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Hybrid LSTM-UKF Framework: Ankle Angle and Ground Reaction Force Estimation

Mundla Narasimhappa, Praveen Kumar

TL;DR

This work tackles accurate, real-time estimation of ankle angle and GRF during gait by integrating temporal learning with nonlinear state estimation. The authors develop a hybrid LSTM–UKF framework that uses LSTM to extract temporal features from multimodal sensor inputs and UKF to refine state estimates, yielding improved robustness over individual LSTM or UKF models. Quantitative results show up to an 18.6% RMSE reduction for GRF at 3 km/h and up to a 22.4% reduction in ankle-angle RMSE at 1 km/h, demonstrating strong performance across subjects and walking conditions. The approach, implemented in Python with TensorFlow/Keras and validated on a 13-subject dataset, has direct implications for wearable-assisted gait devices and prosthetics control, enabling more reliable, physiologically grounded state estimation in variable environments.

Abstract

Accurate prediction of joint kinematics and kinetics is essential for advancing gait analysis and developing intelligent assistive systems such as prosthetics and exoskeletons. This study presents a hybrid LSTM-UKF framework for estimating ankle angle and ground reaction force (GRF) across varying walking speeds. A multimodal sensor fusion strategy integrates force plate data, knee angle, and GRF signals to enrich biomechanical context. Model performance was evaluated using RMSE and $R^2$ under subject-specific validation. The LSTM-UKF consistently outperformed standalone LSTM and UKF models, achieving up to 18.6\% lower RMSE for GRF prediction at 3 km/h. Additionally, UKF integration improved robustness, reducing ankle angle RMSE by up to 22.4\% compared to UKF alone at 1 km/h. These results underscore the effectiveness of hybrid architectures for reliable gait prediction across subjects and walking conditions.

Hybrid LSTM-UKF Framework: Ankle Angle and Ground Reaction Force Estimation

TL;DR

This work tackles accurate, real-time estimation of ankle angle and GRF during gait by integrating temporal learning with nonlinear state estimation. The authors develop a hybrid LSTM–UKF framework that uses LSTM to extract temporal features from multimodal sensor inputs and UKF to refine state estimates, yielding improved robustness over individual LSTM or UKF models. Quantitative results show up to an 18.6% RMSE reduction for GRF at 3 km/h and up to a 22.4% reduction in ankle-angle RMSE at 1 km/h, demonstrating strong performance across subjects and walking conditions. The approach, implemented in Python with TensorFlow/Keras and validated on a 13-subject dataset, has direct implications for wearable-assisted gait devices and prosthetics control, enabling more reliable, physiologically grounded state estimation in variable environments.

Abstract

Accurate prediction of joint kinematics and kinetics is essential for advancing gait analysis and developing intelligent assistive systems such as prosthetics and exoskeletons. This study presents a hybrid LSTM-UKF framework for estimating ankle angle and ground reaction force (GRF) across varying walking speeds. A multimodal sensor fusion strategy integrates force plate data, knee angle, and GRF signals to enrich biomechanical context. Model performance was evaluated using RMSE and under subject-specific validation. The LSTM-UKF consistently outperformed standalone LSTM and UKF models, achieving up to 18.6\% lower RMSE for GRF prediction at 3 km/h. Additionally, UKF integration improved robustness, reducing ankle angle RMSE by up to 22.4\% compared to UKF alone at 1 km/h. These results underscore the effectiveness of hybrid architectures for reliable gait prediction across subjects and walking conditions.
Paper Structure (18 sections, 24 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 18 sections, 24 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Ankle--Foot Prosthesis Simulated Model
  4. Mathematical Equations
  5. State-Space Representation
  6. Sensor Simulation
  7. Ground Reaction Force Torque Model
  8. Combined state-space formulation and GRF estimation
  9. Ankle and Ground Force estimations
  10. UKF-Based State Estimation
  11. LSTM-Based Modeling Framework
  12. Proposed Hybrid LSTM- UKF based Estimation
  13. Loss Function
  14. Materials and Methods
  15. Validation Framework and Input Configuration
  16. ...and 3 more sections

Figures (4)

  • Figure 1: GRF estimation comparison across models during running at 2.5 m/s Zhang2021.
  • Figure 2: Ankle angle and GRF estimation using Hybrid LSTM and UKF based approach.
  • Figure 3: Ankel angle estimation comparison across models during running at 2.5 m/s.
  • Figure 4: GRF estimation comparison across models during running at 2.5 m/s.