Predictive Gait Simulations of Human Energy Optimization Anne D. Koelewijn1, Jessica C. Selinger2

1Machine Learning and Data Analytics Lab, Faculty of Engineering, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)2School of Kinesiology and Health Studies, Queen’s University

Introduction

We aim to recreate an experimental energy

optimization paradigm using predictive gait

simulations.

Humans can adapt their gait to continuously optimizeenergetic cost in real-time. We have previouslydemonstrated this using robotic exoskeletons [1]. Subjectsadapted their step frequency to converge on the newenergetic optima within minutes and in response torelatively small savings in cost.

We aim to create a simulation model of the testbed. Thissimulated testbed will allow us to probe mechanismsunderlying the energy optimization of gait—generatingpredictions of human behaviour and insight into aspects ofoptimization that are inherently difficult to investigateexperimentally.

Adidas AG (faculty endowment to A.D.K.)NSERC Discovery Grant (RGPIN-2019-05677 to J.C.S.)

Methods: Modeling

We use a sagittal plane musculoskeletal model of thelower limbs, with nine degrees of freedom and eightmuscles in each leg. We added an ideal, massless,exoskeleton to our simulations by applying torques atthe knees that resist flexion and extension.

𝑇𝑒𝑥𝑜= ±𝑠 ሶ𝑞𝑘𝑛𝑒𝑒 𝑐𝑇 ≤ 12 Nm

±𝑠: step frequencyሶ𝑞𝑘𝑛𝑒𝑒: knee angular velocity𝑐𝑇: constant

Methods: Trajectory Optimization Problems

We simulated a range of gaits, and solved for energy-optimal

gaits under the penalize -high and -low exoskeleton controllers.

The following objective was used:

𝐽 =1

𝑇𝑡−0

𝑇𝑢3 +

1

1000∑ 𝑞𝑖 𝑡 − 𝑞𝑖,𝑑𝑒𝑠 𝑡

2+ ∑𝐹𝑖 𝑡 − 𝐹𝑖,𝑑𝑒𝑠 𝑡

2dt

𝑢: neural stimulation𝑞: joint angles𝐹: horizontal and vertical ground reaction force𝑑𝑒𝑠: desired joint angles and ground reaction force from [2]

Optimization details [3]:• Left-right symmetry constraint• Direct collocation, 40 nodes per

half-gait cycle• Implicit dynamics formulation

Results: Resistive Torque Effects

Results: Muscle Metabolic Work Rate Discussion

Our simulated exoskeleton torquesresembled those from humanexperiments (AB). These torqueschanged simulated effort, in a wayconsistent with our experimental energylandscapes (C).

The optimal step frequency shifted tolower and higher frequencies for thepenalize-high and penalize-lowconditions, respectively (C).

Simulations created:• Natural, penalize-low and -high• Free, optimized step frequency• Fixed step frequencies: -20% to 20%

of natural preferred, 1% increments

Absolute muscle metabolic rate for the natural walking condition and the relative changes in muscle metabolic rate for the penalize-low and penalize-high conditions.

The metabolic rate in thevastus and quadriceps, and instance the hamstrings andgastrocnemius changes simi-larly in the penalize-high andpenalize-low conditions. Themetabolic rate in the tibialisanterior, hamstrings in swingand hip muscles changedifferently.

The metabolic rate is highest inthe hamstrings, gluteals andankle dorsiflexors duringstance and in the iliopsoas andvastus during swing

We re-created our experimental paradigm where exoskeletons areused to alter preferred and energy optimal gaits using predictivesimulations. We were able to replicate the exoskeleton torque appliedat the knee joint during gait in simulation, produce effort landscapeswith optima at high and low step frequencies, and solve for optimalgaits through adaptations in step frequency.

Using this modelling testbed, we can now explore what particularkinematics of gait or muscles are driving whole body changes inenergy expenditure, offering insight into strategies for improvedexoskeleton control.

Comparison of experimental and simulated resistive torque effects from the exoskeleton.

𝑇𝑒𝑥𝑜 𝑇𝑒𝑥𝑜

We created a lower-limb musculoskeletal model

and added torques at the knees to simulate the

exoskeleton.

References

[1] Selinger et al. Current Biology (2015).

[2] Winter, Biomechanics and Motor Control of Human Movement (2005).

[3] Koelewijn & Van den Bogert. Gait & Posture (2016).

Res

isti

veto

rqu

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m)

Ob

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fun

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valu

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A

C

12

3

4

5

6

78

1 Iliopsoas2 Gluteals3 Quadriceps4 Hamstrings5 Vastus6 Gastrocnemius7 Soleus8 Tibialis Anterior

Step frequency (%)-15 -10 -5 0 +5 +10 +15 -15 -10 -5 0 +5 +10 +15

Step frequency (%)

1

0

B 7

0

Ave

rage

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torq

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(Nm

)

Gait cycle (%)

1086420

0 10 20 30 40 50 60 70 80 90 100

Figure reproduced from [1]