Safe Vector Field for Robot Navigation in N-Dimensions
Arthur Henrique Dias Nunes, Vinicius Mariano Gonçalves, Luciano Pimenta
AI summary
Problem
Traditional reactive obstacle avoidance methods rely on discontinuous Euclidean distance functions, leading to non-smooth control laws, local minima, and a lack of formal safety guarantees for dynamic, generic-shaped obstacles in n-dimensional environments.
Approach
The authors replace the discontinuous distance metric with a smooth, bounded approximation and blend it with a path-following vector field using barrier-function-based switching, ensuring continuous control and formal safety proofs.
Key results
- Smooth half-squared distance function bounded by true Euclidean distance
- Formal safety guarantees via barrier certificates and Lyapunov convergence proofs
- Continuous control law eliminating discontinuities and local minima
- Experimental validation across ground robots, quadcopters, and multi-robot systems
Why it matters
Enables reliable, computationally lightweight safe navigation for autonomous systems in complex, dynamic environments without heavy online optimization or global path planning.
Abstract
In this work, we propose a novel artificial vector field for robot navigation in n-dimensional path-following tasks, designed to ensure safety and convergence with a smoothed control law. Unlike previous methods based on discontinuous Euclidean distance functions, our approach uses a smooth Euclidean-like function to achieve a continuous control law formulation and a field combination to balance the objectives of avoiding obstacles and following the path. This results in a navigation method that follows a target path while preventing robots from approaching obstacles, which can be used in different applications. We provide formal proofs for safety using barrier functions concepts and path convergence via Lyapunov theory. The methodology is validated through extensive numerical simulations and real-world experiments. Those include extrapolations of the methodology in more complex cases, such as quadcopters and multi-robot systems to underline the method’s advantages in achieving safe and reliable robot navigation.