Sim-to-Real Transfer for Biped Locomotion

• Sim-to-real transfer for biped locomotion is a suite of strategies designed to bridge the gap between simulated training and physical robot deployment.
• It employs model-centric gap minimization and policy-centric hardening to address discrepancies in dynamics, actuation, and sensor feedback.
• The approach integrates advanced techniques such as system identification, domain randomization, and vision-based adaptation to enhance robustness on varying terrains.

Sim-to-real transfer for biped locomotion encompasses a suite of methodologies and algorithmic strategies that facilitate the reliable deployment of locomotion policies learned in simulation to physical bipedal robots. The challenge arises from inevitable modeling discrepancies—including actuation dynamics, contact modeling, state estimation errors, and numerical artifacts—that constitute the “sim-to-real gap” and often lead to degraded performance or outright failures when naive policies are deployed outside simulation. Recent research delineates two complementary approaches: (i) model-centric gap minimization, which systematically refines the simulator and aligns it with reality, and (ii) policy-centric hardening, which imposes robustness and adaptive properties into the controller via in-simulation training and post-deployment mechanisms. This article reviews the mathematical underpinnings, algorithmic structures, and practical design patterns that define current practice in sim-to-real transfer for bipedal locomotion.

1. Sources of Sim-to-Real Gap in Biped Locomotion

The performance drop experienced when deploying a simulated biped controller on real hardware is primarily traceable to four mechanisms (Bao et al., 9 Nov 2025):

1. Robot Dynamics and Actuator Mismatch: Simulators typically rely on idealized rigid-body models and first-order actuator models, whereas real robots exhibit multi-timescale motor and transmission dynamics, significant gear friction, backlash, and actuator delays. Omitting these effects yields poor torque prediction and insufficient compliance, destabilizing hardware transfer.
2. Contact and Terrain Modeling Errors: Simulation contact solvers use either complementarity or penalty formulations with approximate stiffness, damping, and friction coefficients. Real terrains introduce nonuniform, unmeasured compliance, friction variability, and stick-slip transitions not captured in simulation, resulting in unanticipated gaits and stance behaviors.
3. State Estimation and Sensing Noise: On real robots, proprioceptive state is recovered via sensor fusion, often affected by latency, drift, and quantization noise. Simulated agents trained on noise-free or privileged observations are not robust to these errors.
4. Numerical and Solver Artifacts: Time discretization, integrator choice, and numerical tolerance settings introduce energy drift and spurious impulses, making dynamics diverge from hardware over time.

These discrepancies motivate comprehensive strategies for both simulator alignment and policy robustness.

2. Model-Centric Gap Minimization Techniques

Reducing the sim-to-real gap via model-centric strategies comprises several complementary approaches:

• High-Fidelity Actuator and Transmission Modeling: For gear-driven bipeds, incorporating nonlinear gear efficiency, backdrivability, and Stribeck friction in simulation (as in the DTE+Stribeck model) accurately predicts torque transmission and compliance critical for hardware transfer (Masuda et al., 2022).
• Offline System Identification: Parameter vectors (inertia, friction, delays, sensor latencies) are estimated via trajectory matching between real hardware and simulation, often using CMA-ES or Bayesian techniques. Two-stage approaches—pre-sysID to bracket parameter bounds, and post-sysID to fine-tune over task performance—are particularly effective (Yu et al., 2019).
• Residual Dynamics Learning: Explicit learning of residual mismatch via a neural additive term in the simulator, or the use of hybrid models such as the GRFM-Net, can compensate for actuator, contact, and friction errors while preserving differentiability for MPC autotuning (Chen et al., 24 Sep 2024).
• Sensor and Filter Emulation: By injecting bias, noise, latency, and applying realistic Kalman or complementary filtering in simulation, the observation pipeline more closely mimics reality, enabling robust policy training (Bao et al., 9 Nov 2025).
• Closed-Chain and Constraint Modeling: For bipeds with parallel kinematic structures, modeling holonomic constraints, constraint forces, and joint couplings is essential. Neglecting these and using serial-chain approximations leads to systematic errors prohibiting successful transfer (Maslennikov et al., 14 Jul 2025).

3. Policy-Centric Robustness: Domain Randomization and Curriculum

Domain randomization and policy hardening complement model-centric gap minimization:

• Dynamics and Actuation Randomization: Randomizing link masses, friction, inertia, joint damping, sensor noise, actuator delay, and even contact parameters across wide—yet physically plausible—intervals induces robustness to real-world parameter drift (Li et al., 2021, Singh et al., 2023). Curriculum schedules, which gradually widen randomization ranges or task difficulty, improve sample efficiency and prevent convergence to trivial behaviors.
• Adversarial Training and Symmetry-Aware Priors: Injecting adversarial perturbations (in target velocities or contact forces) and enforcing left-right gait symmetry via explicit loss terms regularizes the learned policy, increasing gait robustness and recovery under unmodeled disturbances (Maslennikov et al., 14 Jul 2025).
• Smoothing and Policy Regularization: Lipschitz-constrained policies enforce direct bounds on policy output gradients, yielding smooth, jitter-free outputs that obviate the need for hand-tuned low-pass filters or smoothness rewards, and transfer with high fidelity across platforms (Chen et al., 15 Oct 2024).
• Torque-Action Policies and Compliance: Directly learning torque policies, rather than position- or velocity-based controllers, imparts inherent compliance, reducing the dependence on manual gain tuning and improving robustness to early or unanticipated contact, actuator nonlinearity, and contact modeling discrepancies (Kim et al., 2023).

4. System Identification and Adaptive Policy Architectures

System identification and policy architectures contribute to adaptation and transferability:

• Latent-Variable or Projected Universal Policies (PUP): Using a projection network to map high-dimensional physical parameter uncertainties to a compact latent space enables fast post-deployment adaptation via Bayesian optimization on task-relevant outcomes, without retraining the full policy (Yu et al., 2019).
• Memory-Based Architectures for Online System ID: Recurrent networks (LSTM/RNN) equipped with sufficient dynamics randomization explicitly encode uncertain dynamics in memory, enabling the policy to infer and track plant variables such as center-of-mass offset or friction, effectively embedding online system identification within the control loop (Siekmann et al., 2020).
• Residual and Student-Teacher Adaptation: Training “student” policies with only realistic (imperfect) sensors to mimic “teacher” policies privileged with full state mitigates observation mismatch. Residual policy learning allows for post-deployment correction of nominal policies.

5. Integrated Training and Evaluation Pipelines

State-of-the-art pipelines integrate both model and policy-centric methods for robust sim-to-real transfer:

• Zero-Shot Transfer with Minimal Real-World Tuning: Policies trained on heavily randomized dynamical models with appropriate reward structures and observation pipelines succeed without any on-hardware fine-tuning, consistently meeting or exceeding the robustness of classical model-based controllers under variable terrain, actuator degradation, or sensor drift (Singh et al., 2023, Singh et al., 18 Apr 2025).
• Multi-Objective and Constrained RL: For underactuated or point-foot bipeds, constrained RL with explicit gait, posture, and ground-force constraints, enforced as terminations, yields robust, stable behaviors even without online adaptation or sensing beyond proprioception (Roux et al., 4 Aug 2025).
• Specialization vs. Generalization: Training either specialized policies for specific extrinsic conditions (e.g., dynamic loads) or universal policies spanning a distribution of loads illustrates clear trade-offs; bootstrapped policies show improved sample efficiency and higher robustness across dynamic perturbations (Dao et al., 2022). Hybrid strategies may leverage both.

6. Vision-Based and Terrain-Adaptive Sim-to-Real Transfer

Advances in integrating perception for sim-to-real transfer in complex, real-world environments:

• NeRF-based Visual Simulation and Contact Geometry: Scene geometry learned via Neural Radiance Fields provides photorealistic RGB rendering and mesh extraction for contact simulation, enabling vision-based locomotion and object interaction policies transferable to physical robots (Byravan et al., 2022).
• Heightmap and Depth-Predictor Modularization: Biped policies conditioned on local terrain heightmaps predicted by depth-image encoders facilitate robust gait adaptation to challenging terrain without any real-world pose estimation or fine-tuning. Heavy domain randomization over predictor noise, image artifacts, and delays underpins successful transfer (Duan et al., 2023).
• Constraint Learning for Footstep Planning: RL-based policies trained to respect exogenous, potentially vision-driven footstep constraints (e.g., via perception pipelines) and equipped with supervised transition models for one-step feasibility allow seamless integration into locomotive planners (Duan et al., 2022).

7. Metrics, Evaluation, and Practical Guidelines

Objective evaluation of sim-to-real efficacy hinges on:

• Quantitative Metrics: Distance to fall, survival time, tracking error (velocity, position), energy cost, cost of transport (CoT), push recovery threshold, and action/position/velocity jitter serve as standardized benchmarks (Chen et al., 15 Oct 2024, Roux et al., 4 Aug 2025).
• Practical Guidelines:
  • Focus randomization on parameters with the largest reality gap (actuator friction, delay, transmission compliance).
  • Explicitly model closed-chain constraints, friction, and compliance for parallel kinematic bipeds.
  • Prefer simple, well-calibrated randomization sets over overly broad ranges to ensure policy trainability.
  • Use low-gain or compliant control strategies with current feedback to absorb actuation model mismatch (Singh et al., 2023).
  • Conduct pre-deployment simulation in intermediate or higher-fidelity simulators before risking hardware.

The synthesis of precise modeling, disciplined randomization, advanced adaptive architectures, and robust reward structures yields controllers that reliably bridge the sim-to-real gap for bipedal locomotion, enabling deployment in varied, unpredictable, and perceptually demanding environments (Bao et al., 9 Nov 2025).