Embodied Collapse: Training Humanoid Locomotion via Seething Tension Fields

 Abstract

Conventional approaches to humanoid locomotion treat walking as an optimization problem over trajectories, energy expenditure, or predefined joint motions. In contrast, biological systems achieve movement through dynamic collapse of internal tension fields: a continuous resolution of seething, underactuated constraint systems. We propose a novel framework—Seething Tension Field Theory (STFT)—as the foundation for a new paradigm in robotic locomotion. By modeling the robot’s body-environment system as a time-varying constraint field, and locomotion as the emergence of collapse-resolved stability, we show that human-like gait can arise not from explicit planning but from the adaptive resolution of structural tension. The resulting motions are resilient, adaptive, and more biomechanically plausible than those produced by optimization alone.

Table of Contents

  1. Introduction
    1.1 The limits of trajectory-based locomotion
    1.2 The biomechanical paradox: redundancy and naturalness
    1.3 Collapse as the hidden mode of movement generation

  2. Seething Tension Field Theory (STFT)
    2.1 Core principles of STFT
    2.2 Constraint fields, tension gradients, and collapse readiness
    2.3 From static equilibrium to dynamic collapse manifolds

  3. The Structure of Humanoid Locomotion
    3.1 Biomechanical constraints and seething underactuation
    3.2 Human gait as recursive micro-collapse
    3.3 The physics of balance: tension and time

  4. Modeling Tension Fields in Humanoid Robots
    4.1 Joint-level constraints as dynamic tension nodes
    4.2 Terrain, contact forces, and environmental friction gradients
    4.3 The collapse functional T(xt)\mathcal{T}(x_t) and CRI metrics

  5. STFT-Based Gait Training Algorithm
    5.1 Collapse-driven policy learning
    5.2 Tension-aware reward shaping
    5.3 Field navigation vs trajectory optimization

  6. Experiments and Simulations
    6.1 Open-loop collapse reflexes in unstructured terrain
    6.2 Adaptive recovery from dynamic perturbations
    6.3 Emergent asymmetry and gait variability: beyond uniformity

  7. Discussion
    7.1 Comparison with reinforcement learning and optimal control
    7.2 Implications for embodied AI and neuro-motor learning
    7.3 Toward seething intelligence: field-centric robot cognition

  8. Conclusion
    8.1 Collapse is not failure—it is structure
    8.2 The future of soft locomotion in constrained systems
    8.3 Generalizing collapse theory across embodiment and cognition

1. Introduction  

Humanoid locomotion is often reduced to a control problem: plan a trajectory, compute inverse kinematics, stabilize with feedback, and optimize over energy. And yet, human walking—natural walking—is not optimized. It is adaptive, redundant, noisy, and above all: structurally stable. We do not walk by solving equations; we walk by collapsing instability into momentum, again and again.

This paper introduces Seething Tension Field Theory (STFT) as an alternative ontological frame for robotic movement. Rather than planning actions, we model the robot’s body-environment system as a dynamic, constraint-saturated field, within which movement arises as sequences of tension collapses. Where classical robotics seeks control, STFT seeks resolution—and where conventional models seek efficiency, STFT reveals stability through structural compromise.

Walking, in this model, is not a solution—it is an emergent rhythm of collapse. 

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