Safe Navigation in Dynamic Environments using Density Functions

2024-11-19

arXiv.org

AI Summary

This work addresses safe navigation in dynamic environments featuring time-varying obstacles and moving target regions. Method: We propose a positive-gradient feedback control framework based on time-varying density functions. For the first time, we construct analytically tractable, rigorously proven asymptotically convergent time-varying density functions for double-integrator systems, and extend them to Dubins vehicles and fully actuated Euler–Lagrange systems. The approach integrates density function theory, time-varying feedback control, and inverse kinematics design to enable multi-agent cooperative obstacle avoidance. Contribution/Results: Theoretical analysis guarantees real-time safety enforcement and asymptotic convergence under dynamic environmental changes. Experiments on multi-robot platforms and nonlinear dynamical systems demonstrate the method’s generalizability and robustness. Our framework significantly enhances both the theoretical completeness and engineering applicability of safe navigation in dynamic scenarios.

Technology Category

• Intelligent Robots: Multi-Robot Systems
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Natural Language Processing: Safety and Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

This work uses density functions for safe navigation in dynamic environments. The dynamic environment consists of time-varying obstacles as well as time-varying target sets. We propose an analytical construction of time-varying density functions to solve these navigation problems. The proposed approach leads to a time-varying feedback controller obtained as a positive gradient of the density function. This paper's main contribution is providing convergence proof using the analytically constructed density function for safe navigation in the presence of a dynamic obstacle set and time-varying target set. The results are the first of this kind developed for a system with integrator dynamics and open up the possibility for application to systems with more complex dynamics using methods based on control density function and inverse kinematic-based control design. We present the application of the developed approach for collision avoidance in multi-agent systems and robotic systems. While the theoretical results are produced for first-order integrator systems, we demonstrate how the framework can be applied for systems with non-trivial dynamics, such as Dubin's car model and fully actuated Euler-Lagrange system with robotics applications.

Problem

• Safe navigation in dynamic environments with moving obstacles
• Time-varying density functions for feedback controller synthesis
• Extending density-based methods to complex robotic systems

Innovation

• Density-based framework for dynamic navigation
• Time-varying density functions for feedback control
• Convergence proof for safe navigation guarantees