A Stable Nonlinear Switched System for Landmark-aided Motion Planning

Abstract

To guarantee navigation accuracy, the robotic applications utilize landmarks. This paper proposes a novel nonlinear switched system for the fundamental motion planning problem in autonomous mobile robot navigation: the generation of continuous collision-free paths to a goal configuration via numerous land- marks (waypoints) in a cluttered environment. The proposed system leverages the Lyapunov-based control scheme (LbCS) and constructs Lyapunov-like functions for the system’s subsystems. These functions guide a planar point-mass object, representing an autonomous robotic agent, towards its goal by utilizing artificial landmarks. Extracting a set of nonlinear, time-invariant, continuous, and stabilizing switched velocity controllers from these Lyapunov-like functions, the system invokes the controllers based on a switching rule, enabling hierarchical landmark navigation in complex environments. Using the well-known stability criteria by Branicky for switched systems based on multiple Lyapunov functions, the stability of the proposed system is provided. A new method to extract action landmarks from multiple landmarks is also introduced. The control laws are then used to control the motion of a nonholonomic car-like vehicle governed by its kinematic equations. Numerical examples with simulations illustrate the effectiveness of the Lyapunov-based control laws. The proposed control laws can automate various processes where the transportation of goods or workers between different sections is required.