Simulation of Adaptive Running with Flexible Sports Prosthesis using Reinforcement Learning of Hybrid-link System

Yuta Shimane; Ko Yamamoto

cs.ROApr 10, 2026

Simulation of Adaptive Running with Flexible Sports Prosthesis using Reinforcement Learning of Hybrid-link System

Authors: Yuta Shimane, Ko Yamamoto

Organizations: Department of Biological Sciences, The University of Tokyo, Bunkyo-ku, Tokyo, 113-0033, Japan · Institute of Systems and Information Engineering, University of Tsukuba, Ibaraki, 305-8573, Japan

Abstract

This study proposes a reinforcement learning-based framework for adaptive running motion simulation in a unilateral transtibial amputee using a hybrid-link system that incorporates the flexibility of a leaf-spring-type sports prosthesis. The design and selection of sports prostheses typically rely on trial and error. A comprehensive whole-body dynamics analysis that accounts for interactions between human motion and prosthetic deformation can provide valuable insights for user-specific design and selection. The proposed hybrid-link system enables such analysis by integrating a Piece-wise Constant Strain (PCS) model to represent prosthetic flexibility. Based on this system, the simulation methodology generates whole-body dynamic motions of a unilateral transtibial amputee using a reinforcement learning approach. This framework integrates imitation learning based on motion capture data with accurate computation of prosthetic dynamics. Running motions are simulated under multiple virtual prosthetic stiffness conditions, and the corresponding metabolic cost of transport (COT) obtained from these simulations is analyzed. The results suggest that variations in prosthetic stiffness influence running dynamics and performance, and that COT is consistent with values reported in prior study. Our findings demonstrate the potential of the proposed approach for simulation and analysis under virtual conditions that differ from real-world conditions.

Figures & tables

Fig. 1: Overview of the prosthesis integrated skeletal model and motion measurement: (a) Measurement setup using optical motion capture. (b) Integrated prosthetic skeletal model using the hybrid-link system. The model has 33 DOFs including 9 DOFs for the skeleton and 18 DOFs for the prosthesis. (c) Leaf-spring-type sports prosthesis. (d) PCS model for flexible rod. (e) PCS model of the prosthesis comprising 6 segments.

Related works	Whole-body computation	Body dim.	Pros. dim.	Pros. Modeling	Key feature
[ 8 , 9 ]	–	–	3D	FEM	High fidelity; expensive
[ 6 , 3 ]	ID	3D	2D	Rigid-link	Efficient; no deform
[ 13 ]	ID	3D	3D	PCS	Deform; no simulation
[ 15 ]	FD+PD	2D	2D	Flat spring	Efficient; limited control
[ 2 ]	FD+SLIP	3D	2D	Rigid-link	Generative; simplified
[16]-[18]	FD+RL	3D	–	–	Learning-based control

TABLE I: Comparison of related works

	$w_{q}$	$w_{v}$	$w_{e}$	$w_{0}$	$\beta_{\rm q}$	$\beta_{\rm v}$	$\beta_{\rm e}$	$\beta_{0,1}$	$\beta_{0,2}$
Value	1.0	1.0	1.0	0.1	2.0	0.03	40.0	10.0	0.1

TABLE II: Values of Weight and Coefficient

Fig. 4: Learning return on prosthetic walking, running, sprinting: (Left) Return in the pre-training using a rigid-link system. (Right) Return in fine-tuning using the hybrid-link system that considers the prosthesis’s deformation.

Fig. 5: Running simulation results: (a) mean angles of hip and knee joints, Left: intact side), (b) mean prosthetic strain of the PCS model, (c) mean GRFs in the horizontal: braking and vertical: body-support directions with shaded bands indicating the standard deviations.

Joint angle RMSE [%] CI [deg]	Hip (L) 6.0 1.84	Hip (R) 7.8 2.10	Knee (L) 7.1 2.16	Knee (R) 9.5 2.63	Ankle (L) 13.7 2.00	All 9.2
Strain (Stance) RMSE [%] CI [1/m]	Seg.1 8.0 0.031	Seg.2 6.1 0.068	Seg.3 22.8 0.118	Seg.4 22.3 0.103	Seg.5 11.6 0.030	All 16.1
Force (Stance) RMSE [%] CI [kN]	Fx 7.5 0.04	Fy 4.5 0.05	Fz 16.7 0.25			All 10.9

TABLE III: RMSE and peak CI half-width for joint angles, strain, and GRF.

Fig. 6: Simulation results under different stiffness conditions: (a) angle of joints, (b) prosthetic strain of the PCS model, (c) average GRF, and (d) mechanical cost.

Fig. 7: Metabolic costs of transport obtained from running simulations with different prosthetic stiffnesses are shown, with error bars indicating values reported in [ 1 ] .

	Rigid-body	Hybrid-link
Average propulsion force [N]	92.9	187.5
Contact time [s]	0.2	0.26
Time to peak GRF [s]	0.065	0.13

TABLE IV: Comparison of GRF between the Rigid and Hybrid-links on Running Simulation

Fig. 8: Return and episode length under variation of the stiffness parameter

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May 13, 2026J/K move · Enter open · S save

Dynamics Computation of Soft-Rigid Hybrid-Link System and Its Application to Motion Analysis of an Athlete Wearing Sport Prosthesis

Sunghee Kim, Yuta Shimane, Taiki Ishigaki, Ko Yamamoto

Department of Mechano-Informatics, University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo, Japan · Research Institute for Science and Technology, Tokyo University of Science, Katsushika-ku, Tokyo, Japan

Musculoskeletal Modeling Inverse Dynamics

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This paper presents a motion analysis framework for an athlete wearing sport-specific flexible prosthesis based on the soft-rigid hybrid-link system. Such a motion analysis is a challenging problem because we need to consider the interaction force between the rigid human skeleton system and a flexible prosthesis. However, most of human musculoskeletal models are based on the computation framework of a rigid-body multi-link system. Recently in soft robotics research field, fast and efficient modeling methods were developed for a flexible rod deformation, which allows us to build a hybrid-link system that integrates rigid-link and soft-bodies in a unified formulation. We apply inverse kinematics of the hybrid-link system to motion reconstruction from a motion captured data, and also present the estimation of the joint torques and ground reaction force by inverse dynamics. Through a human subject experiment, we show that the inverse dynamics achieved approximately 12% error on the ground reaction force estimation. Furthermore, we provide the muscle force estimation considering muscle amputation and interaction force with the prosthesis leg deformation.

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