Humans expand their locomotion capability by wearing appropriate footwear, such as hiking boots for mountains or skates for ice. Footwear changes the ground-contact interface and enables traversal of otherwise difficult terrain. In contrast, locomotion controllers are typically trained for a fixed morphology, and their performance can degrade when shoes alter foot geometry, mass, and friction. We propose SHOES, a sample-efficient framework for adapting locomotion policies to footwear-induced morphology changes. SHOES freezes a simulation-trained nominal policy and fine-tunes only lightweight, identity-initialized modulation modules on the robot, preserving the initial behavior while enabling efficient hardware adaptation. We also introduce SafeBox, a workspace-aware waypoint sampler that constrains online adaptation within a user-defined workspace. The simulation results with a shoe-equipped Unitree Go2 show that SHOES substantially recovers locomotion performance after footwear-induced morphology changes using limited additional adaptation. Under the same adaptation budget, SHOES outperforms FiLM-only, Linear Adapter-only, and residual-RL baselines. Real-world experiments on a Unitree Go2 fitted with human shoes further evaluate the effectiveness of SHOES for hardware deployment.
Figures & tables
Figure 1: A Unitree Go2 wearing shoes.
Figure 2: Bare-foot nominal degrades with shoes attached. Commanded-direction velocity at the 0.3 m/s setpoint for the same bare-foot nominal policy, executed on bare feet (blue) and after attaching shoes (green); the dashed ring marks the target. The morphology shift induced by shoes particularly degrades backward-command tracking.
Figure 3: SHOES two-stage training pipeline. Stage 1 trains a nominal PPO actor-critic on the bare-foot Go2 in simulation with 4096 parallel envs; the resulting πnom becomes the frozen base for Stage 2. Stage 2 wraps the frozen nominal MLP (gray, ∼190 k params) with a trainable FiLM generator and a Linear Adapter (coral, ∼5.6 k params); PPO online-fine-tunes the trainable modules on the shoe-equipped Go2 with the SafeBox sampler at 1 env ×30 k env-steps.
Figure 4: SHOES recovers bare-foot tracking across speeds and directions. Per-direction tracked velocity at the three command speeds ( 0.3,0.6,1.0 m/s). SHOES (red, best seed from Appendix F ) closely matches the bare-foot nominal reference (blue), while the no-adapt nominal on shoes (green) tracks well inside it across all directions and speeds.
FiLM
Adapter
Trainable
BFP ↑
Δ BFP ↑
✗
✗
0
67.0
0.0
✗
✓
0.2 k
65.1±8.9
−1.9
✓
✗
5.4 k
78.7±10.8
+11.7
✓
✓
5.6 k
93.5±3.9
+26.5
Table 1: Component ablation ( 30 k-step budget). Δ BFP is the gain over the no-adapt nominal (first row).
Figure 5: Method comparison (flat shoes). Bare-Foot Parity (%) mean ± std over six seeds. Dashed line: no-adapt nominal.
Figure 6: Simulated footwear variants: (a) Curve Foot, (b) Single Geta, (c) Double Geta, and (d) Skates.
Table 8
Figure 7: SHOES recovers backward-velocity tracking on hardware. Backward setpoint vxcmd=−0.30 m/s on the physical Unitree Go2 with flat shoes. (a) SHOES (red) substantially improves backward tracking over the no-adapt nominal on shoes (blue); the bare-foot nominal (green) is shown for reference (black dashed line: command). (b) Snapshots of the robot in the three settings overlaid in the left panel.
Figure 8: Real-robot traversal over a slotted surface. With shoes, the robot crosses the openings (top); without shoes, it becomes trapped (bottom).
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Parameter
Value
Parallel environments
1
Steps per environment per rollout
256
PPO epochs per update
3
Mini-batches per epoch
4
Total PPO iterations
117
Total environment steps
30,000
Appendix
Table 4: Stage-2 PPO hyper-parameters.
Reward
Equation ri
Weight wi
Lin. velocity tracking
exp(−[∥vxycmd−vxy∥2+2vz2]/σlin2)
+1.0
Ang. velocity tracking
exp(−[(ωzcmd−ωz)2+0.05∥ωxy∥2]/σang2)
+1.0
Body orientation
∥gxyproj∥2
−1.0
Posture
exp(−∣J∣1∑j(θj−θjdefault)2/σpose,j(vcmd)2)
+1.0
Body angular velocity
∥ωxy∥2
−0.05
Angular momentum
∥Lroot∥2
−0.025
Appendix
Table 5: Stage-1 rewards (bare-foot nominal training). vxycmd,ωzcmd : commanded linear/yaw velocity (body frame); vxy,vz,ωxy : base linear and angular velocities; gxyproj : projected gravity (body horizontal); θ,θ¨ : joint positions and accelerations; θdefault : default joint pose; Lroot : root angular momentum; pzi,vxyi,Fi : foot i height, xy velocity (world), contact force; ci∈{0,1} : stance indicator; ηi∈{0,1} : first-contact (landing) indicator; θjlow,θjup : soft joint position limits; “terminated” covers fall (base tilt >70∘ ) and non-foot contact ( >10 N); Tphase=0.6 s, pztgt=0.10 m, σlin2=0.25 , σang2=0.5 .
Humans readily adapt their movements as their bodies change through aging, injury, or load carrying, but learning-based robot policies often break when hardware properties shift. We introduce an online embodiment adaptation framework for quadrupedal locomotion that infers embodiment parameters from short interaction histories and conditions control on the inferred hardware state. Our method pairs a generalist policy trained under embodiment randomization with a lightweight adaptation module that identifies physical changes within half a second. We evaluate two representative forms of embodiment variation: joint-range constraints and trunk-mass changes, corresponding to joint-level kinematic degradation and body-level dynamic variation. In simulation, the module accurately estimates these changes and enables closed-loop control that substantially outperforms policies conditioned directly on interaction history. On a real Unitree Go2 robot, our system maintains stable locomotion under severe instances of the evaluated changes, including a fully locked leg and a 5 kg payload, where non-adaptive methods fail. These results demonstrate the practicality of explicit online embodiment identification for rapid adaptation to joint-limit and payload-mass changes, and provide a step toward handling broader forms of uncertain, degraded, or changing robot hardware.
Dichen Li, Bo Ai, Nico Bohlinger +3
UC San Diego · Stanford University · TU Darmstadt +2
Simulation trained legged locomotion policies often exhibit performance loss on hardware due to dynamics discrepancies between the simulator and the real world, highlighting the need for approaches that adapt the simulator itself to better match hardware behavior. Prior work typically quantify these discrepancies through precise, time-aligned matching of joint and base trajectories. This process requires motion capture, privileged sensing, and carefully controlled initial conditions. We introduce a practical alternative based on proprioceptive distribution matching, which compares hardware and simulation rollouts as distributions of joint observations and actions, eliminating the need for time alignment or external sensing. Using this metric as a black-box objective, we explore adapting simulator dynamics through parameter identification, action-delta models, and residual actuator models. Our approach matches the parameter recovery and policy-performance gains of privileged state-matching baselines across extensive sim-to-sim ablations on the Go2 quadruped. Real-world experiments demonstrate substantial drift reduction using less than five minutes of hardware data, even for a challenging two-legged walking behavior. These results demonstrate that proprioceptive distribution matching provides a practical and effective route to simulator adaptation for sim-to-real transfer of learned legged locomotion.
Jeremy Dao, Alan Fern
Collaborative Robotics and Intelligent Systems Institute, Oregon State University, Corvallis, Oregon, 97331, USA.
Developing natural and diverse locomotion controllers for quadruped robots that can adapt to complex terrains while preserving motion style remains a significant challenge. Existing imitation-based methods face a fundamental optimization trade-off: strict adherence to motion capture (mocap) references penalizes the geometric deviations required for terrain adaptability, whereas terrain-centric policies often compromise stylistic fidelity. We introduce LatentMimic, a novel locomotion learning framework that decouples stylistic fidelity from geometric constraints. By minimizing the marginal latent divergence between the policy's state-action distribution and a learned mocap prior, our approach provides a conditional relaxation of rigid pose-tracking objectives. This formulation preserves gait topology while permitting independent end-effector adaptations for irregular terrains. We further introduce a terrain adaptation module with a dynamic replay buffer to resolve the policy's distribution shifts across different terrains. We validate our method across four locomotion styles and four terrains, demonstrating that LatentMimic enables effective terrain-adaptive locomotion, achieving higher terrain traversal success rates than state-of-the-art motion-tracking methods while maintaining high stylistic fidelity.
Zhiquan Wang, Yunyu Liu, Dipam Patel +3
Department of Computer Science, Purdue University, USA