Phase-Guided Terrain Traversal (PGTT)

• Phase-Guided Terrain Traversal is an approach that embeds phase or gait awareness with dynamic terrain analysis to inform robust navigation in autonomous ground robots.
• It leverages reward shaping via cubic Hermite spline swing trajectories derived from real-time heightmap data to ensure safe and efficient obstacle negotiation.
• The methodology generalizes across different robot morphologies through simulation-to-real transfer and domain randomization, improving recovery from disturbances and challenging terrains.

Phase-Guided Terrain Traversal (PGTT) is an advanced methodology for autonomous ground robotics that integrates explicit phase or gait structure guidance with terrain-aware perception and planning to achieve robust and adaptive navigation on complex, unstructured surfaces. Unlike traditional approaches which either hard-code gait cycles or operate without explicit phase awareness, PGTT frameworks embed phase variables and terrain analysis directly into control and decision-making processes, enabling efficient, safe, and generalizable locomotion across divergent morphologies and terrains.

1. Core Principles and Motivation

The foundational concept of PGTT is to incorporate phase-awareness—either as a representation of gait cycles (in legged systems) or operational modes (in wheeled/tracked vehicles)—in conjunction with dynamic, perception-driven adaptation to environmental geometry and uncertainty. This paradigm aims to address the limitations of both pure model-based and blind learning-based controllers by guiding trajectory generation and policy optimization according to both robot phase (e.g., swing/stace cycles in legged robots) and up-to-date estimates of terrain parameters such as height, slope, and traversability. The result is a decision-making process that is resilient to partial observations, sensor noise, and sim-to-real gaps, and that does not impose restrictive biases on the action space (Ntagkas et al., 21 Oct 2025).

PGTT leverages three core technical pillars:

• Phase-driven reward shaping or control modulation, using per-leg or per-mode phase variables.
• Explicit terrain analysis, extracting local statistics (e.g., heightmap extrema, roughness, traversability index) in real time from onboard sensors (e.g., stereo, LiDAR, proprioception).
• Morphology-agnostic or adaptable policy architectures, in which phase guidance informs reward or cost, not the direct target trajectory, allowing for generalization across robot types.

2. Technical Implementation: Reinforcement Learning and Reward Shaping

A defining implementation of PGTT for legged robots is the encoding of phase-guided learning in model-free RL. Rather than enforce oscillator or IK-based gait priors (which rigidly prescribe joint commands per phase), the PGTT approach introduces phase variables strictly in the reward function. Each leg is assigned a periodic phase φ_{i,t}, demarcating the stance (φ ∈ [0, π)) and swing (φ ∈ [π, 2π)) portions of the gait.

For each swing phase, the desired trajectory is encoded via a cubic Hermite spline in the vertical direction. The spline parameters are adaptively set based on local terrain heightmap statistics, particularly the apex height d_s increased by the difference δH_i = H_{max,i} – H_{min,i}, where H_{max,i} and H_{min,i} are the maximum and minimum heights in the region surrounding leg i. The spline ensures sufficient vertical clearance for obstacle negotiation.

Formally, the swing trajectory for leg i is:

• For stance: p^{des}{f,z,i}(φ{i,t}, h_t) = d_b (nominal stance foot height)
• For swing up: p^{des}_{f,z,i} = P_{su}(φ{i,t} – T{stance}, h_t)
• For swing down: p^{des}_{f,z,i} = P_{sd}(φ{i,t} – T{peak}, h_t)

where P_{su} and P_{sd} are Hermite splines parametrized on duration and apex height.

Reward shaping terms penalize deviations from this desired foot swing, and a penalty is imposed for contact made outside the stance interval. Importantly, the controller acts in joint space and does not require phase as an observation, resulting in a reduction in inductive bias and facilitating cross-morphology deployment. This enables morphology-agnostic learning and transfer, a critical departure from hard-coded gait generators (Ntagkas et al., 21 Oct 2025).

3. Terrain Perception and Local Environment Representation

PGTT frameworks necessitate accurate terrain representation to inform phase-adaptive planning. This is typically realized by constructing a robot-centric elevation grid map or heightmap from LiDAR or stereo data, combined with inertial fusion for pose stabilization. Each grid cell records the mean and variance of elevation, supporting the extraction of local terrain features required for swing modulation (e.g., swing apex adaptation to the maximum local height).

To ensure robustness in real-time hardware, median-fill filters are used to handle missing sensor data (holes/NaNs in LiDAR), and the terrain map is maintained at high frequency (e.g., 50 Hz) to synchronize with control cycles. These representations are designed to be lightweight and compatible with both simulation (e.g., MuJoCo/MJX environments) and physical robots (e.g., Unitree Go2, ANYmal-C) (Ntagkas et al., 21 Oct 2025).

4. Policy Training, Curriculum Learning, and Domain Randomization

Phase-guided controllers are typically trained using PPO in asymmetric actor-critic RL, where the policy receives partial observations (proprioception, local heightmap) and the critic is provided with privileged information (e.g., ground-truth state). The curriculum begins with simple, near-flat terrains and incrementally introduces more difficult geometries such as stairs and discrete obstacles, gradually increasing maximum step height (up to 13 cm in (Ntagkas et al., 21 Oct 2025)). Domain randomization over sensor noise, friction, robot morphology, and terrain statistics is applied to enhance sim-to-real transfer and generalization.

Performance metrics include:

• Success rates under push disturbances and on discrete obstacles
• Policy convergence speed (PGTT approaches converge over 2× faster than strong end-to-end baselines)
• Velocity tracking performance
• Robustness to morphology change (validated on both Unitree Go2 and ANYmal-C with unchanged hyperparameters)

PGTT achieves improvements of median +7.5% (disturbance recovery) and +9% (obstacle crossing) over competing policies, while maintaining competitive kinematic tracking accuracy (Ntagkas et al., 21 Oct 2025).

5. Hardware Integration and Perception-to-Control Pipeline

In the real-world deployment of PGTT, a real-time perception-to-control pipeline is constructed. LiDAR and inertial measurements are fused by a tightly coupled odometry framework (e.g., Point-LIO). The elevation data is used to generate a robot-centric heightmap, which is cropped and re-projected at runtime to match the policy input shape (e.g., 11×9 grid).

The RL policy receives proprioceptive state and the local heightmap at each timestep, outputs joint space commands, which are converted to torque via a low-level PD controller. This architecture allows the robot to dynamically raise or lower swing trajectory heights according to locally sensed terrain features, without requiring global localization or hand-crafted path plans.

Notable findings from hardware experiments include:

• Robust locomotion across stairs and uneven surfaces
• Minimal tuning required between simulation and deployment platforms
• Reliable operation at high terrain update rates (≥50 Hz) (Ntagkas et al., 21 Oct 2025)

6. Generalization and Broader Implications

The PGTT paradigm stands out by merging phase-awareness with adaptive perception and minimal structural bias. Because phase enters only as a reward shaping variable, the framework is not tied to a particular morphology or foot trajectory model. As a result, PGTT methods exhibit:

• Sample efficient training and rapid convergence
• High adaptability to disturbance and terrain geometry without extensive retuning
• Generalizability across multiple hardware platforms
• Simplicity in reward and control structure

Terrain-adaptive phase-guided reward shaping emerges as a general approach for robust, perceptive legged locomotion and can be extended to other modes of ground locomotion (wheeled, multi-modal) by appropriate redefinition of the phase variable (Ntagkas et al., 21 Oct 2025).

7. Future Directions and Opportunities

Future work may augment the PGTT pipeline with richer terrain descriptors, sensor fusion strategies (e.g., combining visual and tactile feedback), online learning and adaptation to sensor drift or terrain change, and tighter integration with high-level planning modules that leverage phase structure beyond the single-step or swing level. Incorporation of uncertainty-aware world models, semantic terrain labeling, and multi-task learning may further enhance navigation reliability in unseen and complex environments.

The demonstrated morphology-agnostic deployment and robust real-world validation indicate that PGTT represents a significant progression toward scalable, adaptive, and perception-integrated terrain traversal in autonomous ground robots.