Encircling General 2-D Boundaries by Mobile Robots with Collision Avoidance: A Vector Field Guided Approach

2025-01-04

AI Summary

This paper addresses the autonomous boundary-enclosing problem for unknown two-dimensional boundaries of arbitrary shape. We propose a real-time enclosing control method that requires no prior analytical expression of the boundary. Our approach features two key innovations: (1) a novel joint modeling framework combining sampled-point-based Fourier curve fitting with polar-angle parameterization, enabling robust representation of both star-shaped and non-star-shaped boundaries; and (2) a vector-field guidance scheme incorporating distance error, integrated with Control Barrier Functions (CBFs) and Quadratic Programming (QP) to jointly enforce boundary tracking, dynamic obstacle avoidance, and actuator input saturation constraints. Extensive simulations and physical experiments demonstrate the method’s robustness in enclosing complex boundaries—including star-shaped and concave contours—under realistic conditions. The framework is directly applicable to practical scenarios such as border surveillance and environmental contamination containment.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

The ability to automatically encircle boundaries with mobile robots is crucial for tasks such as border tracking and object enclosing. Previous research has primarily focused on regular boundaries, often assuming that their geometric equations are known in advance, which is not often the case in practice. In this paper, we investigate a more general case and propose an algorithm that addresses geometric irregularities of boundaries without requiring prior knowledge of their analytical expressions. To achieve this, we develop a Fourier-based curve fitting method for boundary approximation using sampled points, enabling parametric characterization of general 2-D boundaries. This approach allows star-shaped boundaries to be fitted into polar-angle-based parametric curves, while boundaries of other shapes are handled through decomposition. Then, we design a vector field (VF) to achieve the encirclement of the parameterized boundary, wherein a polar radius error is introduced to measure the robot's ``distance'' to the boundary. The controller is finally synthesized using a control barrier function and quadratic programming to mediate some potentially conflicting specifications: boundary encirclement, obstacle avoidance, and limited actuation. In this manner, the VF-guided reference control not only guides the boundary encircling action, but can also be minimally modified to satisfy obstacle avoidance and input saturation constraints. Simulations and experiments are presented to verify the performance of our new method, which can be applied to mobile robots to perform practical tasks such as cleaning chemical spills and environment monitoring.

Problem

• Mobile Robotics
• Boundary Encirclement
• Autonomous Algorithms

Innovation

• Vector Field Guidance
• Fourier-Based Curve Fitting
• Autonomous Boundary Encirclement