Sim2Real Domain Gap in Robotics

Updated 3 July 2025

Simulation-to-Reality (Sim2Real) domain gap is the performance disparity observed when robotic designs optimized in simulation are applied in real hardware due to modeling discrepancies.
The study employs a parameterized morphology design space, quantifying lift performance using metrics like mean lift force and complexity measures for bio-inspired flapping-wing robots.
Findings reveal a non-monotonic relationship where moderate complexity designs minimize the gap, guiding adaptive simulation improvements and automated design optimizations.

Simulation-to-Reality (Sim2Real) Domain Gap

The simulation-to-reality (Sim2Real) domain gap refers to the performance degradation observed when robotic controllers, policies, or designs optimized in simulation are transferred to real-world hardware. This gap arises due to discrepancies between simulated environments and physical reality in terms of physical laws, dynamics, sensor models, and unmodeled real-world phenomena. Understanding, quantifying, and minimizing the Sim2Real gap is a central challenge in the field of robotics, especially for automated design, control, and learning.

1. Parameterized Morphology Design Space for Sim2Real Study

The investigation of the Sim2Real gap in the context of robot design necessitates a highly parameterized, systematic exploration of the morphological (shape and structure) space. In the examined paper, this is achieved through a bio-inspired, parameterized morphospace for flapping-wing robots, which abstracts key features from a variety of biological exemplars—such as dragonflies, butterflies, and birds—without direct imitation. The design space is characterized by a genotype-phenotype mapping, where the genotype encodes morphological parameters and the phenotype is the assembled physical or simulated robot. Key parameters include wing planform geometry (via segmented “blades”), total span, elasticity profiles (via chordwise and spanwise spring-like ribs), inertia distributions (wing mass allocation), and the number of discrete segments used for modeling (controlling both morphology and simulation fidelity). This provides a tractable yet expressive space for automated design and evolutionary optimization, allowing both simulation and hardware fabrication of resultant morphologies.

2. Measurement and Quantification of the Sim2Real Gap

Empirical quantification of the Sim2Real gap is realized by directly comparing task performance of each design in simulation and on physical hardware using identical actuation protocols (fixed-frequency flapping for all wings). The principal metric is mean lift force ( $L$ ) averaged over repeated flapping cycles. The Sim2Real gap for any morphology $m$ is formalized as a normalized metric:

$\operatorname{STR}(m) = \frac{L_R(m) - L_S(m)}{L^{\max}}$

where $L_R(m)$ is real-world mean lift, $L_S(m)$ is simulated mean lift, and $L^{\max}$ is the highest simulated lift across all designs. $\operatorname{STR}=0$ indicates perfect sim-real alignment; positive values mean reality outperforms simulation; negative values indicate overprediction in sim.

To relate the gap to design complexity and simulation fidelity, a morphological simulation complexity metric is defined:

$C_{MS}(m) = \frac{1}{2} \left( \frac{B(m)}{B^{\max}} + \frac{S(m)}{S^{\max}} \right)$

Here, $B(m)$ is the number of blades (segments), $S(m)$ is span, $B^{\max}$ and $S^{\max}$ are maximal values in the dataset, and $C_{MS}$ thus combines mesh granularity and size.

3. Non-Monotonicity of the Reality Gap with Respect to Morphological Complexity

Contrary to the intuitive expectation that more complex or high-fidelity simulations would monotonically close the Sim2Real gap, the findings in flapping-wing robots reveal pronounced non-monotonicity as a function of morphological complexity. For wings with $C_{MS} \lesssim 0.6$ , the Sim2Real gap remains bounded ( $|\operatorname{STR}| < 0.2$ ), and some designs even show positive $\operatorname{STR}$ —the real robot outperforms simulation. Beyond this threshold, $\operatorname{STR}$ sharply worsens, with simulation increasingly overestimating real performance. Morphological details, especially moderate complexity with low-to-mid aspect ratio, correlate with better transfer—a result confirmed by mapping STR versus $C_{MS}$ and fitting a second-order polynomial, evidencing a clear minimum.

The positive Sim2Real gap in some designs is ascribed to real-world aerodynamic effects such as "wake capture", which are absent from the quasi-static simulation model. Thus, intermediate-complexity designs may uncover performance advantages from physical effects that are not yet faithfully represented in simulation, while highly complex designs become dominated by simulation artifacts.

4. Implications for Automated Design and Optimization

These empirical insights have direct consequences for both automated robot morphology optimization and simulation methodology:

Complexity should not be maximized indiscriminately; design search should focus on the band of $C_{MS}$ where Sim2Real transfer is most reliable.
Identification of morphologies where reality consistently beats simulation can pinpoint missing physical phenomena in simulators, guiding targeted upgrades rather than blanket increases in simulation fidelity.
Optimization frameworks may benefit from incorporating complexity-aware or Sim2Real-aware reward criteria, for instance by dynamically excluding or down-weighting regions of the search space with poor transfer characteristics.
The evidence supports the feasibility of end-to-end, feedback-driven design loops, where Sim2Real outcomes are used to adapt both the design search and simulator calibration iteratively, eventually allowing more robust and automated discovery of transferable robot forms.

5. Key Mathematical Models

Sim2Real Disparity Metric

$\operatorname{STR}(m) = \frac{L_R(m) - L_S(m)}{L^{\max}}$

with $L_R(m)$ (real lift), $L_S(m)$ (simulated lift), and $L^{\max}$ given as above.

Morphological Simulation Complexity

$C_{MS}(m) = \frac{1}{2} \left( \frac{B(m)}{B^{\max}} + \frac{S(m)}{S^{\max}} \right)$

Blades $B(m)$ and maximal values are set by empirical ranges in the design set.

6. Contribution to the Field and Future Directions

This paper provides the first empirical mapping of the Sim2Real gap as a function of morphology in a parameterized robot design space, crucially revealing that this gap is non-monotonic. It identifies a middle regime where simulation remains predictive and transfer is robust—a "sweet spot" for practical automated design. These results suggest future design automation tools should incorporate complexity-sensitive criteria and Sim2Real transferability metrics, and may motivate adaptive or hybrid simulation techniques that evolve with real-world feedback.

The general form of the non-monotonic Sim2Real gap is likely to depend on the nature of the chosen domain, simulator accuracy, and the physical phenomena involved. Thus, analogous methodologies could be adapted for other robot classes, control approaches, or optimization domains.

Summary Table: Sim2Real Gap and Morphological Complexity

Metric	Description	Result in Study
$\operatorname{STR}$	Sim-to-real lift disparity	Non-monotonic in complexity
$C_{MS}$	Composite complexity of morphology/sim	Gap minimized for moderate $C_{MS}$
Best Transfer Regime	Moderate complexity, low aspect ratio	Reality matches/exceeds sim

Advancing Sim2Real understanding to this level of quantitative mapping sets the stage for more principled, efficient, and automated design of high-performing physical robots, reliably transferring from simulation to reality.

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