PGTT: Phase-Guided Terrain Traversal for Perceptive Legged Locomotion (IROS 2026)

Created on August 19, 2026

2026   ·   legged   rl   terrain   ·   paper-review

Item Details
Authors Alexandros Ntagkas, Chairi Kiourt, Konstantinos Chatzilygeroudis (University of Patras LAR, Archimedes/Athena RC)
Venue IROS 2026 (accepted; arXiv v1 2025-10, v2 2026-07)
Links arXiv · Code

One-line Summary

PGTT is a perceptive quadruped locomotion reinforcement learning method that, instead of forcing a gait rhythm (gait prior) into the action space through oscillators or IK, puts a terrain-adaptive Hermite-spline foot trajectory “only in the reward.” The policy acts freely in joint space while still gaining the benefits of rhythmic structure. It was trained with MuJoCo MJX on a single consumer-grade GPU and transferred to a real Unitree Go2 with LiDAR elevation-map perception, raising the success rate by 7.5-9 percentage points over the baselines under disturbances and on discrete obstacles.

Success and limits of blind RL. Lee et al. (2020) showed rough-terrain locomotion using proprioception only, but because it could not “anticipate” obstacles, it was vulnerable to terrain under the hind legs and to discrete obstacles.

Two approaches to perception. End-to-end egocentric depth cameras (Agarwal 2022) suffer from a limited field of view, noise, and the burden of temporal memory, and in particular cannot observe the terrain under the hind legs. Global elevation maps with multiple sensors (Miki 2022) add foresight but are fragile because they depend on calibration and global pose estimation. As a compromise, robot-centric local heightmaps have recently become the convergence point.

Convention and problem of gait priors. The Wild (Miki 2022) family prescribes foot and joint targets from per-leg phases and tracks them with IK + PD. It is stable but constrains the action space and ties the policy to the robot morphology. CPG-RL inherits the same limitation. On the prior-free side is MassLoco (Rudin 2022 + Margolis rewards), which is free but has many reward terms and converges slowly.

Position of PGTT. Its place in the lineage is combining the “put the phase in the objective” direction opened by Shao et al. (RA-L 2022) with terrain adaptation (adjusting the swing apex from local heightmap statistics). By putting the structure in the reward rather than the action, it aims at “the benefits of rhythm + an unconstrained action space + morphology independence” all at once. The training infrastructure also moves away from the Isaac Gym monoculture to MuJoCo MJX + BRAX + PPO, presenting accessibility itself as a contribution, in step with the contemporary trend of MuJoCo Playground. Citation accumulation is at an early stage.

Problem and Motivation

Perceptive locomotion RL controllers either (i) constrain the action space with oscillator/IK gait priors, biasing optimization and blocking transfer between robot morphologies, or (ii) operate blind, failing to anticipate terrain under the hind legs and being vulnerable to observation noise. What is needed is a method that “keeps the benefits of rhythmic structure but leaves the action space untouched.” Where to put the structure, in the action or in the reward, is the question of this paper.

Key Ideas and Method

In one sentence: a terrain-adaptive cubic Hermite-spline foot-height trajectory, defined from per-leg phases and local heightmap statistics, is used only as a term that “rewards the policy for tracking it” (no IK), while the policy itself acts directly in joint space.

Perception: robot-centric heightmap

An N×M uniformly spaced grid is anchored to the robot body frame and used directly as policy input. No global pose or multi-sensor calibration is needed, and it captures the local geometry under both front and hind legs. Simulation uses ground truth; the real robot extracts it online from LiDAR elevation mapping.

Phase encoding and terrain-adaptive spline (reward only)

Each leg has a phase \(\phi_i \in [0, 2\pi)\), where \([0, \pi)\) is interpreted as stance and \([\pi, 2\pi)\) as swing. The phase advances at a base frequency \(f\) and enters the observation as \(\cos\phi, \sin\phi\).

The swing trajectory is a three-segment cubic Hermite spline: stance (holding the nominal foot height \(d_b\)) → swing-up (\(d_b \to d_s + \delta H\)) → swing-down (\(d_s + \delta H \to d_b\)). The key here is the terrain adaptation term.

\[\delta H_i = H_{max,i}(h_t) - H_{min,i}(h_t)\]

Since the difference between the highest and lowest heights in the heightmap around the leg is added to the swing apex, the foot automatically rises higher on rougher terrain, guaranteeing obstacle clearance. The spline parameters are expressed in phase coordinates rather than time.

The reward adds only two PGTT-specific terms to the common terms (velocity tracking, posture, torque, etc.).

Term Definition Weight
foot phase \(\sum_i \exp\big(-(p^{des}_{f,z,i} - p_{f,z,i})^2 / \sigma_f\big)\), \(\sigma_f = 0.05\) 1.0
foot contact penalty for contact during the swing phase \(\sum_i \mathbb{1}[\pi \le \phi_i < 2\pi] \cdot c_i\) -0.25

This is fewer than the four additional terms that MassLoco requires (clearance, slip, air time, stand still).

Training architecture

  • Action: \(q_{des} = q_{stand} + k \cdot a\), direct output of 12 joint target angles (no IK), converted to torque by a low-level PD.
  • Observation: \(o = [\omega, g, q, \dot{q}, \cos\phi, \sin\phi, h, f, a_{prev}, v_{cmd}]\): body angular velocity, gravity vector, joint angles and velocities, phase, height scan, base frequency, previous action, command.
  • Asymmetric actor-critic: Only the critic receives privileged information (body linear velocity). This choice avoids the problem of teacher-student distillation being “tied to the teacher’s occupancy measure.”
  • Terrain generation: Wave Function Collapse (WFC) places stair segments, corners, and flat tiles in a constraint-satisfying manner. 5×5 tiles, robot spawned in the center.
  • Four-level curriculum: Step heights [1,3] → [1,7] → [1,10] → [1,13] cm. Promotion when the velocity tracking metrics reach \(m_v, m_\omega \ge 0.65\). Domain randomization covers observation noise, mass, base pose, motor gains, and friction.
  • Stack: MuJoCo MJX (GPU physics) + BRAX + PPO, physics dt 5 ms, control 50 Hz. Both actor and critic are MLPs of 512-256-128. Following prior evidence that heightmap input needs no memory mechanism. \(f \sim U[1,3]\), command resampled once per episode.

Experiments and Results

Training environment: i9-14900K + a single RTX 5070. Mean wall time to complete all four levels was 195 minutes for PGTT, 198 for Wild, and 239 for MassLoco, demonstrating “half a day on a consumer GPU.”

Baseline design: MassLoco and Wild had only their reward terms swapped in, with observations, privileged state, network, terrain, and common reward weights all kept identical. This is a controlled design that isolates the effect of the “reward structure” alone. 5 seeds, median + IQR reported.

Evaluation: 2-9 cm obstacles, 1000 rollouts, success rate SR = 1 − early-termination rate, random disturbances of 7.5-30 N applied.

Real robot: Unitree Go2 + L1 LiDAR + Point-LIO → per-cell (mean height, variance) elevation grid map (Fankhauser 2018) + median-fill (inpainting only small holes) → robot-centric 11×9 grid (1.1×0.9 m) heightmap. Policy at 50 Hz, PD \(k_p = 60, k_d = 3\). ANYmal-C was a preliminary experiment with no hyperparameter changes.

Item Value
Discrete-obstacle SR (median, 25%, 75%) PGTT 0.848 / 0.842 / 0.855 · Wild 0.756 / 0.756 / 0.769 · MassLoco 0.702 / 0.659 / 0.711
Disturbance SR PGTT highest, median +7.5% over the runner-up (Wild)
Velocity tracking \(\bar{v} / \bar{\omega}\) PGTT 0.965 / 0.991, similar across the three methods
Convergence PGTT ≈ Wild, MassLoco about 2x slower at level 1
Ablation (7 cm stairs) full 0.834 / w/o foot phase 0.755 / w/o foot contact 0.826
Real robot Go2 qualitative success (video), up to 0.4 m/s. ANYmal-C preliminary: gait generated with no hyperparameter changes

The three key results are as follows.

  1. Discrete-obstacle SR of 0.848, 9 percentage points above the runner-up compared with Wild 0.756 and MassLoco 0.702, while velocity tracking is equal across the three methods. The success-rate gain was achieved without sacrificing tracking.
  2. The ablation confirms the mechanism. Removing the foot phase term drops SR from 0.834 to 0.755, showing that this term is the main driver, while the foot contact term reinforces edge cases from 0.826 to 0.834. PGTT’s slight drop in velocity tracking reflects behavior that prioritizes balance over speed on stairs.
  3. Successful sim-to-real on the Go2. It walked over stairs and discrete obstacles and withstood real disturbances. The sparsity of the L1 LiDAR (21,600 points/s) limited it to a maximum of 0.4 m/s.

Weighing claims against evidence, there are two caveats. First, the compared “Wild” is not the original paper’s full teacher-student/belief-encoder system but a reimplementation with only its reward terms ported. This is correct as a controlled experiment, but reading it as “beat the Wild system” would be an overinterpretation. Second, the evidence for the “morphology-agnostic” claim is only the qualitative, preliminary result that a gait was generated on ANYmal-C with no hyperparameter changes, with no success rate. The authors themselves label it preliminary.

Conclusion and Significance

This paper changed the answer to “where to put the structure.” It showed through controlled experiments that moving the gait prior from the action space (oscillator/IK) to the reward maintains or improves performance, and from here on an “IK-free phase prior” becomes a legitimate default option in perceptive locomotion RL. That a minimal device adjusting the swing apex with a single scalar \(\delta H\) raised discrete-obstacle SR by 9 percentage points is a case showing that the connection from perception to locomotion is possible without a complex terrain encoder. Lowering the training cost to a single consumer GPU and about three hours with the MJX + BRAX stack is also a substantive contribution from the community’s perspective.

From a robotics practice perspective, the takeaways are as follows.

  • Where it can be used: When you want to train and swap stair and discrete-obstacle locomotion policies yourself on a quadruped simulation testbed. The repository is complete with training (3 variants: PGTT/baseline/wild, curriculum), simulation deployment, real-robot deployment (Unitree SDK, joystick, Docker + ROS 2 perception pipeline), WFC terrain generation, and evaluation utilities. Reproduction difficulty is low to moderate; the likely sticking points are JAX/CUDA version matching and the real-robot Point-LIO Docker setup. Whether pretrained checkpoints are provided was not confirmed from the documentation.
  • Standardization of the perception stack: The real-robot pipeline is built from general-purpose components, namely Point-LIO + probabilistic elevation map + median-fill + robot-centric heightmap, so a team that already has an elevation mapping stack for autonomous mobile-robot navigation in multi-floor indoor buildings can supply the perception input themselves.
  • Limits of the training distribution: With a curriculum maximum step height of 13 cm and a focus on local 5×5-tile scenes, long continuous staircases (switchbacks), unstructured continuous terrain mixing gravel and slopes, and slippery surfaces are unverified. Stationary and low-speed behavior is also not trained (there is no MassLoco stand-still term), so a stop gate must be added at the operations layer.
  • Real-robot speed and sensors: The L1 LiDAR’s sparsity imposed the 0.4 m/s ceiling, but the quantitative relationship between heightmap update latency and speed was not presented. A denser LiDAR is expected to alleviate this, but there is no verification.
  • Unevaluated items: Energy efficiency (acknowledged by the authors), failure modes of median-fill correction (large holes, dynamic objects), and the boundaries of policy robustness. A single multi-morphology policy (morphology conditioning of the reward) is future work.

References

  • Paper: arXiv 2510.18348 · Code: github.com/NtagkasAlex/phase_guided_terrain_traversal
  • Miki et al., Learning Robust Perceptive Locomotion for Quadrupedal Robots in the Wild (2022)
  • Shao et al., Learning Free Gait Transition for Quadruped Robots via Phase-Guided Controller (2022)
  • Rudin et al., Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning (2022)
  • Lee et al., Learning Quadrupedal Locomotion over Challenging Terrain (2020)
  • Fankhauser et al., Probabilistic Terrain Mapping for Mobile Robots with Uncertain Localization (2018)