What is the effect of running-specific prostheses on long jumps? Optimization-based prediction and analysis using biomechanical models
Authors: Anna Lena Emonds, Johannes Funken, Wolfgang Potthast, Katja Mombaur
Organizations: Institute of Computer Engineering, Heidelberg University, 69120 Heidelberg, Germany · Institute of Biomechanics and Orthopaedics, German Sport University Cologne, 50933 Köln, Germany · Institute for Anthropomatics and Robotics, Optimization and Biomechanics for Human-Centred Robotics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany · Canada Excellence Research Chair in Human-Centred Robotics and Machine Intelligence, Systems Design Engineering & Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, N2L 3G1, Canada
Long jumpers with below the knee amputation (BKA) that take off from their running-specific prosthesis (RSP) improved performances significantly over the last years. The long jump biomechanics differs compared to athletes without BKA and the question arises whether the spring-like properties of the RSP facilitate achieving long jumping distances. The aim of this work is to propose a long jump model for athletes with and without BKA, to evaluate it and to apply it for comparing long jump motions with and without RSP. We establish rigid multi-body system models of one athlete with and one athlete without below the knee amputation (BKA). Long jump motions are computed by solving a specific optimal control problem (OCP) with constraints enforcing a physically correct dynamics, both for motion reconstruction or motion synthesis. With the proposed long jump model, we are able to compute realistic long jump motions. We discuss the causes of differences in measured long jumps and show directions for eliminating them. For both athletes, the synthesized solutions reveal potential for performance improvement. The jumping distance of the athlete without BKA is 64cm (6.9%) longer than the one of the athlete with BKA in the synthesized solutions.
Figures & tables
Figure 1: Overview of the study design: The computations are divided into two steps, the first reconstructing the motion dynamics based on motion capture recordings and the second predicting long jump motions based on a combination of optimization criteria. The solutions are then used to conduct two distinct comparisons, one between the reconstructed and the optimized solutions and the other between the athletes with and without BKA.
Figure 2: Subject-specific models of a non-amputee and an amputee athlete: Visualization and degrees of freedom. The coordinate system is aligned such that the x-axis points in the forward direction of the sprinting motion. Movements to the right and left are along the y-axis, and movements up and down are along the z-axis.
Figure 3: Phase description of the investigated long jump motions for a non-amputee athlete (top) and an athlete with below the knee amputation (bottom)
Figure 4: Animated sequences of the optimal control problem generated long jump motions. The upper row shows the reconstructed and the lower row the synthesized motion. The dashed vertical line indicates the take-off position and motions are aligned to it. As immediately visible, the motion capture recordings for the reconstruction end during the jump.
Figure 5: Anterior-posterior, mediolateral and vertical ground reaction forces during take-off for the reconstructedsilutions of the athlete without (a/blue) and with (b/red) BKA during the take-off. The grey lines show the measured raw force plate data and the colored lines the reconstructed forces. The time on the x-axis is given in percent of the stance time.
Figure 6: Joint torques of the stance leg (right/affected leg) during the take-off for the reconstructed solutions of the athlete with (red) and the athlete without (blue) BKA. The time on the x-axis is given in percent of the stance time and the joint torques are normalized by body mass.
Figure 7: The diagrams show the movement of the CoM in horizontal and vertical directions for the reconstructed (dashed lines) and synthesized (solid lines) long jump solutions for the athlete with (red) and without (blue) BKA. Phase durations are normalized individually per phase and the abbreviations ‘F’ and ‘C’ denote flight and contact phases (cf. Figure 3 ).
Figure 8: Ground reaction forces in horizontal and vertical direction for the reconstructed (dashed lines) and synthesized (solid lines) long jump solutions for the athletes with (red) and without (blue) BKA. Each force is normalized by the body mass of the individual athlete. Phase durations are normalized individually per phase and the abbreviations ‘F’ and ‘C’ denote flight and contact phases (cf. Figure 3 ).
Figure 9: Joint angles of the respective contact leg for the three contact phases of the reconstructed (dashed lines) and synthesized (solid lines) long jump solutions for the athletes with (red) and without (blue) BKA. Phase durations are normalized to stance time.
Figure 10: Joint torques of the respective contact leg for the three contact phases of the reconstructed (dashed lines) and synthesized (solid lines) long jump solutions for the athletes with (red) and without (blue) BKA. Phase durations are normalized to stance time. Each torque is normalized by the body mass of the individual athlete. The passively generated joint torque of the prosthetic ankle is computed via Eq. ( 1 ).
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.
Yuta Shimane, Ko Yamamoto
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
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.
Hanjun Kim, Sixu Zhou, John Shim +3
Woodruff School of Mechanical Engineering, Georgia Tech, Atlanta, GA 30332-0405 USA · Woodruff School of Mechanical Engineering, Georgia Tech, Atlanta, GA 30332-0405 and with the Institute for Robotics and Intelligent Machines, Georgia Tech, Atlanta, GA 30332-0405 USA
Personalization of impedance controllers for powered prosthetic legs is critical to accommodating individual gait biomechanics but remains challenging. Existing methods rely on time-intensive human-in-the-loop exploration and/or constrain optimization to low-dimensional, single-joint parameter subspaces. Sim-to-real transfer has enabled high-dimensional locomotion control for legged robots, but in assistive device control the human partner remains un-modelable. We present a replay-constrained simulation framework: a MuJoCo-based simulator reproduces prosthetic knee-ankle dynamics while replaying recorded hip kinematics and feedback-based ground reaction forces from individual walking data, bypassing the need to model complex human neuromuscular control mechanisms. We demonstrate the framework with a deep reinforcement learning policy that personalizes phase-dependent stiffness, damping, and equilibrium angle at both joints simultaneously, maximizing a biomimicry-based reward computed solely from onboard prosthesis measurements. Experiments with three participants with transfemoral amputation during level-ground walking at 0.8~m/s demonstrate strong simulation-to-hardware predictive validity (Pearson r=0.96--0.997). The best-performing policy on hardware was consistently predicted within the top five simulation policies for all participants. The learned controllers improved overall biomimicry rewards by 42--59% relative to the unpersonalized baseline. The framework supports scalable high-dimensional personalization of powered prosthetic legs and is amenable to extension to higher-dimensional controller parameterizations such as neural-network controllers.
Duong Le, Ryan Posh, Shihao Cheng +2
College of Engineering, University of Michigan, Ann Arbor, MI 48109, USA