An Autonomous Dynamical System for Smooth Trajectory Generation in Path Tracking

The precise and smooth control of a robot along a predefined path underpins a multitude of applications, enabling complex environments and task navigation. This paper proposes an innovative autonomous dynamical system for online trajectory generation tailored specifically for the tracking of the desired path with the desired velocity profile. The resultant trajectory serves as the input for the robot's motion controller. The proposed algorithm employs a continuous dynamical system to provide global convergence to the desired path. To achieve this, the desired path is parameterized using so-called phase and speed scale states, which define a position on the path along with a designated velocity, referred to as the target point. The continuous dynamical system is formulated to track this target point while concurrently regulating the evolution of phase and speed scale states to ensure the smooth tracking of the desired path. Upon the convergence to the desired path, the system ensures the convergence of the first time derivative of the trajectory to the desired velocity profile. The efficacy of the proposed algorithm is substantiated through Lyapunov stability analysis and comprehensive simulations.