A Stable Nonlinear Switched System for Landmark-aided Motion Planning

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