Path Following Using Dynamic Transverse Feedback Linearization for Car-Like Robots

Abstract

This paper presents an approach for designing pathfollowing controllers for the kinematic model of car-like mobile robots using transverse feedback linearization with dynamic extension. This approach is applicable to a large class of paths and its effectiveness is experimentally demonstrated on a Chameleon R100 Ackermann steering robot. Transverse feedback linearization makes the desired path attractive and invariant, while the dynamic extension allows the closed-loop system to achieve the desired motion along the path.

A Guiding Vector-Field Algorithm for Path-Following Control of Nonholonomic Mobile Robots

“…The simplest model of this type is the unicycle, which can move only in the longitudinal direction while the lateral motion is impossible. Examples of robots, reducing under certain conditions to the unicycle-type kinematics, include differential drive wheeled mobile robots [13], [39], fixed wing aircraft [30], [31], [36], marine vessels at cruise speeds [35] and car-like vehicles, whose rear wheels are not steerable [13], [20], [39]. The most interesting are unicycle models where the speed is restricted to be sufficiently high, making it impossible to reduce the unicycle to a holonomic model via the feedback linearization [40].…”

“…Suppose that t * = ∞. Differentiating the function (11) along the trajectories, it can be shown thaṫ V = u r eψ ′ (ψ −1 (e))n ⊤m (20) = (20) = u r eψ ′ (ψ −1 (e))n ⊤ [m d cos δ − Em d sin δ] (14) = (14) = u r eψ ′ (ψ −1 (e)) |v|n ⊤ [v cos δ − Ev sin δ]…”

Path Following for a Class of Underactuated Systems Using Global Parameterization

“…A path following problem is more general compared to a trajectory tracking problem, as a path can be treated as a set of trajectories [4]. Moreover, the path following framework allows achieving path invariance, which means that once the system converges to the path, it stays on it for all future time [5].…”

Control Design of LCL Type Grid-Connected Inverter Based on State Feedback Linearization

“…In order to solve the global control problem, many solutions have been put forward [8,9]. Among them, the state feedback linearization method that develops from differential geometry [10,11] has become an effective way to solve the nonlinear power electronics system control problems. Based on the differential homeomorphism, Lie derivative is used to analyze the numerical relation between the state variables, the input variables, and the output variables.…”