Technical Summary: GaitSpan

Problem Statement

Current approaches to humanoid locomotion often treat walking, jogging, and running as distinct competencies. To achieve diverse gaits, existing methods typically rely on prescribing gait schedules, imitating human motion clips, training separate expert policies for different speeds, or distilling these experts into a single policy. While these strategies can produce impressive behaviors, they suffer from limited flexibility across continuous speed commands, terrains, and morphologies. Furthermore, they often fail to demonstrate how a single learned policy can naturally expand from a basic walking skill into faster locomotion regimes without relearning from scratch or relying on external human demonstrations. The core challenge is to develop a learning principle where an acquired skill (walking) serves not merely as an endpoint, but as a "seed" for a family of related behaviors.

Methodology: GaitSpan Framework

The authors propose GaitSpan, a framework designed to expand a pretrained, frozen walking policy into faster locomotion regimes (jogging and running) through three integrated components. The system treats the walking policy as a reusable motor structure for balance, support, and coordination, which is then regenerated at new rhythms and extended into longer strides.

1. Rhythm Generation (GaitWave)

Instead of training separate experts or using hard gait switches, GaitSpan modulates the frozen seed walking policy using multiple internal clocks.

• Phase-Scaled Canonical Action Waves: The seed policy is queried at different phase scales (temporal resolutions) to generate a family of "action waves." These are not external templates but self-generated structures derived from the robot's own walking policy.
• Hierarchical Multi-Resolution Memory: A learnable memory bank combines these action waves using command-conditioned coefficients. This hierarchy (e.g., 2, 4, and 8 bins) allows the system to capture broad gait splits at low resolutions and fine-grained transitions at higher resolutions, ensuring smooth, continuous gait changes as speed commands increase without abrupt switches.

2. Stride Shaping (H-SLIP)

Rhythmic expansion alone does not guarantee physically meaningful dynamic gaits. To address this, GaitSpan introduces H-SLIP, a hierarchical virtual-leg objective inspired by the Spring-Loaded Inverted Pendulum (SLIP) model.

• Hierarchical Virtual Legs: The system defines virtual legs at three levels: root-to-foot (global), root-to-knee (upper), and knee-to-foot (lower).
• Dynamic Event Rewards: The reward function shapes four key dynamic events: compression, rebound, touchdown, and flight. It encourages the policy to absorb and release energy through the virtual-leg hierarchy and to execute controlled contact transitions. This guides the expanded motions toward jogging and running regimes while maintaining physical coherence.

3. Residual Adaptation

A residual policy branch captures motion details not accounted for by rhythm generation or stride shaping. This branch learns state-dependent corrections to handle specific dynamics and environmental interactions, resulting in a comprehensive policy that combines the stability of the seed with the flexibility of new regimes.

Training Objective

The total reward combines standard locomotion tasks, the H-SLIP dynamic shaping reward, and Self-Anchored (SA) Regularization. The SA terms (seed anchoring, residual compactness, phase-aware self-similarity, and temporal consistency) ensure that the policy preserves the stable structure of the walking seed at low speeds and only deviates when necessary for higher speeds, preventing the overwriting of foundational skills.

Key Contributions

1. Skill Growth Paradigm: GaitSpan is the first framework to demonstrate a single command-conditioned humanoid policy that spans walking, jogging, and running-like regimes as a continuous family, treating walking as a generative seed prior rather than a static endpoint.
2. GaitWave Mechanism: Introduces a method to grow locomotion rhythms by hierarchically composing action waves derived from a frozen seed policy, avoiding the need for separate gait experts or explicit gait labels.
3. H-SLIP Integration: Incorporates a physically grounded, hierarchical SLIP objective to shape dynamic stride events (compression, rebound, flight) without relying on rigid trajectory templates.
4. Zero-Shot Generalization: The resulting policy transfers across different humanoid morphologies (tested on Unitree G1, Booster T1, and Booster K1) and deploys zero-shot on unseen sim-to-sim and real-world terrains (including sand and uneven ground) despite training only on flat and mildly uneven terrains.

Experimental Results

The authors evaluated GaitSpan on five humanoid configurations (varying DoF and morphology) and compared it against several baselines:

• Seed Policy: The frozen walking policy evaluated on extended speed ranges.
• Energy Multi-Experts: A set of separately trained energy-shaped gait policies combined for different speeds.
• Human Demonstration: A policy trained using human motion priors (AMP).
• From-Scratch & Fine-Tuning: Variants without the structured seed expansion.

Key Findings:

• Command Tracking: GaitSpan maintains low tracking error across a continuous speed range (up to ~2.2 m/s) while developing substantial flight time at high speeds. In contrast, the multi-expert baseline showed degraded tracking and failed to produce command-appropriate flight, while the human-demonstration baseline incurred higher energy costs and exhibited less speed-dependent gait differentiation.
• Emergent Gaits: The system successfully transitions from stable walking to jogging and running-like behaviors. Foot-contact plots reveal smooth transitions from alternating support to dense contact-flight patterns as speed increases.
• Efficiency: GaitSpan consumes less energy than human-demonstration baselines in low-to-mid speed regimes and achieves competitive performance at high speeds.
• Ablation Studies: Removing GaitWave or H-SLIP individually resulted in either poor high-speed flight emergence or unstable tracking. The full framework was shown to be necessary for balancing command tracking with dynamic gait emergence. Furthermore, structured expansion (GaitSpan) outperformed direct fine-tuning and training from scratch, which either overwrote stable walking behaviors or failed to learn coherent high-speed gaits.

Significance and Claims

The paper posits that existing skills should not remain endpoints but can serve as seed priors for behavior families. By expanding a walking policy through rhythm generation and physically guided stride shaping, GaitSpan offers a more efficient and scalable route for humanoid skill acquisition compared to methods that rely on imitation, multi-expert distillation, or training from scratch.

The authors claim that this approach demonstrates a concrete realization of skill growth, where a humanoid learns to run not by discarding its ability to walk, but by reusing the motor structure of walking and adapting it to new rhythms and dynamics. This points toward a future where humanoid robots can acquire complex, continuous locomotion capabilities through structured expansion of foundational skills, rather than through the assembly of disjointed, task-specific experts. The work suggests that human-like imitation is not strictly necessary for learning dynamic, energy-efficient, and command-adaptive gaits, as the robot's own motor structure can be the primary source of growth.