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A Mode-Unified, Continuous, and Biomimetic Control Strategy of a Robotic Lower Limb Prosthesis

Hanjun Kim, Sixu Zhou, John Shim, Xinyuan Guo, Kinsey R. Herrin, Aaron J. Young

arXiv:2610.19183v1cs.RO

TL;DR

Mode-specific biomimetic prosthesis controllers commonly use separate parameterizations for walking, ramps, and stairs, while unified controllers do not generally prescribe continuous healthy joint biomechanics across terrain geometry. This paper unifies local biomechanics with RBF interpolation and implements them in a single FSM controller; experiments reproduced principal slope-dependent trends in knee measures and ankle kinematics.

  • Problem

    Existing controllers commonly use separate mode-specific parameterizations, while unified control approaches generally do not prescribe healthy joint biomechanics continuously across terrain geometry.

    Source: §I · pp. 1–2, §VI · p. 13

  • Method

    The framework unifies locally modeled biomechanics over terrain slope and gait phase, then uses bilateral sensing in a single FSM to modulate impedance continuously across locomotion conditions.

    Source: §I · p. 2

  • Results

    Knee-related measures agreed with the RBF-unified model at r^2 = 0.82–0.99, and ankle kinematics at r^2 = 0.78–0.96.

    Source: §V · p. 11, §VII · p. 16

  • Takeaways & Limitations

    The framework supports terrain-adaptive control across walking, ramps, and stairs without separately tuned impedance parameter sets for each locomotion mode.

    Source: §VII · p. 16

    Cross-study comparison is constrained by differences in participant groups, experimental protocols, and prosthesis hardware.

    Source: §VI · p. 14

Abstract

from arXiv · show

Existing biomimetic lower-limb prosthesis controllers are commonly designed for discrete locomotion modes, requiring separate parameterizations for level walking, ramps, and stairs. We present a mode-unified prosthesis control framework that represents knee and ankle biomechanics continuously as functions of terrain slope and gait phase across those locomotion conditions. Locally optimized ascent and descent polynomial models were unified using radial basis function (RBF) interpolation, preserving the accuracy of the partitioned models while outperforming a global polynomial representation. The resulting biomechanics were transformed into continuous and slope-dependent impedance parameters and implemented within a single finite-state-machine (FSM) controller using bilateral sensing for gait-state estimation. Experiments with 10 individuals with transfemoral amputation demonstrated terrain-adaptive locomotion from level walking through ramps and stairs up to 35 degrees, including 13 degree ramp and 15 degree stair conditions absent from the underlying able-bodied (AB) dataset. Experimental results reproduced the principal slope-dependent biomechanical trends predicted by the unified model, with high agreement for knee-related measures (r-square = 0.82 - 0.99) and ankle kinematics (r-square= 0.78 - 0.96). These findings demonstrated that unified biomechanical parameterization enables a prosthesis control architecture across diverse terrain conditions while preserving key features of AB biomechanics without requiring independently tuned impedance parameter sets for each locomotion mode.

I. INTRODUCTION

Existing prosthesis controllers often separate locomotion modes, while continuous gait-phase estimates alone do not remove mode-specific controller structures. This work proposes continuous slope- and phase-dependent biomechanics and a unified controller, evaluated across terrain conditions that include slopes absent from the reference dataset.

I. INTRODUCTION

  • Existing approaches typically address biomechanical fidelity within separate domains or unified control across tasks, leaving their simultaneous achievement largely unaddressed.Discrete, finite datasets can require extra modeling for new environments, while mode-specific FSM transitions can increase tuning complexity and limit generalizability.Source: §I · pp. 1–2
  • The proposed framework represents lower-limb biomechanics continuously over terrain slope and gait phase, then converts them into slope-dependent impedance parameters for a single FSM using bilateral sensing.The controller was evaluated on intermediate ramp and stair conditions absent from the able-bodied reference dataset.Source: §I · p. 2

A. Locomotion Biomechanics Dataset

  • Knee and ankle kinematics and moments from healthy individuals were drawn from level walking, ramp, and stair conditions and segmented into stance and swing phases.The dataset included ramps at ±5°, 7°, 9°, and 11° and stairs at ±20°, 24°, 30°, and 35°; trajectories were phase-normalized to 101 samples.Source: A. Locomotion Biomechanics Dataset · p. 3

B. Determining the Polynomial Fitting Domain

The method fits local ascent and descent polynomial models and unifies them with Gaussian RBF interpolation over terrain slope and gait phase. It selects full-ascent and full-descent fits to retain local accuracy while creating continuous biomechanics surfaces.

B. Determining the Polynomial Fitting Domain

  • Full-ascent and full-descent polynomial models were selected for RBF unification because they achieved the best reconstruction performance among the evaluated fitting configurations.Leave-ramp-out models retained reasonable reconstruction of omitted ramps, whereas leave-stair-out models failed to extrapolate to stairs.Source: B. Determining the Polynomial Fitting… · p. 3

C. RBF-Interpolation for Mode Unification

  • Gaussian RBF interpolation unifies the local ascent and descent models with a smooth transition at their shared level-walking condition while preserving their local biomechanical characteristics.The stacked models duplicate slope-zero coordinates; regularization was introduced because those duplicates make the kernel system singular or ill-conditioned.Source: C. RBF-Interpolation for Mode… · pp. 3–4
  • The RBF representation is evaluated across the unified slope-phase domain to produce continuous, mode-unified biomechanics surfaces.The resulting surfaces form the basis for subsequent impedance parameterization.Source: C. RBF-Interpolation for Mode… · pp. 4–5

D. Validation of the Unified Biomechanics Representation

The RBF-unified representation retained the reconstruction accuracy of local polynomial fits while improving on a global polynomial model. Its continuous slope-phase trajectories closely reproduced the underlying able-bodied biomechanics.

D. Validation of the Unified Biomechanics Representation

  • The leave-ramp-out fits retained reasonable reconstruction of omitted ramps, but leave-stair-out fits failed to extrapolate to stair locomotion.The full-ascent and full-descent models achieved the best reconstruction performance and were selected for unification.Source: D. Validation of the Unified… · p. 5
  • RBF-unified models consistently achieved lower mean absolute errors than global polynomials while preserving partitioned-polynomial accuracy; the only significant difference was lower ankle swing-angle MAE during descent.The comparison covered kinematics and kinetics across evaluated terrain slopes.Source: D. Validation of the Unified… · p. 5
  • The RBF-unified models produced continuous slope-phase trajectories that closely reproduced the underlying able-bodied biomechanics.These unified biomechanics were used as the foundation for impedance parameterization.Source: D. Validation of the Unified… · p. 5

III. MODE-UNIFIED IMPEDANCE PARAMETERS

The section turns continuous slope- and phase-dependent biomechanics into impedance parameters for a unified controller. It prescribes equilibrium-angle trajectories, then identifies stiffness and damping under design constraints.

III. MODE-UNIFIED IMPEDANCE PARAMETERS

  • Equilibrium angles provide the biomechanical reference, while stiffness and damping are identified afterward under design constraints rather than fitting all three impedance parameters simultaneously.This extends the parameterization to a continuous terrain-slope domain.Source: A. Biomechanically Inspired… · p. 5, §III · p. 5

A. Biomechanically Inspired Equilibrium Angle Trajectory

  • The support angle is the joint angle at the mid-to-late-stance minimum of the biological moment, with its timing relative to the late-stance peak distinguishing two cases.Case I occurs in the knee during level walking and ascent; Case II occurs in the knee during descent and in the ankle across evaluated environments.Source: A. Biomechanically Inspired… · p. 5, Figure 4 · p. 5
  • The stance equilibrium angle moves from heel contact toward the support angle during weight acceptance, holds it during single support, then shifts toward toe-off during unloading.These three regions correspond approximately to 25%, sustained single support, and around 75% of stance, respectively.Source: A. Biomechanically Inspired… · p. 6, Figure 5 · p. 6
  • During descending knee locomotion, a slope-dependent P-value lets the equilibrium angle follow measured knee angle more closely as descent steepens before converging to the support angle.The equilibrium angle then remains fixed through single support and transitions toward toe-off during unloading.Source: A. Biomechanically Inspired… · p. 6
  • The ankle support angle is capped at 10° dorsiflexion to accommodate prosthesis constraints while preserving its slope-dependent trend.During weight acceptance, the ankle equilibrium angle converges toward the support angle to provide controlled plantarflexion yielding.Source: A. Biomechanically Inspired… · p. 6

B. Stance Phase Parameterization

Stance stiffness and damping are represented as continuous functions of slope and phase, then fitted by sequential constrained least squares to the unified biomechanics and equilibrium-angle trajectories.

B. Stance Phase Parameterization

  • Stiffness and damping increase during weight acceptance, remain approximately constant through single support, and stay constant or decrease during unloading.The same three-region structure is used for both parameters.Source: B. Stance Phase Parameterization · p. 7
  • Fourth-order polynomials of normalized stance phase represent stiffness and damping at each terrain slope.Their phase derivatives support constraints on impedance progression.Source: B. Stance Phase Parameterization · pp. 7–8
  • Constrained least-squares optimization identifies early-stance parameters first, then initializes late stance from the terminal early-stance solution before combining the results into continuous slope-dependent surfaces.Early stance covers heel contact to p = 0.49; late stance covers the subsequent support and unloading phases.Source: B. Stance Phase Parameterization · p. 7
  • Slope-dependent upper bounds and constant empirical lower bounds constrain stiffness and damping throughout stance.The upper envelopes use arctangent functions connecting impedance parameters from validated 35° stair-ascent and stair-descent controllers.Source: B. Stance Phase Parameterization · p. 7
  • Equality and bound constraints anchor the early- and late-stance trajectories and prevent late-stance impedance from exceeding the support level established during early stance.Late stance is initialized from the terminal early-stance solution and preserves support-level impedance until unloading.Source: B. Stance Phase Parameterization · pp. 7–8

𝑟𝑟2 VALUES OF RECONSTRUCTED MOMENT MODELS

Moment reconstruction closely matched target able-bodied trajectories for level walking and ascent, while descending models showed lower early-stance accuracy but stronger late-stance agreement.

𝑟𝑟2 VALUES OF RECONSTRUCTED MOMENT MODELS

  • For level walking and ascent, reconstructed moments yielded overall r^2 values of 0.94 ± 0.04 for the knee and 0.76 ± 0.15 for the ankle.High early- and late-stance accuracies indicated preservation of primary biomechanical characteristics.Source: 𝑟𝑟2 VALUES OF RECONSTRUCTED MOMENT… · p. 8
  • During descent, early-stance r^2 values were 0.41 ± 0.37 for the knee and 0.26 ± 0.17 for the ankle, while late-stance values were 0.75 ± 0.21 and 0.91 ± 0.05, respectively.The lower early-stance accuracy reflects the design choice not to reproduce the initial weight-acceptance moment peak.Source: 𝑟𝑟2 VALUES OF RECONSTRUCTED MOMENT… · p. 8
  • The descending strategy prioritizes reproducing support and unloading dynamics despite reduced early-stance reconstruction performance.The support-angle-based yielding strategy intentionally omits the initial stance moment peak during weight acceptance.Source: 𝑟𝑟2 VALUES OF RECONSTRUCTED MOMENT… · p. 8

IV. EXPERIMENTAL METHODS

The controller was implemented on a powered knee-ankle prosthesis with bilateral sensing, onboard computation, and synchronized motion-capture measurements.

IV. EXPERIMENTAL METHODS

B. Controller Implementation

A shared four-state FSM uses bilateral limb progression to detect gait events across locomotion conditions. IMU-based limb geometry supports transition detection, while slope-dependent impedance parameters vary continuously through the gait cycle.

B. Controller Implementation

  • The controller uses one four-state FSM across locomotion modes, with T1 triggered when the intact foot advances beyond the prosthetic foot during stance under sufficient prosthetic load.Transitions T2–T4 follow conventional prosthesis-control logic.Source: B. Controller Implementation · p. 9
  • Wearable IMU orientations and subject-specific segment lengths reconstruct intact and prosthetic ankle positions from hip position and limb-segment directions.The relative ankle position and prosthetic forward direction support a limb-crossing metric used for T1 detection.Source: B. Controller Implementation · p. 10
  • Stance stiffness and damping are load-reactively interpolated, while equilibrium angles follow prescribed or proportional-yielding strategies; swing uses constant stiffness and damping with slope-dependent angles.The implementation also stores normalized vertical load at the early-to-late stance transition as the unloading reference.Source: B. Controller Implementation · p. 10

C. Experimental Protocol

Experiments with ten people with unilateral transfemoral amputation tested the unified controller across level walking, ramps, and stairs, including two terrain conditions absent from the able-bodied reference data. The controller reproduced slope-dependent biomechanical trends, with stronger agreement for knee measures and ankle kinematics than for ankle stance torque.

C. Experimental Protocol

  • Ten participants with unilateral transfemoral amputation tested level walking and ramps at 0–13° and stairs at 15–35°; selected swing parameters and descending heel-contact angles were adjusted for comfort and stability.Testing used treadmill speeds of 0.4–0.5 m/s for level and ramp walking; the 13° ramp and 15° stair conditions were excluded from the able-bodied reference data.Source: C. Experimental Protocol · p. 10

D. Statistical Analysis

  • Terrain slopes were weighted by the interval each represented when quantifying agreement with model predictions and able-bodied reference data.Source: D. Statistical Analysis · p. 10

V. RESULTS

  • Smooth trajectories were observed on the 13° ramp and 15° stair, both absent from the able-bodied dataset used to construct the models.Those intermediate conditions were completed by 9 and 6 participants, respectively.Source: §V · p. 10, Figure 8 · p. 11
  • The controller preserved continuous slope-dependent adaptation: ascent increased knee flexion and ankle dorsiflexion, while descent increased knee yielding and late-stance ankle dorsiflexion.Steeper terrain also produced larger swing flexion and clearance angles; descent increased knee toe-off yielding while ankle toe-off remained relatively constant.Source: §V · pp. 10–11
  • Knee-related metrics agreed with the RBF-unified model at r² = 0.82–0.99 and ankle kinematic metrics at r² = 0.78–0.96, while ankle stance-moment peaks had r² = 0.08 in ascent and 0.25 in descent.Agreement with the able-bodied reference was also high for knee metrics (r² = 0.75–0.99) and ankle kinematics (r² = 0.85–0.97); ankle stance-torque agreement was r² = 0.47 in ascent and 0.51 in descent.Source: §V · p. 11, Figure 9 · p. 12
  • Across slopes, ankle stance torque under-realization coincided with insufficient late-stance dorsiflexion, whereas knee peak stance torques reached 101.4% and 79.3% of model values in ascent and descent.Ankle peak stance torques reached 74.8% and 56.2% of model values in ascent and descent, respectively.Source: §V · p. 13

VI. DISCUSSION

The unified framework preserved the locally optimized biomechanical models while supporting continuous terrain-adaptive control, and experiments reproduced principal slope-dependent trends. Its scope is qualified by ankle-kinetic discrepancies, implementation trade-offs, and limits in terrain and speed coverage.

VI. DISCUSSION

  • RBF-unified biomechanics preserved locally optimized ascent and descent reconstruction accuracy and outperformed the global polynomial representation; ten participants reproduced principal trends, except for ankle stance kinetics.The ankle stance torque trends showed lower agreement with both the unified model and the able-bodied reference.Source: §VI · p. 13
  • Continuous terrain-slope and gait-phase parameterization enabled testing at 13° ramps and 15° stairs absent from the reference data, but transition-region outputs remain controller priors, not confirmed able-bodied biomechanics.The formulation also reduces reliance on mode-specific parameter sets and additional FSM transitions while preserving continuous scaling across the modeled domain.Source: §VI · p. 13
  • Impedance design prioritized prosthesis function over exact biomechanical replication; bilateral limb-progression transitions can start late stance before sufficient dorsiflexion, limiting ankle torque.The design used constrained impedance parameters and functional landmarks; during steep stair descent, modeled dorsiflexion can exceed the prosthesis range.Source: §VI · pp. 13–14
  • Experimental knee trajectories showed terminal-swing plateaus before initial contact, which may reflect users preparing for stable contact rather than a limitation of the continuous representation.Prior work cited in the discussion reports latency between full prosthetic knee extension and initial contact.Source: §VI · p. 14
  • The bilateral sensing architecture supported reliable gait transitions across evaluated terrains, but its sagittal-plane limb geometry omits out-of-plane pelvic motion and hip tilt.The computed geometry is intended as a robust gait-state variable, not an anatomically exact estimate of bilateral limb configuration.Source: §VI · p. 14
  • The comparison with a prior hand-tuned controller is descriptive, not a direct test of controller superiority, because cohorts, protocols, and hardware differed.The earlier prosthesis had ±15° ankle motion, versus ±30° in the proposed study; Figure 10 compares common terrain conditions.Source: §VI · p. 14, Figure 10 · p. 15
  • During stair ascent, prosthetic-side vGRF was greater throughout stance while intact-side loading was comparatively similar; descent profiles were similar, and stance vGRF alone does not establish functional improvement.Figure 10B presents weight- and stance-phase-normalized vGRF profiles for prosthetic and intact sides during stair ascent and descent.Source: §VI · pp. 15–16, Figure 10 · p. 15
  • The framework assumes terrain slope is supplied, is based on able-bodied data collected at speeds up to 0.6 m/s, and blends ramp and stair datasets across a transition region.Slope estimation is needed for fully autonomous operation; the transition-region interpolation should not be treated as true able-bodied biomechanics.Source: §VI · p. 16

VII. CONCLUSION

The RBF-unified models preserved locally optimized biomechanical accuracy while enabling continuous impedance parameterization across level walking, ramps, and stairs. Experiments with ten prosthesis users demonstrated terrain adaptation, including conditions absent from the reference able-bodied dataset.

VII. CONCLUSION

  • r-square = 0.82 - 0.99 for knee-related measures and 0.78 - 0.96 for ankle kinematics, with ankle stance torque less accurately reproduced.The controller reproduced principal slope-dependent biomechanical trends in experiments with ten prosthesis users, including 13 ° ramp and 15 ° stair conditions absent from the reference AB dataset.Source: §VII · p. 16
  • The RBF-unified models preserved the accuracy of locally optimized biomechanics while enabling continuous impedance parameterization across level walking, ramps, and stairs.The framework reduces mode-specific tuning without requiring separately parameterized controllers for each locomotion mode.Source: §VII · p. 16

APPENDIX – COMPARISON WITH PREVIOUS STUDY

Compared with a previously reported mode-specific controller, the unified controller had significantly lower MAEs in six of 24 evaluated comparisons. Stair-ascent prosthetic-side loading was higher, while stair-descent loading remained comparable between controllers.

APPENDIX – COMPARISON WITH PREVIOUS STUDY

  • Six of 24 comparisons had significantly lower MAEs with the unified controller, including knee swing-clearance MAE during ramp ascent decreasing from 27.1 ° to 6.6 °.Other significant decreases included ankle heel-contact MAE from 14.2 ° to 2.2 ° during stair ascent and from 19.3 ° to 5.8 ° during stair descent.Source: APPENDIX – COMPARISON WITH PREVIOUS… · p. 16
  • Ankle peak stance torque showed no consistent improvement across terrain conditions, in line with comparatively weaker reproduction of ankle kinetics.Several other outcomes had lower mean MAEs without statistically significant between-group differences.Source: APPENDIX – COMPARISON WITH PREVIOUS… · p. 16
  • During stair descent, prosthetic- and intact-side loading remained comparable between controllers; during stair ascent, prosthetic-side vGRF was higher with the unified controller.The visual comparison was restricted to matched overground stair conditions.Source: APPENDIX – COMPARISON WITH PREVIOUS… · p. 16
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