig. 8c, f). On an obstacle, this trend reversed. The SoftFoot adapted to the ground profile, maintaining broad contact from heel to forefoot (Fig. 8h, m), showing closer alignment with the human pressure distribution (Fig. 8g, l), whilst the carbon foot contacted only at the midfoot (Fig. 8i, n), as confirmed also by the shorter centre of pressure trajectory. Pressure peaks occurred at the obstacle’s edges. RMSE values quantified this inversion relative to the human condition: on flat ground, the carbon foot showed lower deviation (0.29) than the SoftFoot (0.59), but on obstacles the SoftFoot improved (0.47 vs human-on-obstacle) whilst the carbon foot’s deviation increased (0.50 vs human-on-obstacle) (Supplementary Table 12). When comparing prosthetic performance on the obstacle to normative flat-ground patterns, the SoftFoot remained closer to human behaviour (RMSE: 0.51) than the carbon foot (RMSE: 0.62), suggesting better overall terrain adaptation.

Fig. 8: Plantar pressure.
Fig. 8: Plantar pressure.
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Plantar pressure distribution (kPa) during (a–f) level walking (averaged over 8 strides, n = 8) and (g–n) rectangular obstacle negotiation (right foot stepping on the obstacle, one single stride). a–c, g–i Peak pressure values. d–f, l–n Average peak values. a, d, g, i Able-bodied footprints are from an unimpaired subject, while those (b, e, h, m) of the SoftFoot and (c, f, i, n) of the carbon foot VariFlex (by Ӧssur) are from the same subject walking on the prosthetic feet through customised walking boots. The centre of pressure trajectory is shown in fuchsia.

Discussion

We have introduced an anthropomorphic prosthetic foot, whose distinctive feature is the ground adaptability provided by its flexible and inextensible sole. This design widens the ground contact area by conforming to obstacle profiles (Fig. 9b, e, Supplementary Fig. 13), filtering disturbances. Plantar pressure mapping showed this ground adaptation capabilities resembling those of the human foot. In contrast, prosthetic feet featuring carbon fibre laminates limit adaptability with smaller ground contact areas. Visual inspection, in the authors’ opinion, suggested that the user might have improved control of forward body progression with the adaptive foot. Conversely, the carbon foot seemed to lead to pivoting on reduced contact areas (Fig. 9a, d), with apparent poor control of body progression and an increase in compensatory movements in both lower limbs. However, quantitative assessment of body progression control requires dedicated analysis in future studies.

Fig. 9: The SoftFoot Pro in action.
Fig. 9: The SoftFoot Pro in action.
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a, b, d, e SoftFoot Pro versus a carbon fibre foot in case study II, and c with a prosthetic user with unilateral transfemoral amputation. Participant stepping on (a, b) the arch- and (d, e) the rectangular-shaped obstacles with (a, d) his own carbon fibre foot (Triton by Ottobock), and with (b, e) the SoftFoot Pro. c Foot deformation while kneeling on the ground: from top to bottom, sound foot, carbon fibre foot (Triton by Ottobock), and SoftFoot Pro.

Testing with prosthetic users highlighted that the SoftFoot Pro performed better on uneven terrains than passive carbon fibre prosthetic feet, achieving overall a biomechanics closer to that of unimpaired individuals. Notably, prosthetic ankle ROM approached unimpaired values more closely than the carbon foot, and contralateral knee and hip torques on obstacles were substantially reduced with the SoftFoot and closer to unimpaired patterns. These findings support the initial hypothesis that the adaptive prosthesis mitigates gait modifications in LLPUs, improving gait symmetry.

Results of case study I demonstrated the advantages of the anthropomorphic prosthetic design, particularly the greater prosthetic ankle joint ROM compared to the carbon foot. Case study II confirmed these benefits and highlighted those for the contralateral sound limb. The SoftFoot Pro exhibited also in case study II, indeed, greater prosthetic ankle ROM than the Triton across all tasks, with values closer to able-bodied data and smaller ROM decrements on obstacles. The revolute joint connecting the frontal to the rear arch allowed for some plantarflexion during early stance and push-off. In contrast, most passive prostheses, which are rigidly connected to the shank, dorsiflex under the user’s load and then return to their neutral angle (i.e., the ankle angle where the net external torque on the joint is zero54) at toe-off, without plantarflexing. However, like the carbon foot, the SoftFoot does not provide sufficient push-off ankle power for forward propulsion, despite the wide and stable toes-ground contact during forefoot loading. Moreover, the ankle ROM and torque peaks in the contralateral stride on flat ground (following prosthetic limb’s step on obstacle) approximated unimpaired data more closely with the SoftFoot than with the carbon foot.

GRF data corroborated LLPU’s tendency to offload the prosthetic limb and overload the contralateral limb14,55, causing gait asymmetries. However, the SoftFoot exhibited increased sagittal loading on the prosthetic limb during the second half of stance, reducing the first contralateral vGRF peak. This trend was particularly evident during obstacle stepping (visible in both vGRF and apGRF), bringing the overall pattern closer to able-bodied GRF values compared to the carbon foot. This resulted in a more balanced inter-limb load distribution on obstacles, improving gait symmetry, as quantified by the smaller increase in the symmetry index when transitioning from level to obstacle walking with the SoftFoot, and with cascading benefits for joint mechanics in both limbs.

Reduced forces acting on the contralateral limb with the SoftFoot led to smaller increases in contralateral stance knee flexion angle, torque (increase occurring mainly during load acceptance for stability and shock absorption), and power peaks compared to the Triton. This trend was particularly noticeable on obstacles, where contralateral knee torque with the SoftFoot was substantially lower than with the carbon foot during the first half of stance. Similarly, the SoftFoot stabilised both the prosthetic and the contralateral hip torque in all tasks, avoiding the noticeable increase in stance torque and power peaks observed with the Triton, especially for the contralateral limb on obstacles, which could exacerbate fatigue. Thus, the SoftFoot mitigated excessive compensations in the contralateral sound limb. Compared to a carbon foot prosthesis, both limbs exhibited patterns closer to those of unimpaired subjects overall.

In the prosthetic limb, smaller hip positive work with the SoftFoot aligns with the literature investigating the benefits of flexible toe joints on uneven terrain40, as well as level hip extensor torques at stance onset larger than control data with both prostheses (also in the contralateral limb56), and greater energy generation57. Greater stance knee flexion is consistent with strategies to lower the body’s centre of mass on uneven ground7. This tendency further increased with the SoftFoot, supported by the longer braking phase in the apGRF, which suggests a GRF vector mainly posterior to the knee joint centre of rotation for most of the stance, facilitating knee flexion and increased extensor moment. Videos prove this behaviour, which is likely related to the GRF progression from heel to forefoot within the SoftFoot. The knee flexed while the GRF acted on the soft sole between the heel and metatarsophalangeal joints, and then extended during load transfer to the metatarsophalangeal joints, which corresponded to the second vGRF peak (observed also in apGRF and mlGRF). By contrast, in case study I, the knee joint in the prosthetic limb remained extended until push-off across all tasks. This is typical in individuals with knee rotationplasty58, exhibiting a stance flexor torque, slightly mitigated with the SoftFoot, and reduced energy absorption and generation for the first 50% of the gait cycle – seen also in case study II.

The users provided highly positive subjective feedback regarding obstacle navigation with the SoftFoot. For instance, feedback from the participant of case study II highlighted enhanced confidence, as he reported feeling more secure than with his own prosthesis. In contrast, when describing his conventional carbon fibre foot, he mentioned that going over obstacles sometimes felt a little unsafe. Users also appreciated the lightweight and anthropomorphic design of the SoftFoot, which offers a more natural foot shape, particularly beneficial for tasks like kneeling (Fig. 9c). This design feature may enhance users’ body image and potentially encourage device embodiment and acceptance59.

However, participants reported fatigue from insufficient push-off propulsion in the SoftFoot, especially at higher walking speeds. We speculate that also the shorter stride length and reduced walking speed with the adaptive prosthesis in case study II might be related to this lack of propulsion (in addition to the fact that the subject was more familiar with the carbon foot, which was his daily-use prosthesis). Future design improvements will primarily focus on enhancing push-off propulsion through passive or active solutions at the ankle joint. Furthermore, a comprehensive assessment of dynamic stability remains to be conducted. Future studies will employ established metrics60,61,62 to quantitatively assess it during locomotion on various surfaces, comparing the SoftFoot Pro with conventional non-adaptive prostheses and unimpaired subjects. Lastly, it will also be interesting to evaluate the cognitive load associated with our adaptive prosthetic foot during locomotion in unstructured environments.

In conclusion, the SoftFoot Pro combines stiffness for stability with flexibility for ground adaptation, surpassing the limited capabilities of commercial prostheses and research prototypes. Compensatory strategies on obstacles were relieved compared to the carbon foot: torque and power peaks of the knee joint in the contralateral sound limb and the hip joint in both limbs were reduced. This reduction may lower energy expenditure, a hypothesis to be explored in future studies by evaluating the metabolic cost of walking. By redistributing the load to the prosthetic limb, the SoftFoot Pro improves gait symmetry and may potentially reduce the risk of osteoarthritis in the contralateral sound limb14,63,64,65,66,67, benefiting users’ long-term health. By providing adaptability on all terrains, it mitigates fall risks and the associated societal costs, making it particularly suitable for populations requiring greater stability, such as the elderly, individuals in rugged environments, and those with dysvascular conditions68. Moreover, leveraging 3D printing for sole components could democratise access to the prosthesis by lowering production costs. Overall, the SoftFoot Pro promises to enhance mobility, safety, and quality of life for those with lower-limb loss.

Methods

Prosthetic foot design

The size and mass of the SoftFoot Pro match those of the missing anatomy. Anthropometric data from the \(70{\mathrm{th}}\) percentile69 were considered for the design process, indicating height and weight of about 178 cm (the average male height in most European countries is between 175 cm and 180 cm70) and 80 kg, with a foot length of 26.9 cm and a width of 9.9 cm. The height and mass of the SoftFoot prototype are approximately 11 cm from the ground to the base of the male adapter and 0.70 kg. The latter is close to the mass of common carbon fibre feet (e.g. around 0.65 kg for the Vari-Flex by Össur with aesthetic cover, size 27), and it is smaller than the mass of the human foot and shank segments at the same height as the SoftFoot (~1.35 kg71). The prosthetic foot measures about 26 cm in length and 7.5 cm in width.

Anthropometric proportions in the sagittal plane typically position the ankle joint axis at a horizontal distance from the posterior extremity of the calcaneus of ~25% of the foot length, whilst the metatarsophalangeal joint is located at ~50% of the foot length from the ankle axis69. The ankle joint and metatarsophalangeal joint axes of the SoftFoot Pro were designed accordingly. Similarly, in the vertical direction, the prosthetic ankle joint axis distance from the ground follows that of the intact counterpart of ~5% of the person’s height. As previously mentioned, the frontal and rear arches are connected through a revolute joint with a ball bearing, acting as the ankle joint. The rotational DoF in the sagittal plane around this transverse axis is only limited by the motion of the frontal arch being flush with respect to the rear arch. The rear arch is linked to the heel via a revolute joint given by a steel pin.

The foot sole comprises five parallel modules, each consisting of eight small 3D-printed rigid bodies (Fig. 2). They were sized to be as compact as possible whilst accommodating the internal components (i.e., plastic plain bearing bushing - GSM-0608-05 by IGUS, the wire, and the elastic bands) and ensuring proper functionality. The sole, particularly the longitudinal distance between the calcaneus and the metatarsophalangeal joint in the unloaded foot configuration, was constructed using the maximum whole number of those small bodies, with the remaining space filled through appropriate sizing of the first small body. The frontal and rear arches and the heel are made of AlSi10Mg aluminium alloy, while the sole bodies of Nylon PA12. A Finite Element Analysis validation was conducted for the main structural components of the prosthesis (i.e. the frontal and rear arches) according to the loading conditions defined for a static proof test by the ISO 10328 standard (Supplementary Fig. 14a, b). A pair of elastic bands (natural rubber, diameter of 2.5 mm, length of 10 mm, nominal stiffness of 35 ShA) connects each small body to the following one (Supplementary Fig. 1). An inextensible wire (Liros pre-stretched coated Dyneema SK 75 DC000-0200 with a 1.6 mm diameter) connects all the small bodies of each sole module, from the heel to the toe tip, according to a specific route within the bodies to obtain a flexible but inextensible sole, with specific sole kinematics and dynamics (Supplementary Fig. 1).

The 3D-printed components of each sole module have different shapes based on functional considerations. The 2nd, 3rd, 4th, 7th, and 8th small bodies have the same design, with the last two constituting the two phalanges of the toes (Fig. 2, Supplementary Fig. 1). The distal one is closed at its distal end, being this the toe tip. The rearmost body, i.e. the 1st one, is longer than the others to allow a rigid connection with the heel through steel pins. The 5th and 6th bodies have different shapes and a different path of the inextensible wire within them, to ensure relative rotation in the opposite direction with respect to the other bodies. The 6th body also allows the connection with the frontal arch through a steel pin, constituting a revolute joint and representing the metatarsophalangeal joint.

Two coil springs (music wire, spring constant ~40 N/mm, T.100.200.0296.A by Vanel) connect the rearmost small rigid body to the rear arch through steel pins (Fig. 2, Supplementary Fig. 1). The stiffness of the two springs was determined to prevent foot sole slapping at heel contact, thereby ensuring a smoother loading response phase, whilst withstanding the load acting on the heel at the beginning of the gait cycle. Specifically, the springs were sized considering a 2065 N load acting at the heel, as defined by the ISO 10328 standard for static proof testing of ankle-foot devices at a P4 loading level (body mass up to 80 kg). Based on the geometry of the links, the force transmitted to the springs was calculated using static equilibrium principles, and subsequently their required stiffness was determined (refer to Supplementary Note 2 for further details). As a result of the spring preload, the unloaded sole features a slightly curved shape in the sagittal plane (see for instance the prototype in Supplementary Fig. 13). The two springs contribute to shock absorption at heel contact and to ankle plantarflexion during load acceptance. When the foot is loaded, the small dorsiflexion of the frontal arch relative to the rear arch stretches the foot sole in between the heel and the metatarsophalangeal joints, replicating the plantar fascia stance elongation in the human foot, as well as the springs. When stretched, the elastic bands and the inextensible wire in the sole work together, tightening the sole according to a stiffening-by-compression behaviour48. Meanwhile, thanks to its flexible structure, the sole passively conforms to that of the ground (Fig. 9b, e, Supplementary Fig. 13). In addition, as a result of the peculiar design of the 5th and 6th bodies and the routing of the inextensible wire within them, the toes are passively underactuated and assume a curved configuration when loaded. The distal phalanges exert a pushing force on the ground, enlarging the base of support for the prosthesis user. When obstacles are encountered between the heel and metatarsophalangeal joint, the wire further strains, passively increasing toe plantarflexion and enhancing the foot’s grip on the ground, similar to the human foot (Supplementary Fig. 13). During push-off, when the forefoot is the primary load-bearing region, the toes maintain their supportive role, as evidenced by the high plantar pressures recorded on these segments, particularly in the external modules (Fig. 8).

Mathematical model

Technically, the advantage of having an adaptive sole is to achieve a uniform pressure distribution on the largest possible contact area when the foot is in contact with small asperities, without requiring large ankle compensations.

On flat terrain, a traditional artificial foot with a rigid flat sole enables a uniform pressure distribution across the base of support. The support length (i.e. the projection of the base of support in the sagittal plane, S in Supplementary Fig. 18), within which the vertical projection of the center of mass (COM) must lie for stability, is given by the entire foot length (L in Supplementary Fig. 18a). However, this support length reduces when negotiating obstacles. In such conditions, indeed, maintaining balance requires either positioning the COM projection within the substantially reduced support length (corresponding to the obstacle area) (Supplementary Fig. 18b), or an active compensation at the ankle joint (α in Supplementary Fig. 18c) to counteract the foot rotation induced by the obstacle, mitigating the reduction of the support length. A possible solution to address the limitations of flat feet on ground irregularities involves artificial feet with compliant flat soles, obtained for instance by adding layers of visco-elastic materials, silicon, or rubber at the bottom of the foot sole72.

The compliant sole allows absorption of small obstacles, enhancing ground adaptation, and avoiding ankle compensations and the reduction of the support length (Supplementary Fig. 18e). However, even a homogeneously compliant sole introduces tilting, which necessitates compensation. Moreover, such tilting phenomenon persists also on flat terrains, jeopardising stability (Supplementary Fig. 18d).

An alternative solution to both rigid and homogeneously compliant flat feet is given by the adoption of an adaptive sole like the one embodied in the SoftFoot Pro. On flat terrain, it ensures the same performance of a traditional flat foot, with a support length corresponding to the entire foot whilst eliminating tilting issues (Supplementary Fig. 18f). On ground asperities, the foot sole conforms, distributing contact forces along an extended support length that more closely approximates that achieved on a flat terrain (Supplementary Fig. 18g). In addition, the sole stiffens under load once the contact with the ground has occurred. Consequently, stability improves and ankle compensation is not required. To achieve such conformability while maintaining sufficient support of all foot parts in contact, a detailed design of the SoftFoot components has to be developed based on accurate but manageable mathematical modelling.

To do so we adopt the general framework presented in Piazza et al.48 and apply it to the specific prosthetic-oriented design of the SoftFoot Pro, including eight sole bodies of various lengths and the heel component. The complete model is presented in the Supplementary Note 3 (Mathematical Model). By imposing the force and torque equilibria on the foot as a whole and on each of its components, by considering the elastic effects and tendon coupling in the sole as well as the constraints imposed by the ground and tendon, and by applying the small angles hypothesis, we obtain a set of n+6 equations in n+6 unknowns (q, T, F)

$$\left[\begin{array}{cc}-{{\bf{B}}} & \left[\begin{array}{cc}{{{\bf{p}}}}^{T} & {{\bf{d}}}\end{array}\right]\\ \left[\begin{array}{c}{{\bf{p}}}\\ {{\bf{C}}}\end{array}\right] & {{\bf{0}}}\end{array}\right]\left[\begin{array}{c}{{\bf{q}}}\\ \left[\begin{array}{c}T\\ {{\bf{F}}}\end{array}\right]\end{array}\right]=\left[\begin{array}{c}{{{\boldsymbol{m}}}}_{{{\bf{E}}}}\\ \left[\begin{array}{c}\sigma \\ \delta \end{array}\right]\end{array}\right]$$
(1)

where \({{\boldsymbol{q}}}=\left[{q}_{1}\cdots {q}_{n+2}\right]\in {{\mathbb{R}}}^{n+2}\) represents the prosthetic foot configuration (\(n=6\), being \(n\) the number of sole bodies included between the heel and the metatarsophalangeal joint); \(T{\mathbb{\in }}{\mathbb{R}}\) the tendon tension; \({{\bf{F}}}\in {{\mathbb{R}}}^{3}\) the vector of contact forces between the foot and the ground; \({{\bf{p}}}\in {{\mathbb{R}}}^{1\times n+2}\) collects the pulley radii \({r}_{i}\); \(\delta\) and \(\sigma\) \({\mathbb{\in }}{\mathbb{R}}\) represent the constraints imposed by ground contact and by the tendon, respectively; \({{\bf{B}}}\in {{\mathbb{R}}}^{n+2\times n+2}\) collects the elastic terms and also depends on the sole bodies’ size, on the design of the frontal and rear arches, and on the body weight acting on the foot; \({{\bf{d}}}\in {{\mathbb{R}}}^{n+2\times 3}\) and \({{\bf{C}}}\in {{\mathbb{R}}}^{1\times n+2}\) depend on the length of the foot sole bodies; and \({{{\boldsymbol{m}}}}_{{{\bf{E}}}}\in {{\mathbb{R}}}^{n+2}\) depends on the sole bodies’ size, on the design of the frontal and rear arches, on the body weight acting on the foot, and on the stiffness of the heel springs.

Through this equation, an optimization procedure to select the design parameters can be used that maximizes the contact area over a set of shapes and forces encountered in standard walking conditions, as originally envisioned in our initial conceptualization of adaptive feet compared to rigid and fully compliant designs (Supplementary Fig. 18). A list of design parameters selected for the SoftFoot Pro described in this paper is presented at the end of Supplementary Note 3 (Mathematical Model).

Data collection and processing

The SoftFoot Pro was tested on two male individuals aged 34 y with unilateral amputation on the left side (from 25 y in CSI and 4 y in CSII). Their mean height was 1.85 m and their mean body mass was 87.5 kg. Both participants used a Triton by Ottobock as their prescribed prosthesis. They both gave their informed written consent to the testing protocol, which was approved by the local Ethics Committee of the Hannover Medical School and the Bioethical Committee of the University of Pisa. The two prosthetic users were fitted to the prototype by a certified prosthetist, and a 30-minute familiarization session preceded data collection in both case studies to allow the participants to gain some experience with the adaptive foot.

Participants were asked to walk at a self-selected speed on level ground, and then to repeat the task while stepping on an obstacle placed on a force plate. An arched-shaped (maximum height of 50 mm) and a rectangular-shaped (100 mm × 30 mm) obstacles were used (Supplementary Fig. 15 and further details in ref. 53), which were previously used in the bench testing of the SoftFoot48. Each task was performed 6 times in CSI and 5 times in CSII. Testing was conducted first using the participant’s own carbon fibre foot (Triton by Ottobock), then with the SoftFoot Pro. Comments by both studies’ participants about the prostheses’ performance were gathered.

In Case Study I, which consisted of a one-day assessment, tasks were performed donning the same pair of trekking shoes (model Quechua NH100) with both prostheses. Kinematic data were collected at 200 Hz through a 12-camera motion capture system (type MX, Vicon Motion Systems Ltd., Oxford, UK). Sixteen reflective passive markers were placed on the participant’s body according to the Helen Hayes marker set73. GRFs were captured at 1 kHz through two force plates (AMTI BP400600, Watertown, USA). Data were processed offline in Vicon Nexus v1.8.5, and filtered using a low-pass filter with a cut-off frequency of 12 Hz.

In Case Study II – a two-day assessment – the participant wore a pair of skate shoes with flat soles with both prostheses. Kinematic data were collected at 100 Hz through a 12-camera motion capture system (Vicon Motion Systems Ltd., Oxford, UK) and 39 reflective markers placed on the participant’s lower limbs and trunk, according to a modified Cleveland Clinic marker set74. The GRFs were collected at 1 kHz through two force plates (AMTI BMS6001200, Watertown, MA, USA), and processed in MATLAB (R2021a, The MathWorks, Inc., Natick, MA, USA) by using a zero-lag, fourth-order, low-pass Butterworth filter, with a cut-off frequency of 20 Hz. Data were then processed in OpenSim v. 4.3 to determine joint angles, torques, and powers (using the musculoskeletal model Gait2392), which were then further processed in MATLAB by using the aforementioned filter with a cut-off frequency of 15 Hz (20 Hz for powers).

Data are displayed normalized to stride duration (i.e. time between two consecutive heel strikes of the same limb) for both studies. The GRFs are shown as a percentage of the participant’s body weight (%BW), and joint torques and powers are normalized by body mass. Torques are shown as resistive internal joint torques generated by muscles and joint contact forces, which oppose the torques externally generated at each joint by the GRF75. Standard deviation shading for the contralateral sound limb ankle torques is displayed in CSII results to visually support the inferential statistical analysis in Supplementary Note 1.

Reference data from 12 unimpaired individuals walking on level ground and stepping on obstacles (10 repetitions per task, using the Oxford Foot Model and the Vicon Plug-in Gait lower body marker sets) are used for comparison in the sagittal plane. For the obstacle condition in CSII, contralateral sound limb data refer to the stride on flat ground immediately following the prosthetic limb’s stride on the obstacle. This allows direct comparison with level ground reference data, as the contralateral limb should ideally replicate the walking pattern on flat terrain during that stride. Reference data for the frontal plane during level walking in Supplementary Figs. 7–11 are from 20 unimpaired adult individuals walking at their natural speed52.

Plantar pressure was measured with the in-shoe system Intelligent Insoles Pro (XSensor, Calgary, Canada), positioned between the sole of a skate shoe and the human foot or the prosthesis (the latter was mounted at the bottom of the sole of customised walking boots to allow unimpaired subjects to walk on prostheses, Supplementary Fig. 12).

Statistical analyses

All analyses were conducted in MATLAB. Mean values (±1 SD) of joint angles, torques, and power were calculated across 6 valid (i.e. a clean foot strike on the force plate) gait cycles for CSI and 5 for CSII, except level walking with the participant’s own carbon foot in CSII, which had only 3 valid gait cycles.

For each task of CSII, a symmetry index (SI) between the prosthetic and contralateral sound limbs was calculated for each of the two peaks of the mean value of each GRF component (mean values across 5 gait cycles for obstacles, and 3 cycles for level walking) while using each prosthesis, as follows: \({{\rm{SI}}}\left(\%\right)=\frac{2({{{\rm{GRF}}}}_{{{\rm{sound}}}}-{{{\rm{GRF}}}}_{{{\rm{prosth}}}})}{({{{\rm{GRF}}}}_{{{\rm{sound}}}}+{{{\rm{GRF}}}}_{{{\rm{prosth}}}})}*100\)76, where \({{{\rm{GRF}}}}_{{{\rm{prosth}}}}={F}_{1,{{\rm{prosth}}}}\) or \({F}_{2,{{\rm{prosth}}}}\) and \({{{\rm{GRF}}}}_{{{\rm{sound}}}}={F}_{1,{{\rm{sound}}}}\) or \({F}_{2,{{\rm{sound}}}}\). \({F}_{1}\) and\(\,{F}_{2}\) are respectively the first and second peak values of the mean value of the GRF components for the prosthetic and contralateral sound limbs (Supplementary Fig. 2). Lower SI values indicate greater symmetry.

To assess the similarity between mean plantar pressure distributions, the root mean square error (RMSE) was computed between the pressure map of each prosthetic foot and that of the human foot on both flat ground and the obstacle. Calculations were restricted to the non-zero elements of the human foot’s mean pressure map on flat ground – the condition with the largest contact area – thus excluding non-contact regions. Mean pressure values were normalised by the subject’s body weight to account for the use of walking boots during prosthesis testing.

An inferential statistical analysis was performed to compare the torques of the contralateral joints when using the two prostheses, despite the small sample size. Since data were not normally distributed according to the Kolmogorov–Smirnov test, a Statistical Parametric Mapping (SPM) non-parametric paired two-tailed t-test was performed (\(\alpha=0.05\)) using the open-source SPM1d code (vM.0.4.12, www.spm1D.org) in MATLAB. The statistical non-parametric mapping \({SnPM}\{t\}\) and the null hypothesis rejection threshold at each point of the gait cycle were generated. Whenever the \({SnPM}\{t\}\) crossed the critical threshold, this indicated a statistically significant difference between the two torque patterns (\(p < 0.05\)). Results are reported in Supplementary Note 1.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.