Performance Comparison of Classical and Neural Sampling Algorithms for Robotic Navigation

Sampling-based algorithms for robot path planning offer probabilistic completeness and strong empirical convergence properties across environments with diverse obstacle configurations. However, in practice, these methods often require many iterations to obtain high-quality solutions. This paper proposes Convex-Neural RRT*, an enhanced RRT* variant that incorporates neural guidance to predict informative waypoint regions near high-quality paths. Convex candidate regions are extracted from these predictions, enabling the planner to concentrate exploration on geometrically relevant areas while preserving global exploration. The proposed algorithm is evaluated against Neural RRT*, Neural Informed RRT*, classical RRT*, and LTA* across three environment types and 18 benchmark maps. Experimental results show that Convex-Neural RRT* reduces computation time by 30-75% compared to neural-guided variants and up to 88-98% relative to LTA*, while achieving an average path length reduction of approximately 5% compared to classical RRT*, with larger improvements observed in complex environments. The method also maintains an overall success rate above 99% across varying obstacle densities. These findings indicate that convex-guided neural sampling provides an effective balance between computational efficiency and solution quality, supporting its applicability to time-sensitive robotic navigation tasks.

Mobile robot path planning methods are often constrained by vast search spaces, resulting in latency in samplingbased algorithms. Learning-based approaches frequently suffer from local region fragmentation and global topological inconsistency. To tackle the problem, we present the Connectivity- Preserving Region Proposal Network (CP-RPN), a segmentationguided model designed to predict compact and topologically connected candidate regions, significantly compressing the search space. Specifically, we design a segmentation model that leverages a Deformable Attention Transformer (DAT) to capture long-range dependencies for global connectivity, with a Deconvolutional decoder to preserve fine-grained spatial details. To guarantee the connectivity of the predicted mask, we design a composite loss function that combines Cross-Entropy loss for pixelwise supervision, a Connectivity-Aware loss to enhance local coherence, and a Topological Continuity loss based on persistent homology to enforce global connectivity. Building on these highconnectivity corridor-like regions, the Voronoi diagram is used to plan the path, backed by a local A* fallback mechanism to ensure robustness. Experimental results demonstrate that CPRPN reduces the candidate region size by over 60.13% compared to the MPT baseline and achieves deterministic low-latency planning (avg. 0.11s) with a 99.60% success rate, outperforming traditional sampling-based algorithms in stability.

The exploration of high-dimensional spaces remains a challenging problem, in particular in the presence of narrow passages and small clearances. We propose novel sampling-based path-planning methods for high-dimensional spaces combining Rapidly-exploring Random Trees (RRT) and Hit-and-Run (HAR) random walks by decoupling the point being extended from the direction of extension. We also show that RRT and HAR appear as special cases of a generic algorithm coupling the biases used for the point and direction extension, respectively. We further study a sparse-move strategy in which only a fraction p_r of the robots is moved at each step, helping both RRT and the proposed HAR algorithms handle cluttered instances. Tests are presented for two families of models: classical piano mover problems in 3D, and complex molecular systems involving tens of rigid domains moving relatively to one another -- the latter viewed as independent robots exploring the motion space SE(3)N . Within seconds on a standard laptop, our algorithms solve instances with up to 64 robots and 384 degrees of freedom. We conclude by suggesting one of our methods, HARF, as the method of choice for complex multi-robot planning problems, being up to two orders of magnitude faster than the classical RRT moving all robots at each step--when it succeeds at all, and still up to 2.4 fold faster on most instances when both use their best p_r.