Connectivity-Aware Exploration of Robotic Grasp Spaces

Maksim A Kazanskii

cs.ROSep 19, 2026

Connectivity-Aware Exploration of Robotic Grasp Spaces

Authors: Maksim A Kazanskii

Organizations: Independent Researcher

Abstract

Robotic grasping is typically formulated as the problem of identifying successful actions from a space of candidate grasp poses. However, the organization of successful actions within this space has received less attention. We study the multiscale structure of viable robotic grasps in $SE(3)$ and investigate whether this structure can be exploited for more efficient exploration. Using a large-scale grasp dataset, we show that successful grasp sets exhibit heterogeneous and reproducible connectivity structure across objects. We then introduce a connectivity-aware sampling strategy that incrementally explores the currently observed grasp space by prioritizing potential bridges between components, structural frontiers, boundary extensions, and geometric novelty. In controlled reconstruction experiments, the method recovers the connectivity structure of successful grasp sets substantially more efficiently than random sampling and farthest-point sampling. We further evaluate whether connectivity acquired under hidden grasp viability can improve subsequent grasp discovery, and whether structural experience from previously explored objects can be retrieved and transferred to unseen objects. These results suggest that the spatial organization of viable actions provides information relevant to grasp-space exploration beyond the viability of individual candidate actions. More broadly, they motivate structure-aware exploration as a means of exploiting the geometry of viable action spaces in robotic manipulation.

Figures & tables

Fig. 1 : Convergence of the grasp-space connectivity signature with sample size. The curve shows the mean within-object structural distance $E(N)$ across 100 objects, with 95% bootstrap confidence intervals across objects. Independent samples become increasingly consistent as the number of successful grasps increases.

Fig. 2 : Within-object and between-object structural distances at $N=50$ , $100$ , and $300$ successful grasps. Within-object distances decrease strongly with sample size, whereas between-object distances remain substantially larger and comparatively stable. Sampling variability therefore decreases with $N$ while object-specific differences in multiscale connectivity persist. Vertical lines show the interquartile range and circles denote medians.

Panel of Figure 3 — Fig. 3 : Examples of viable grasp-space structure across six objects. Successful grasps are colored according to connected components computed in the original normalized SE(3) grasp space, while failed grasps are shown in gray. The two-dimensional MDS embedding is used only for visualization. Each panel reports the connectivity radius $\epsilon$ , number of connected components $\beta_{0}$ , and relative size $L$ of the largest component.

Random observations	Objects matched by CA	Median CA observations	Median speedup
50	200/200	12	$4.17\times$
100	200/200	21	$4.76\times$
200	192/200	93	$2.15\times$

TABLE I : Sample efficiency of connectivity-aware (CA) exploration in E2. For each Random sampling budget, we report the median number of CA observations required to achieve the same connectivity-reconstruction error. Speedup is computed per object as the Random budget divided by the required CA observations and then summarized by the median.

$N$	Exploration	Method	Phase 2 successes	Normalized AUC	Mean gain [95% CI] (%)
200	Random	Random	$25.13\pm 1.14$	$0.5020\pm 0.0295$	–
		NS	$30.97\pm 4.45$	$0.6638\pm 0.1054$	$+32.66\;[+29.62,\,+35.80]$
		LV	$31.20\pm 4.16$	$0.6699\pm 0.1007$	$+33.94\;[+30.93,\,+37.04]$
		CA	$31.02\pm 4.18$	$0.6528\pm 0.0983$	$+30.56\;[+27.61,\,+33.57]$
	CA	Random	$25.13\pm 1.14$	$0.5020\pm 0.0295$	–
		NS	$29.77\pm 4.47$	$0.6526\pm 0.1050$	$+30.44\;[+27.39,\,+33.51]$

TABLE II : Hidden-viability exploitation under Random and connectivity-aware (CA) Phase 1 exploration across candidate-set sizes. Phase 2 success counts and normalized AUC are reported as mean

\pm

SD across objects after averaging over five seeds. Gains are computed relative to Random exploitation under the same Phase 1 exploration policy and reported as mean [95% CI]. NS denotes nearest-success and LV local viability.

Panel of Figure 6 — Fig. 4 : Phase 2 exploitation performance following connectivity-aware (CA) Phase 1 exploration. Left: mean Phase 2 AUC gain relative to Random exploitation as a function of total candidate-set size $N$ ; error bars show 95% bootstrap confidence intervals across objects. Right: distributions of object-level Phase 2 AUC gains relative to Random exploitation at $N=1600$ ; points denote individual objects, circles indicate medians, and vertical bars indicate interquartile ranges.

Fig. 5 : E4 cross-object viability-history transfer as a function of memory-library size $M$ and transfer weight $\alpha$ at 200 attempts. Cells show mean normalized AUC $\pm$ 95% confidence intervals. Random, FPS, and CA are shown as non-transfer baselines. Moderate transfer weights improve CA, whereas complete reliance on transferred information ( $\alpha=1$ ) reduces performance.

Fig. 6 : Performance across interaction budgets at fixed memory size $M=200$ . Cells report mean normalized AUC $\pm$ 95% confidence intervals across target objects for Random, FPS, CA, and memory-assisted CA at different transfer weights $\alpha$ .

Fig. 7 : Ranked per-object memory gain at $M=200$ and $\alpha=0.5$ . Target objects are independently ranked by $\Delta\mathrm{nAUC}=\mathrm{nAUC}_{\mathrm{CA+Memory}}-\mathrm{nAUC}_{\mathrm{CA}}$ for each budget. Positive values indicate improvement from cross-object memory.

Attempts	CA	CA+Memory	Mean $\Delta$	Median $\Delta$	Win rate
100	0.720	0.737	+0.017	+0.012	68.5%
200	0.747	0.756	+0.009	+0.004	61.0%
400	0.750	0.749	-0.001	$\approx 0.000$	48.0%

TABLE III : Effect of cross-object memory across interaction budgets at

M=200

and

\alpha=0.5

\Delta

denotes the paired per-object difference

\mathrm{nAUC}_{\mathrm{CA+Memory}}-\mathrm{nAUC}_{\mathrm{CA}}

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

\widetilde{H}_{A}=\left(S_{A}^{+}\cup S_{j^{*}}^{+},\,S_{A}^{-}\cup S_{j^{*}}^{-}\right)

Appendix

Algorithm 1 Cross-Object Viability-History Transfer

$M$	Method	Retrieval (s)	Pool- $\mathcal{B}$ (ms)	Total (s)
–	Random	–	$1.59\pm 1.58$	$(1.61\pm 1.58)\times 10^{-3}$
–	FPS	–	$0.74\pm 0.09$	$(2.87\pm 0.31)\times 10^{-3}$
–	CA	–	$27.45\pm 1.57$	$3.73\pm 0.23$
200	E4	$37.98\pm 0.67$	$1067\pm 133$	$42.73\pm 0.81$
400	E4	$75.90\pm 1.37$	$1073\pm 103$	$80.64\pm 1.42$
600	E4	$113.91\pm 2.19$	$1077\pm 95$	$118.66\pm 2.27$

Appendix

TABLE IV : Runtime per target at

Q=400

(mean

\pm

SD; 25 runs). Retrieval and Pool-

\mathcal{B}

costs are one-time operations.

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EigenDEXplore: Structured Exploration for Dexterous Manipulation with Human Priors

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Dexterous manipulation poses a challenging high-dimensional optimization problem, as useful behaviors require coordinated motion across many hand joints. In reinforcement learning (RL) and sampling-based trajectory optimization, exploration commonly relies on independent robot joint perturbations, making coordinated behaviors difficult to discover. Prior work reduces this search space for grasp learning using low-dimensional spaces of coordinated joint motions learned from human hand data, but this restricts the expressivity required for general manipulation. Some combine learned and joint-space actions to restore expressivity, but this increases dimensionality and introduces redundancy. We study these effects across diverse manipulation settings, varying action dimensionality, exploration strategy, and the source of human data. Our experiments suggest that human-motion priors are most effective when used to structure exploration rather than change the action representation. Motivated by this finding, we propose EigenDEXplore, which induces correlated exploration by adding perturbations along human-derived eigenvectors to independent joint-space noise, leaving the action space unchanged. Across multiple dexterous hands, EigenDEXplore consistently outperforms joint-space and learned action-space baselines in grasping, in-hand reorientation, and contact-rich manipulation. These gains span unstructured and reference-guided RL, trajectory optimization, and sim-to-real deployment, and are largest in settings with less reward shaping and curriculum design.

Abstract

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