Efficient Path Generation with Curvature Guarantees by Mollification

• URL: http://arxiv.org/abs/2512.13183v2
• Date: Thu, 05 Mar 2026 09:41:45 GMT
• Title: Efficient Path Generation with Curvature Guarantees by Mollification
• Abstract summary: We present a method to regularize non-differentiable functions and generate feasible paths through mollification.<n>Specifically, we approximate an arbitrary path with a differentiable function that can converge to it with arbitrary precision.<n>The proposed approach is analytically more efficient than standard methods, enabling real-time implementation on microcontrollers.
• Score: 2.6381163133447836
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Path generation, the process of converting high-level mission specifications, such as sequences of waypoints from a path planner, into smooth, executable paths, is a fundamental challenge in mobile robotics. Most path following and trajectory tracking algorithms require the desired path to be defined by at least twice continuously differentiable functions to guarantee key properties such as global convergence, especially for nonholonomic robots like unicycles with speed constraints. Consequently, path generation methods must bridge the gap between convenient but non-differentiable planning outputs, such as piecewise linear segments, and the differentiability requirements imposed by downstream control algorithms. While techniques such as spline interpolation or optimization-based methods are commonly used to smooth non-differentiable paths or create feasible ones from sequences of waypoints, they either produce unnecessarily complex trajectories or are computationally expensive. In this work, we present a method to regularize non-differentiable functions and generate feasible paths through mollification. Specifically, we approximate an arbitrary path with a differentiable function that can converge to it with arbitrary precision. Additionally, we provide a systematic method for bounding the curvature of generated paths, which we demonstrate by applying it to paths resulting from linking a sequence of waypoints with segments. The proposed approach is analytically shown to be computationally more efficient than standard interpolation methods, enabling real-time implementation on microcontrollers, while remaining compatible with standard trajectory tracking and path following algorithms.

Related papers

• Utility-Based Path Selection and Configuration in Quantum Networks via Layered Shortest Paths [20.986889484035093]
  A path in a quantum network is a chain of repeaters that distributes entanglement between two users.<n>We show how a path's performance depends jointly on its route and its per-link settings.<n>A single run returns the full rate fidelity frontier, from which the path maximizing any nondecreasing utility function can be selected.
  arXiv  Detail & Related papers  (2026-09-14T18:30:46Z)
• AutoPath: Learning Transferable Goal-Conditioned Stochastic Path Prior for Safe Navigation Without Human Demonstrations [103.61864552260316]
  Real-time navigation in dynamic environments requires collision-free and dynamically feasible motion under limited perception.<n>We formulate navigation as learning a transferable goal-aligned path prior that models a reusable distribution over goal-aligned geometry-consistent local paths conditioned on local observations.<n>We develop a structured prior learning framework that parameterizes local paths using a geometry-aware polar action manifold and incorporates risk-sensitive utility shaping with multi-goal distributional rollouts for stable and safety-aware planning.
  arXiv  Detail & Related papers  (2026-07-13T16:00:41Z)
• Integrated Graph Search and Model Predictive Control for Smooth and Efficient Path Planning in Autonomous Vehicles [1.228397872697275]
  A rough path is first obtained via Dijkstra search on a discretized grid.<n>A Model Predictive Control problem is formulated to refine the path.<n>The proposed algorithm is evaluated in multiple overtaking scenarios on both straight and curved roads.
  arXiv  Detail & Related papers  (2026-07-05T12:14:33Z)
• Directional Mollification for Controlled Smooth Path Generation [2.6381163133447836]
  Mollification has been recently proposed as a computationally efficient and analytically tractable tool for path generation.<n>We introduce directional mollification, a novel operator that resolves this limitation while retaining the analytical tractability of classical mollification.
  arXiv  Detail & Related papers  (2026-03-23T11:18:43Z)
• Smooth trajectory generation and hybrid B-splines-Quaternions based tool path interpolation for a 3T1R parallel kinematic milling robot [0.0]
  This paper presents a smooth trajectory generation method for a four-degree-of-freedom parallel milling robot.<n>The proposed approach integrates B-spline and Quaternion kinematic techniques to manage decoupled position and orientation data points.<n>The method offers enhanced accuracy, reduced velocity fluctuations, and computational efficiency compared to conventional methods.
  arXiv  Detail & Related papers  (2026-02-18T11:57:52Z)
• Enhanced UAV Path Planning Using the Tangent Intersection Guidance (TIG) Algorithm [0.0]
  Tangent Intersection Guidance (TIG) is an advanced approach for UAV path planning in both static and dynamic environments.<n>It generates two sub-paths for each threat, selects the optimal route based on an algorithm rule, and iteratively refines the path until the target is reached.<n>TIG demonstrates efficient real-time path planning capabilities for collision avoidance, outperforming APF and Dynamic APPATT algorithms.
  arXiv  Detail & Related papers  (2025-08-26T12:11:59Z)
• Enhancing Path Planning Performance through Image Representation Learning of High-Dimensional Configuration Spaces [0.4143603294943439]
  We present a novel method for accelerating path-planning tasks in unknown scenes with obstacles.<n>We approximate the distribution of waypoints for a collision-free path using the Rapidly-exploring Random Tree algorithm.<n>Our experiments demonstrate promising results in accelerating path-planning tasks under critical time constraints.
  arXiv  Detail & Related papers  (2025-01-11T21:14:52Z)
• Pathwise optimization for bridge-type estimators and its applications [49.1574468325115]
  Pathwise methods allow to efficiently compute the full path for penalized estimators.<n>We apply these algorithms to the penalized estimation of processes observed at discrete times.
  arXiv  Detail & Related papers  (2024-12-05T10:38:29Z)
• Finding Transformer Circuits with Edge Pruning [71.12127707678961]
  We propose Edge Pruning as an effective and scalable solution to automated circuit discovery.<n>Our method finds circuits in GPT-2 that use less than half the number of edges compared to circuits found by previous methods.<n>Thanks to its efficiency, we scale Edge Pruning to CodeLlama-13B, a model over 100x the scale that prior methods operate on.
  arXiv  Detail & Related papers  (2024-06-24T16:40:54Z)
• GraphWalks: Efficient Shape Agnostic Geodesic Shortest Path Estimation [93.60478281489243]
  We propose a learnable network to approximate geodesic paths on 3D surfaces. The proposed method provides efficient approximations of the shortest paths and geodesic distances estimations.
  arXiv  Detail & Related papers  (2022-05-30T16:22:53Z)
• On Constraints in First-Order Optimization: A View from Non-Smooth Dynamical Systems [99.59934203759754]
  We introduce a class of first-order methods for smooth constrained optimization. Two distinctive features of our approach are that projections or optimizations over the entire feasible set are avoided. The resulting algorithmic procedure is simple to implement even when constraints are nonlinear.
  arXiv  Detail & Related papers  (2021-07-17T11:45:13Z)
• DiffCo: Auto-Differentiable Proxy Collision Detection with Multi-class Labels for Safety-Aware Trajectory Optimization [5.35056843248536]
  We present DiffCo, the first, fully auto-differentiable, non-parametric model for collision detection. It provides robust gradients for trajectory optimization via backpropagation and is often 10-100x faster to compute than its geometric counterparts.
  arXiv  Detail & Related papers  (2021-02-15T09:31:26Z)
• Hybrid Trilinear and Bilinear Programming for Aligning Partially Overlapping Point Sets [85.71360365315128]
  In many applications, we need algorithms which can align partially overlapping point sets are invariant to the corresponding corresponding RPM algorithm. We first show that the objective is a cubic bound function. We then utilize the convex envelopes of trilinear and bilinear monomial transformations to derive its lower bound. We next develop a branch-and-bound (BnB) algorithm which only branches over the transformation variables and runs efficiently.
  arXiv  Detail & Related papers  (2021-01-19T04:24:23Z)
• Accelerated Message Passing for Entropy-Regularized MAP Inference [89.15658822319928]
  Maximum a posteriori (MAP) inference in discrete-valued random fields is a fundamental problem in machine learning. Due to the difficulty of this problem, linear programming (LP) relaxations are commonly used to derive specialized message passing algorithms. We present randomized methods for accelerating these algorithms by leveraging techniques that underlie classical accelerated gradient.
  arXiv  Detail & Related papers  (2020-07-01T18:43:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.