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Closing the realism gap in physics-based gait simulations with a learned state prior
Markus Gambietz, Zhihao Zhao, Theodoros Balougias, Xiang Wang, Anne D. Koelewijn
TL;DR
Predictive movement simulations are useful for studying unmeasured conditions, but their realism and dependence on condition-specific data remain challenges. This paper adds a learned state prior to physics-based simulations; the resulting gait matches measured walking and running across speeds and supports hypothesis testing and sparse-marker reconstruction.
Problem
Predictive simulations can study unmeasured movement conditions, but existing physics-based methods have realism limitations and reference tracking requires data for each new condition.
Source: §1 · p. 1Method
The authors train a probabilistic state prior on gait data and use it as an objective term in physics-based predictive simulations.
Source: §1 · p. 2Results
Takeaways & Limitations
The framework supports hypothesis testing under altered objectives, body models, or environmental constraints and is directly applicable to healthy-gait simulations.
Source: §3 · pp. 7, 10The shoe simulations omit the foot-shoe interface and rely on a ground-contact model that can overestimate energy loss, so their estimated metabolic-cost reduction may be overstated.
Source: §3 · p. 8
Abstract
from arXiv · showhide
Predictive simulation of human movement is a promising tool for studying ``what-if'' scenarios in human movement and its underlying motor control, yet its realism is often limited. To address this gap, we incorporate a learned state prior that is trained on a large-scale dataset of human gait kinematics and external forces into predictive simulations. Resulting gait simulations yield kinematics and kinetics across diverse walking and running speeds that better match experimental data than current physics-based simulations, achieving accuracy comparable to data-driven models that reproduce learned data. Furthermore, our method enables robust hypothesis testing by demonstrating how varying optimality assumptions, muscle weakness, and footwear choices influence predicted gait. We also show that this prior generalizes well beyond its training data, successfully reconstructing full-body kinematics for curved running and cutting maneuvers from sparse marker sets. Ultimately, these results suggest that state priors should be broadly integrated into predictive simulations.
1 Introduction
Predictive simulations can test unmeasured movement scenarios, but hand-designed regularizers and reference tracking limit realism or require data for each condition. The paper integrates a learned state prior into physics-constrained optimal control, producing human-like states without prescribing a specific trajectory, speed, or gait mode.
1 Introduction
- Hand-designed regularizers do not yield realistic motion across speeds and gait modes, while reference tracking requires measurements for every new condition.Data-driven models generate realistic motion but condition it on recorded patterns, so new conditions still require experimental data.Source: §1 · p. 1
- A learned state prior, trained once on gait data, is added as an objective alongside task costs in optimal control, guiding solutions toward likely human states.It represents a smooth, differentiable probability over measured joint angles, velocities, and ground reaction forces.Source: §1 · p. 2
- Across walking and running speeds, simulations reproduce measured kinematics and ground reaction forces with r = 0.94–0.98, outperforming existing physics-based simulations.Their accuracy is comparable to data-driven models trained to reproduce the data.Source: §1 · p. 2
- The state prior also reconstructs full-body kinematics for curved running and cutting manoeuvres from sparse marker sets, despite those motions being outside its training data.The framework is presented as applicable to unmeasured conditions such as footwear or assistive-device design.Source: §1 · p. 3
2 Results
State-prior simulations match measured walking and running across speeds, with realistic cadence and gait transitions emerging without being imposed. Further experiments show how objectives, muscle weakness, contact models, and sparse tracking affect predicted gait and reconstruction.
2 Results
- Across reference speeds, kinematics and ground reaction forces correlate at r = 0.94–0.98; walking kinematic W2 error is 4.96 ± 0.43° versus PredSim’s 9.19 ± 1.04°.The full method also matches running kinematics and kinetics more closely overall than physics-based baselines, at accuracy comparable to data-driven models.Source: Figure 3 · p. 4, State prior simulations yield… · p. 4
- Realistic cadence, the walk-to-run transition, and a self-chosen walking speed emerge without being imposed; the predicted speed is 1.21 ± 0.02 m s−1.The self-chosen speed is close to the measured energetic optimum of 1.23 m s−1.Source: State prior simulations yield… · p. 4
- Removing the state prior increases kinematic distribution error 2.6- to 4.5-fold, while removing the task objective raises ground-reaction-force error two- to threefold.Neither ablation reproduces both kinematics and forces as closely as the full objective.Source: State prior simulations yield… · p. 4
State prior-based simulations enable hypothesis testing in gait
- At 4.5 m s−1, stiffer or undamped contact increases peak vertical force and reduces metabolic cost; some undamped solutions become non-human-like plyometric running.The prior scores these plyometric solutions as less likely than nominal ones but does not exclude them.Source: State prior-based simulations enable… · pp. 5–7
- Neither metabolic-cost nor effort objectives fits the full speed range: metabolic cost better describes walking and low-speed running, while effort better describes faster running.Effort underestimates walking push-off force, whereas its running force fit is closer at higher speeds.Source: State prior-based simulations enable… · p. 5
- Changing the energy model shifts emergent walking speed by 0.14 m s−1, from 1.14 ± 0.02 to 1.29 ± 0.02 m s−1 across the models tested.The endpoints correspond to the Houdijk and Umberger models, respectively.Source: State prior-based simulations enable… · p. 6
- With reduced hip-abductor strength, simulations develop compensation including trunk lean up to 6.2° and pelvic drop up to 3.7°; metabolic cost rises as strength falls.Below 30% of nominal strength, the abductors saturate during stance; at 5% strength, metabolic cost reaches 4.51 J kg−1 m−1.Source: State prior-based simulations enable… · p. 6
The state prior enables reconstruction from sparse marker sets
- With reduced marker sets, the prior lowers mean per-joint position error from 70.8 to 49.0 mm for leg markers and from 65.4 to 42.2 mm for distal markers.Error instead rises from 5.3 to 8.9 mm with the full marker set; curved running and cutting were not in the prior’s training data.Source: The state prior enables reconstruction… · p. 7
3 Discussion
The learned state prior improves the realism of predictive gait simulations across walking and running speeds, supporting comparisons of movement objectives and model conditions. Its benefits depend on task alignment and model assumptions, with sparse reconstruction and altered ground contact exposing important boundaries.
3 Discussion
- Across walking and running speeds, simulations matched measured kinematics and ground reaction forces more closely than prior physics-based methods and comparably to data-driven models.The results support using the framework for hypothesis testing and motion reconstruction.Source: §3 · p. 7
- Metabolic cost better described low-speed gait, while effort better described faster running; neither objective reproduced the full speed range.For walking, effort yielded a 53% lower triceps surae activation peak but 9.2% more positive mechanical power across joints; it also required 2.3× fewer iterations on average than metabolic cost.Source: §3 · p. 7
- With weak hip abductors, simulations predicted compensated Trendelenburg gait, but also faster walking and narrower steps not observed in humans.The authors suggest that pain, discomfort, stability, and fear of falling—factors beyond metabolic cost—may shape real compensation.Source: §3 · p. 8
- Stiffer, less damped ground contact raised impact peaks and lowered metabolic cost, but the 5.9% cost reduction is likely overstated.The foot-shoe interface is not modeled, and the ground-contact model is known to overestimate energy loss.Source: §3 · p. 8
- Removing damping sometimes produced non-human-like plyometric running; simulations did not rule out its competitive potential, but its sustainability remains uncertain.At 6.0 m s−1, peak vertical force was 5.82 ± 0.85 BW; the authors call for experimental testing and note that pain, discomfort, or injury risk is not captured.Source: §3 · p. 8
- The prior improved reconstruction with sparse markers, including unseen cutting and curved running, but not with a full marker set; sparse results retained backward trunk lean.The prior only partially corrected the lean at the end of the motion.Source: §3 · pp. 8–9
- Use the prior when a task is underdetermined and resembles its gait training data; well-constrained tracking gains little, while non-gait motions risk gait-like bias.For impaired gait, the authors recommend caution and fine-tuning on impairment data; objective choices may also need to represent stability or pain.Source: §3 · p. 9
- The prior uses joint angles, velocities, and external forces to remain general across musculoskeletal models, while model bias toward male morphology remains a limitation.Negative log-likelihood gives unitless per-channel costs and accounts for differing noise levels; the authors recommend considering female models and studying impaired gait and assistive devices.Source: §3 · pp. 9–10
4 Methods
The methods train a probabilistic prior on measured gait states and integrate it into trajectory optimization alongside task-specific objectives. Three experiments use the framework for speed-range prediction, hypothesis testing, and sparse-marker reconstruction.
Learned State Prior
- A variational autoencoder is trained once on about 58 hours of synchronized motion-capture and force-plate data, using probabilistic reconstruction and a GNLL-plus-KL objective.The training set uses 23 of the runMaD model’s 33 degrees of freedom; smooth activations support continuous gradients for trajectory optimization.Source: Learned State Prior · p. 10
- The prior represents individual gait instants with joint coordinates, velocities, and ground-reaction forces, omitting muscle activations and model-dependent joint torques.Those omitted quantities are unmeasured or depend on uncertain musculoskeletal-model parameters.Source: Learned State Prior · p. 10
Integration into predictive simulations
- Direct collocation evaluates the prior at trajectory nodes and combines it with task-specific objectives under musculoskeletal dynamics.The simulations use the runMaD-SIPP full-body model, with 92 lower-limb muscles and torque-actuated arms.Source: Integration into predictive simulations · pp. 10–11
Experiments for predictive gait simulations
- The speed-range experiment compares simulated joint-angle and ground-reaction-force distributions with experimental data and eligible predictive-simulation baselines.It also tests walking with unconstrained speed and cadence, using metabolic cost as the task objective.Source: Experiments for predictive gait… · p. 11, Table 1 · p. 11
- Hypothesis tests vary energy-cost versus effort objectives, metabolic-cost models, hip-abductor strength, and ground-contact properties.The comparisons assess resulting gait patterns, forces, and metabolic costs.Source: Experiments for predictive gait… · pp. 11–12
- Sparse-tracking experiments reconstruct straight and curved running and cutting from leg-only or ankle-and-hand markers, comparing results with full-marker and prior-free reconstructions..Source: Experiments for predictive gait… · p. 12