Peg-Insertion Success Rate in Robotics

• Peg-insertion success rate is defined as the ratio of successful robotic insertions to total attempts under strict geometric and clearance criteria.
• Methodologies incorporate tactile, force/torque, and vision-based feedback to enhance accuracy under varying pose uncertainties.
• Advanced control strategies and adaptive techniques directly improve robustness and reliability in industrial robotic assembly.

A peg-insertion success rate is a core quantitative metric in robotic assembly research, defined as the empirical proportion of attempted insertions in which a robotic system achieves a specified criterion of successful peg entry into a mating hole under task-imposed constraints. This concept appears as a primary evaluation index in a wide range of peg-in-hole studies, spanning force/torque-controlled, vision-driven, tactile-based, and hybrid control strategies. The success rate allows direct benchmarking of controllers, sensory feedback modalities, policy architectures, and adaptation techniques under varying mechanical clearances, pose uncertainties, and object geometries.

1. Formal Definition and Variants

Across the literature, the success rate $SR$ is universally defined as the ratio of the number of successful insertions, $N_{\text{success}}$, to the number of attempted trials, $N_{\text{total}}$:

$$\text{Success Rate} = \frac{N_{\text{success}}}{N_{\text{total}}} \times 100\%$$

as explicitly detailed in "Tactile-based Active Inference for Force-Controlled Peg-in-Hole Insertions" (Kamijo et al., 2023), "Design of Adaptive Compliance Controllers for Safe Robotic Assembly" (Jha et al., 2022), and other works.

The precise criterion for a "successful" insertion is task-specific but typically demands that the peg be fully inserted to a nominal depth inside the hole within prescribed geometric clearances (on the order of sub-millimeter to several millimeters), with no detectable jamming, catastrophic collision, or forced termination from safety limits or cycle timeouts. For example, (Kamijo et al., 2023) requires full entry under a clearance $\leq 0.1\,\mathrm{mm}$. Some works use stricter definitions incorporating pose error (e.g., position $<3\,\mathrm{mm}$ and orientation $<0.05$\,rad (Liu et al., 5 Apr 2025)) or controller horizon constraints (e.g., within 600 steps or 30\,s (Vezzani et al., 2020)).

A common extension is stratification of $SR$ by object geometry, clearance, or external perturbation, with empirical counts (e.g., 36/40 successes $\rightarrow$ 90\%). Confidence intervals are rarely reported, but direct binomial or Wilson estimates are implied (cf. (Yajima et al., 4 Mar 2026)).

2. Methodologies for Measuring and Reporting

• Experimental Trials: Most papers execute $N_{\text{total}}$ independent insertion attempts under randomized initial conditions (object pose, grasp angle, hole position) to empirically estimate $N_{\text{success}}$0. Typical $N_{\text{success}}$1 ranges from 20–100 per geometry (Kamijo et al., 2023, Jha et al., 2022, Negi et al., 25 May 2025).
• Closed-Loop Control Interventions: Policies may include re-planning or iterative corrective trials, reporting both $N_{\text{success}}$2 and average/maximum number of corrective actions (Lee et al., 2023, Kim et al., 2021).
• Multiple Metrics: Some studies subdivide $N_{\text{success}}$3 into task phases—for instance, hole identification $N_{\text{success}}$4 versus end-to-end insertion $N_{\text{success}}$5 (Yajima et al., 8 Mar 2025).
• Generalization: Performance on both "seen" and "unseen" pegs/holes is documented to validate robustness (Lee et al., 2023, Zhang et al., 14 May 2025).

3. Reported Success Rates across Approaches

A survey of recent results demonstrates that state-of-the-art methods routinely achieve high ($N_{\text{success}}$6) peg-insertion success rates under carefully engineered feedback and control architectures, while baseline or ablated methods exhibit substantially lower $N_{\text{success}}$7, particularly in tight-clearance or uncertain pose conditions.

Method/Reference	Task/Modalities	Object(s)	Clearance	$N_{\text{success}}$8	Success Rate (\%)
RL+Active Inference (Kamijo et al., 2023)	RL + Tactile Feedback	Cuboid	0.08 mm	40	90
RL+Active Inference (Kamijo et al., 2023)	RL + Tactile Feedback	Pulley	0.3 mm	40	93
RL-Only Baseline (Kamijo et al., 2023)	RL Only, No Tactile	Cuboid	0.08 mm	20	5
Multi-Task RL (Vezzani et al., 2020)	SAC-X+RHPO (RL)	Star Peg	5 mm	1000s (ep.)	85-90 (real, sim)
Privileged Sim2Real (Fuchioka et al., 2024)	Privileged FT Sim2Real	Circle peg	--	20	80–100
Adaptive Compliance (Jha et al., 2022)	Linear GP+Accom.	Cylinder	1.0 mm	20	100
Contact Manifold (Negi et al., 5 Jul 2025)	Contact-Only, SE(3) est.	5 complex, indus.	0.1–1.0 mm	125–375	96.7 (10s)

These $N_{\text{success}}$9 values demonstrate step-changes as algorithmic innovations (active alignment, contact-manifold registration, privileged learning) are introduced.

4. Key Factors Influencing Success Rates

• Uncertainty Compensation: Approaches explicitly addressing grasp and hole pose uncertainty, through online inference (Kamijo et al., 2023, Fuchioka et al., 2024), compliance (Jha et al., 2022), or multimodal perception (Zhang et al., 14 May 2025), consistently achieve higher $N_{\text{total}}$0 in the presence of perturbations.
• Sensing Modality: The inclusion of tactile or force–torque feedback dramatically boosts $N_{\text{total}}$1 for tight clearance insertions ($N_{\text{total}}$20.1\,mm), where vision-only methods saturate at lower levels (Kamijo et al., 2023, Liu et al., 5 Apr 2025).
• Policy and Controller Design: Dual-policy architectures, privileged sim-to-real teacher-student pipelines, and physically-grounded contact-manifold registration (MLP or ICP-based) are correlated with near-perfect $N_{\text{total}}$3 (Negi et al., 25 May 2025, Lee et al., 2023, Negi et al., 5 Jul 2025).
• Data and Training Strategies: Methods not requiring large datasets (self-augmentation, feature-level sim2real adaptation) offer high $N_{\text{total}}$4 at minimal real-world labeling effort (Kamijo et al., 2023, Lee et al., 2023).
• Geometry Generalization: Frameworks validated on multiple object geometries maintain $N_{\text{total}}$5 even on unseen shapes (Lee et al., 2023, Fuchioka et al., 2024).

5. Comparative Baseline Performance and Limitations

Baseline policies, such as pure force-control RL without tactile feedback, classical compliance without learned correction, or direct insertion without pose estimation, manifest marked declines in $N_{\text{total}}$6 under uncertainty or tight tolerances. For example, in (Kamijo et al., 2023), $N_{\text{total}}$7 drops to $N_{\text{total}}$8 for a cuboid under $N_{\text{total}}$9 clearance when tactile alignment is removed, versus $$\text{Success Rate} = \frac{N_{\text{success}}}{N_{\text{total}}} \times 100\%$$0 with the dual-policy. Non-adaptive compliance fails $$\text{Success Rate} = \frac{N_{\text{success}}}{N_{\text{total}}} \times 100\%$$1 of the time when misalignment exceeds $$\text{Success Rate} = \frac{N_{\text{success}}}{N_{\text{total}}} \times 100\%$$2 (Jha et al., 2022); primitive-based insertion without state estimation yields $$\text{Success Rate} = \frac{N_{\text{success}}}{N_{\text{total}}} \times 100\%$$3 $$\text{Success Rate} = \frac{N_{\text{success}}}{N_{\text{total}}} \times 100\%$$4 on complex industrial shapes (Negi et al., 5 Jul 2025).

6. Mathematical Formulations and Statistical Considerations

• Success Rate Formula: See above.
• Specialized Success Criteria: Some studies impose explicit geometric or statistical criteria, e.g., successful if $$\text{Success Rate} = \frac{N_{\text{success}}}{N_{\text{total}}} \times 100\%$$5 (Negi et al., 5 Jul 2025), or $$\text{Success Rate} = \frac{N_{\text{success}}}{N_{\text{total}}} \times 100\%$$6 before a timeout (Fuchioka et al., 2024).
• Correction and Step Counts: Mean corrections per insertion are reported to contextualize efficiency ($$\text{Success Rate} = \frac{N_{\text{success}}}{N_{\text{total}}} \times 100\%$$7 for adaptive linear GP (Jha et al., 2022), $$\text{Success Rate} = \frac{N_{\text{success}}}{N_{\text{total}}} \times 100\%$$8 for PolyFit on seen shapes (Lee et al., 2023)).
• Variance and Confidence Intervals: Most works report only empirical counts; formal error bars are infrequent but computable via binomial models (see (Yajima et al., 4 Mar 2026) for Wilson intervals).

7. Impact, Applications, and Future Prospects

High peg-insertion success rates underpin progress in autonomous industrial assembly, zero-shot generalization, and safety in contact-rich environments. They are directly linked to reliability, cycle time, and adaptability of robotic systems to variable geometries, tolerances, and environmental conditions. Emerging research leverages active inference, compliant hardware (soft wrists, impedance), contact-rich pose estimation, and cross-modal learning to continually raise $$\text{Success Rate} = \frac{N_{\text{success}}}{N_{\text{total}}} \times 100\%$$9, even for previously intractable assembly scenarios.

Ongoing challenges include scaling $\leq 0.1\,\mathrm{mm}$0 to tasks with dynamic misalignment, deformable parts, or sub-10\,$\leq 0.1\,\mathrm{mm}$1m clearance, systematic reporting of confidence intervals, and standardizing protocols across platforms and assembly geometries. The success rate remains the canonical, yet evolving, quantitative measure of progress in this domain.