🧠 neuroscience

Feedback control stabilizing the center of mass can be identified in unperturbed, upright standing

This study demonstrates that human walking stabilizes both linear and whole-body angular momentum simultaneously, explaining observed correlations between center of pressure and center of mass states through a feedback control mechanism that predicts ground reaction forces and moments based on preceding momentum deviations.

Original authors: Geng, Y., Bruijn, S. M., van Dieën, J. H.

Published 2026-02-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Geng, Y., Bruijn, S. M., van Dieën, J. H.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine walking is like balancing a tall, wobbly stack of books on a skateboard. If the stack leans too far forward, it falls. If it spins too much, it falls. To keep walking without falling, your brain and body have to do two things at the exact same time:

Stop the stack from falling forward or backward (Linear Momentum).
Stop the stack from spinning or twisting (Angular Momentum).

For a long time, scientists thought you only had to worry about the first thing (falling). They believed that if you moved your foot (the "Center of Pressure" or CoP) in a specific spot relative to your belly button (the "Center of Mass" or CoM), you were automatically fixing your balance.

This paper says: "Actually, you're doing both at once, and that's why it works."

Here is the breakdown using simple analogies:

1. The Misunderstanding: The "Magic Foot"

Imagine you are riding a unicycle. If you lean forward, you pedal faster to catch yourself. Scientists used to think that simply moving your foot forward or backward was the "magic switch" that fixed your speed and direction. They thought, "If I move my foot here, my body will naturally stop falling."

The Problem: The authors point out that mechanically, moving your foot doesn't actually change your forward speed directly. It's like trying to steer a car by just waving your hands out the window; it doesn't turn the wheels.

2. The Real Secret: The "Tightrope Walker's Dance"

The authors discovered that when we walk, our body is actually juggling two balls at once:

Ball A (Linear Momentum): How fast we are moving forward or side-to-side.
Ball B (Angular Momentum): How much our body is twisting or rotating.

In a perfect world, these two balls would move in perfect sync, like a dance partner. If you lean forward (Ball A), your body naturally starts to twist (Ball B) in a predictable way.

The Analogy: Think of a figure skater spinning. If they pull their arms in, they spin faster. If they push their arms out, they slow down. But they also have to keep their feet moving forward. The paper shows that human walkers are like skaters who have learned to move their arms and legs in a way that controls both the spin and the forward motion simultaneously.

3. The "Foot Placement" Trick

So, why did the old scientists think moving the foot was the answer?

Because in human walking, moving the foot actually controls both balls at the same time.

The Scenario: Imagine you are walking and you start to fall forward too fast (too much Linear Momentum).
The Reaction: You need to hit the ground with your foot to create a force that slows you down.
The Catch: If you just hit the ground hard to slow down, you might accidentally make your upper body twist or spin (creating bad Angular Momentum).
The Solution: You have to place your foot in the exact right spot so that the force slows you down without making you spin.

It's like a tightrope walker holding a long pole. If they lean left, they don't just step left; they shift the pole to counterbalance the spin. The paper shows that our feet act like that pole. By placing the foot in a specific spot relative to our belly button, we are simultaneously fixing our speed and our rotation.

4. The "Feedback Loop"

The researchers looked at data from people walking on treadmills. They found a clear pattern:

When a person's body was slightly off-balance (too much forward speed or too much twist), their brain sent a signal to the muscles.
This signal changed the force of the foot hitting the ground and the twist of the ground reaction.
Crucially, these changes happened in a way that perfectly corrected both problems at once.

The "Negative Correlation" (The Braking System):
Think of it like a car with a smart braking system.

If the car is going too fast (positive error), the brakes apply a negative force to slow it down.
The paper found that our bodies do this for both speed and spin. If we are spinning too much, our feet apply a "brake" to the spin. If we are moving too fast, our feet apply a "brake" to the speed. And they do it in a coordinated dance.

Why This Matters

This study changes how we understand walking stability.

Old View: We control walking by just watching where our feet land relative to our belly button.
New View: We are actually running a complex, simultaneous control system that manages both our forward speed and our body's rotation.

The Takeaway:
Walking isn't just about not falling over; it's about not falling over and not spinning out of control at the same time. Our brains are incredibly smart engineers that place our feet in the "Goldilocks zone"—not too far, not too close—so that one single action fixes both problems instantly. This is why humans are so good at walking, even when the ground is uneven or we are tired!

1. Problem Statement

Stabilizing bipedal gait is mechanically challenging due to the body's upright, segmented, and "top-heavy" nature. Previous research has largely focused on controlling the Center of Mass (CoM) linear momentum, often interpreting the distance between the CoM and the Center of Pressure (CoP) (or foot placement) as a primary mechanism for correcting linear momentum deviations.

However, the authors identify a fundamental mechanical contradiction in this prevailing view:

The Paradox: Shifting the CoP relative to the CoM does not directly alter the linear momentum of the system (governed by Newton's second law, $\sum F = \dot{p}$ ). Instead, CoP shifts primarily generate torques that alter the body's angular momentum ( $\sum \tau = \dot{H}$ ).
The Gap: Despite this mechanical reality, empirical studies consistently show strong correlations between CoM-CoP distance and horizontal ground reaction forces (GRF), suggesting these variables are used to control linear momentum. The authors question why this correlation exists if the mechanical causality is flawed, and propose that the control of linear and angular momentum is simultaneous and coupled.

2. Methodology

The study utilized a combination of theoretical derivation and re-analysis of existing experimental data.

Data Source: Data from 13 healthy young adults walking on an instrumented dual-belt treadmill at normal and slow speeds.
- Measurements: Ground reaction forces (200 Hz) and full-body kinematics (Optotrak, 50 Hz).
- Processing: Calculated whole-body CoM trajectories, linear momentum ( $p_{CoM}$ ), and angular momentum ( $H_{CoM}$ ) relative to the CoM.
Theoretical Framework:
- The authors combined the equations of motion for linear and rotational dynamics of a system of linked rigid segments.
- They hypothesized that if linear and angular momentum follow correlated quasi-periodic functions (as observed in steady walking), the horizontal distance between CoM and CoP must be correlated with horizontal GRF to satisfy both equations of motion simultaneously.
Statistical Analysis:
- Correlation Analysis: Assessed temporal correlations and cross-correlations between linear and angular momentum time series.
- Regression Modeling: Fitted regression models to test if deviations in momentum (from a quasi-periodic average trajectory) predict subsequent deviations in:
  1. Horizontal GRF (for linear momentum control).
  2. GRF moments about the CoM (for angular momentum control).
- Feedback Delay Optimization: The models optimized time delays ( $\tau$ ) across the gait cycle (1–49% delay) to identify the strongest negative feedback gains, simulating a stabilizing control system.

3. Key Contributions

Mechanical Clarification: The paper clarifies that while CoP shifts do not mechanically cause changes in linear momentum, they are mechanically coupled to linear momentum changes because the body must simultaneously satisfy constraints for both linear and angular momentum.
Simultaneous Control Hypothesis: It provides evidence that the human nervous system does not control linear and angular momentum independently. Instead, it controls them simultaneously, where a correction for one inevitably affects the other, requiring a coordinated strategy.
Reinterpretation of Foot Placement: It explains why foot placement (CoP location) is a successful predictor of linear momentum control in previous studies: it is not just a linear momentum controller, but a dual controller managing the trade-off between linear and angular stability.

4. Key Results

Momentum Correlation:
- Linear and angular momentum in both the frontal (mediolateral) and sagittal (anteroposterior) planes followed quasi-periodic patterns with similar frequencies.
- In the frontal plane, they were highly correlated. In the sagittal plane, they showed a clear phase difference but high cross-correlation.
CoP-Force Correlation:
- There was a strong correlation between the horizontal distance (CoM' to CoP) and the horizontal ground reaction force in both planes and at both speeds. This validates the empirical success of using CoP distance as a proxy for linear momentum control, despite the theoretical mechanical nuance.
Feedback Control Evidence:
- Regression models confirmed that deviations in linear momentum ( $p_{CoM}$ ) and angular momentum ( $H_{CoM}$ ) negatively predicted future deviations in horizontal GRF and GRF moments, respectively.
- Significant Negative Gains: Significant negative feedback gains were found throughout most of the gait cycle, indicating active stabilization.
- Delays:
  - Frontal Plane: Linear momentum corrections had a delay of ~210 ms; Angular momentum corrections had a delay of ~53–78 ms.
  - Sagittal Plane: Linear momentum corrections had a delay of ~133–173 ms; Angular momentum corrections had a delay of ~38–45 ms.
- Early Stance: The strongest corrections for linear momentum occurred in early stance, likely due to collision forces and foot placement adjustments.

5. Significance and Conclusion

Unified Control Theory: The study concludes that linear and angular momentum are mechanically coupled through external forces (GRF). Therefore, they cannot be controlled in isolation. The nervous system must manage a multi-variable control problem where adjusting the CoP (foot placement) serves to decouple or coordinate the control of both momenta.
Implications for Stability: The findings suggest that "sacrificing" one momentum to stabilize the other (e.g., allowing linear momentum to deviate to restore angular stability after a trip) is a necessary strategy in human gait.
Future Directions: The authors note that while this study focused on steady-state walking, the coupling likely persists in perturbed gait, running, and stair negotiation. The regression models presented offer a framework for quantifying the "lumped effect" of passive mechanics and active neural feedback in gait stability, which could be vital for developing better rehabilitation protocols and robotic exoskeletons.

In summary, the paper resolves a long-standing mechanical paradox in gait analysis by demonstrating that the observed correlation between CoP location and linear momentum is a byproduct of the simultaneous necessity to control both linear and angular momentum to maintain stable bipedal walking.