Path following using dynamic transverse feedback linearization for car-like robots

Akhtar, A., Nielsen, C., & Waslander, S. L. (2015). Path Following Using Dynamic Transverse Feedback Linearization for Car-Like Robots. IEEE Transactions on Robotics, 31(2), 269–279. https://doi.org/10.1109/TRO.2015.2395711This paper presents an approach for designing path following 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.Partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC

Dynamic path following controllers for planar mobile robots

In the field of mobile robotics, many applications require feedback control laws that provide perfect path following. Previous work has shown that transverse feedback linearization is an effective approach to designing path following controllers that achieve perfect path following and path invariance. This thesis uses transverse feedback linearization and augments it with dynamic extension to present a framework for designing path following controllers for certain kinematic models of mobile robots. This approach can be used to design path following controllers for a large class of paths. While transverse feedback linearization makes the desired path attractive and invariant, dynamic extension allows the closed-loop system to achieve the desired motion along the path. In particular, dynamic extension can be used to make the mobile robot track a desired velocity or acceleration profile while moving along a path

Nonlinear and Geometric Controllers for Rigid Body Vehicles

In this thesis we investigate the motion control problem for a class of vehicles C V , which includes satellites, quadrotors, underwater vehicles, and tailsitters. Given a globally represented model of C V , and a curve, the motion control problem entails following the curve using control inputs. In this thesis the motion control problem is viewed under two settings, 1) as a local path following problem, 2) as a geometric trajectory tracking problem. We provide solutions to both problems by designing controllers based on the concept of feedback linearization. In the local path following problem, the C V class of vehicles is represented by a local chart. The problem is solved in a monolithic control setting, and the path that needs to be followed is treated as a set to be stabilized. The nonlinear model under study is first dynamically extended and then converted into a fully linear form through a coordinate transformation and smooth feed- back. This approach achieves path invariance. We also design a fault tolerant local controller that ensure path following and path invariance in the presence of a one rotor failure for a quadrotor. The second major problem addressed is the geometric trajectory tracking problem, which is treated in an inner-outer loop setting. Specifically, we design a controller class for the attitude dy- namics of the C V class of vehicles. The novel notion of Lie algebra valued functions are defined on the Special Orthogonal group SO(3), which constitutes a family of functions. This family of functions induces a novel geometric controller class, which consists of almost globally stable and locally stable controllers. This class is designed using the idea of feedback linearization, and is proven to be asymptotically stable through a Lyapunov-like argument. This allows the system to perform multiple flips. We also design geometric controllers for the position loop, which are demonstrated to work with the attitude controller class through simulations with noisy sensor data

Synchronized closed-path following for a mobile robot and an Euler-Lagrange system

We propose and solve a synchronized path following problem for a differential drive robot modeled as a dynamic unicycle and an Euler-Lagrange system. Each system is assigned a simple closed curve in its output space. The outputs of systems must approach and traverse their assigned curves while synchronizing their motions along the paths. The synchronization problems we study in this thesis include velocity synchronization and position synchronization. Velocity synchronization aims to force the velocities of the systems be equal on the desired paths. Position synchronization entails enforcing a positional constraint between the systems modeled as a constraint function on the paths. After characterizing feasible positional constraints, a finite-time stabilizing control law is used to enforce the position constraint

Robust Spline Path Following for Redundant Mechanical Systems

Path following controllers make the output of a control system approach and traverse a pre-specified path with no a priori time-parametrization. The first part of the thesis implements a path following controller for a simple class of paths, based on transverse feedback linearization (TFL), which guarantees invariance of the path to be followed. The coordinate and feedback transformation employed allows one to easily design control laws to generate arbitrary desired motions on the path for the closed-loop system. The approach is applied to an uncertain and simplified model of a fully actuated robot manipulator for which none of the dynamic parameters are measured. The controller is made robust to modelling uncertainties using Lyapunov redesign. The experimental results show a substantial improvement when using the robust controller for path following versus standard state feedback. In the second part of the thesis, the class of paths and systems considered are extended. We present a method for path following control design applicable to framed curves generated by spline interpolating waypoints in the workspace of kinematically redundant mechanical systems. The class of admissible paths include self-intersecting curves. Kinematic redundancies of the system are resolved by designing controllers that solve a suitably defined constrained quadratic optimization problem that can be easily tuned by the designer to achieve various desired poses. The class of redundant systems considered include mobile manipulators for a large class of wheeled ground vehicles. The result is a path following controller that simultaneously controls the manipulator and mobile base, without any trajectory planning performed on the mobile base. The approach is experimentally verified using the robust controller developed in the first part of the thesis on a 4-degree-of-freedom (4DOF) redundant manipulator and a mobile manipulator system with a differential drive base

Coordinated path following of unicycles : A nested invariant sets approach

The final publication is available at Elsevier via http://dx.doi.org/https://doi.org/10.1016/j.automatica.2015.06.033. © 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We formulate a coordinated path following problem for N unicycle mobile robots as an instance of a nested set stabilization problem. Stabilization of the first set corresponds to driving the unicycles to their assigned paths. Stabilization of the second set, a subset of the first, corresponds to meeting the coordination specification. The first set is stabilized in a decentralized manner using feedback linearization. For arbitrary coordination tasks we utilize feedback linearization to stabilize the nested set in a centralized manner. In the special case in which coordination entails making the unicycles maintain a formation along their paths, we propose semi-distributed control law under less restrictive communication assumptions. Experimental results are provided

Wheeled Mobile Robots: State of the Art Overview and Kinematic Comparison Among Three Omnidirectional Locomotion Strategies

In the last decades, mobile robotics has become a very interesting research topic in the feld of robotics, mainly because of population ageing and the recent pandemic emergency caused by Covid-19. Against this context, the paper presents an overview on wheeled mobile robot (WMR), which have a central role in nowadays scenario. In particular, the paper describes the most commonly adopted locomotion strategies, perception systems, control architectures and navigation approaches. After having analyzed the state of the art, this paper focuses on the kinematics of three omnidirectional platforms: a four mecanum wheels robot (4WD), a three omni wheel platform (3WD) and a two swerve-drive system (2SWD). Through a dimensionless approach, these three platforms are compared to understand how their mobility is afected by the wheel speed limitations that are present in every practical application. This original comparison has not been already presented by the literature and it can be used to improve our understanding of the kinematics of these mobile robots and to guide the selection of the most appropriate locomotion system according to the specifc application

Coordinated path following: A nested invariant sets approach

In this thesis we study a coordinated path following problem for multi-agent systems. Each agent is modelled by a smooth, nonlinear, autonomous, deterministic control-affine ordinary differential equation. Coordinated path following involves designing feedback controllers that make each agent's output approach and traverse a pre-assigned path while simultaneously coordinating its motion with the other agents. Coordinated motion along paths includes tasks like maintaining formations, traversing paths at a common speed and more general tasks like making the positions of some agents obey functional constraints that depend on the states of other agents. The coordinated path following problem is viewed as a nested set stabilization problem. In the nested set stabilization approach, stabilization of the larger set corresponds to driving the agents to their assigned paths. This set, under suitable assumptions, is an embedded, controlled invariant, product submanifold and is called the multi-agent path following manifold. Stabilization of the nested set, contained in the multi-agent path following manifold, corresponds to meeting the coordination specification. Under appropriate assumptions, this set is also an embedded controlled invariant submanifold which we call the coordination set. Our approach to locally solving nested set stabilization problems is based on feedback equivalence of control systems. We propose and solve two local feedback equivalence problems for nested invariant sets. The first, less restrictive, solution gives necessary and sufficient conditions for the dynamics of a system restricted to the larger submanifold and transversal to the smaller submanifold to be linear and controllable. This normal form facilitates designing controllers that locally stabilize the coordination set relative to the multi-agent path following manifold. The second, more restrictive, result additionally imposes that the transversal dynamics to the larger submanifold be linear and controllable. This result can simplify designing controllers to locally stabilize the multi-agent path following manifold. We propose sufficient conditions under which these normal forms can be used to locally solve the nested set stabilization problem. To illustrate these ideas we consider a coordinated path following problem for a multi-agent system of dynamic unicycles. The multi-agent path following manifold is characterized for arbitrary paths. We show that each unicycle is feedback equivalent, in a neighbourhood of its assigned path, to a system whose transversal and tangential dynamics to the path following manifold are both double integrators. We provide sufficient conditions under which the coordination set is nonempty. The effectiveness of the proposed approach is demonstrated experimentally on two robots