Optimal and global autonomous navigation in environments with convex obstacles

Abstract

Motion planning for autonomous navigation in unknown environments cluttered with obstacles is a fundamental challenge in robotics, requiring efficient, safe, and reliable strategies for path planning. This thesis introduces two novel autonomous navigation

strategies for vehicles operating in static, unknown n-dimensional environments clut- tered with convex obstacles. The first strategy proposes a continuous feedback controller

that steers a vehicle safely to a target destination in a quasi-optimal manner within a “sphere world,” where each obstacle is enclosed by a sphere-shaped boundary. Under this

approach, the robot avoids obstacles by navigating along the shortest path on the sur- face of the cone enclosing the obstacle and proceeds directly toward the target when no

obstacles obstruct the line of sight. This controller guarantees almost global asymptotic stability in two-dimensional (2D) environments under specific obstacles configurations. An extension of this method is also developed for real-time navigation in unknown, static 2D environments with sufficiently curved convex obstacles, maintaining the same stability guarantees. Simulation and experimental results demonstrate the practical effectiveness of this approach in navigating real-world environments. While the first strategy ensures almost global asymptotic stability only under specific conditions related to the obstacles configuration and for 2D environments, the second strategy aims to provide a more robust solution with stronger stability guarantees. This second strategy introduces a hybrid feedback controller designed to navigate a vehicle in static n-dimensional Euclidean spaces cluttered with spherical obstacles. This approach ensures safe convergence to a predefined destination from any initial position within the

obstacle-free workspace while optimizing obstacle avoidance. A novel switching mecha- nism is proposed to alternate between two operational modes: the motion-to-destination

mode and the obstacle-avoidance mode, ensuring global asymptotic stability regardless of the obstacles’ configuration. Numerical simulations in both known and unknown 2D and 3D environments, along with experimental validation in a 2D setting, demonstrate the effectiveness the proposed approach.

These strategies provide robust solutions for autonomous navigation in static, un- known environments, contributing to the advancement of safe, efficient, and optimal

motion planning techniques for robotic systems in complex, obstacle-laden spaces.