A bipedal robot increased its stride length when an unannounced test changed the surface beneath it from high stiffness to low stiffness, according to a preprint. The controller reportedly maintained dynamic stability during the transition.
The system, called MILD, targets tractable terrain modeling for bipedal locomotion on deformable surfaces. It pairs a contact solver with terrain-aware reinforcement learning.
How the model was built
The contact solver represents the robot’s foot as 154 elements and models penetration independently across them, allowing contact forces to vary across the foot rather than treating the interaction as uniform.
MILD’s learning stack combines an asymmetric actor-critic, a VAE-based estimator and a modulation network. These components create latent terrain representations—internal signals associated with the surface under the robot.
In simulation, the controller was trained with 4,096 parallel Isaac Gym agents for 20,000 episodes, while contact scenarios were randomized during training.
What the comparisons showed
In simulation, MILD was reported to produce 38% deeper penetration than the Ecc-Spring contact model, along with longer slip distances. Compared with a passivity-based whole-body controller, it was also reported to show smaller centre-of-mass oscillations and greater stability during dynamic walking.
The hardware evaluation covered six terrain types. The authors report increased foot clearance on softer surfaces, as well as the highest success rate and energy efficiency among the approaches compared; exact success rates and variability were not given.
Across seven terrain types, the robot completed 10 forward-and-backward walking cycles at a commanded 1.2 metres per second on each terrain without a reported failure. Baseline contact-model controllers tested on 45d foam were reported to use insufficient swing-foot clearance and to encounter joint-limit violations or loss of stability.
At a commanded speed of 1.2 metres per second, MILD’s reported cost of transport—a measure calculated from actuator power, weight and velocity—was 0.83, compared with 1.08 for HT-2 and 1.42 for Clock. Maximum torque was 88.4 newton-metres for MILD, 91.6 for HT-2 and 115.2 for Clock; measured velocities were 1.15, 1.28 and 1.09 metres per second, respectively.
What the evidence does—and does not—say
A t-SNE visualization showed distinct latent clusters associated with the spectrum from stiffer to more deformable terrain. The plot is a qualitative visualization, not a quantitative measure of terrain-identification accuracy.
The design does not isolate the contact solver’s contribution from the rest of MILD. The solver, estimator, modulation network and reinforcement-learning components are combined in the reported system.
Hardware validation used an EngineAI SA01 bipedal robot with 12 degrees of freedom and a 100 Hz PD joint controller. The results therefore do not establish how the approach would perform on other robot morphologies, materials or long-term operations.
Independent repeated-trial counts were not reported, and the performance table gives point values without stated variability. The authors identify visual terrain-deformation perception and extensions to multiple gaits as future work; the current results do not establish performance with visual-only terrain perception.
Paper data and sources
Original title: MILD: Tractable Terrain Modeling for Learning Improved Bipedal Locomotion on Deformable Surfaces
Authors: Zeren Luo, Jiahui Zhang, Zhe Xu et al.
Journal/Repository: IEEE Robotics and Automation Letters (2025)
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text