Exponential ε-tracking and ε-stabilization of second-order nonholonomic SE(2) vehicles using dynamic state feedback

In this paper, we address the problem of ε-tracking and ε-stabilization for a class of SE(2) vehicles with second-order nonholonomic constraints. We introduce a class of transformations called near-identity diffeomorphism that allow dynamic partial feedback linearization of the translational dynamics of this class of SE(2) vehicles. This allows us to achieve global exponential ε-stabilization and ε-tracking (in position) for the aforementioned classes of autonomous vehicles using a coordinate-independent dynamic state feedback. This feedback is only discontinuous w.r.t. the augmented state. We apply our results to ε-stabilization and ε-tracking for an underactuated surface vessel

A layered fuzzy logic controller for nonholonomic car-like robot

A system for real time navigation of a nonholonomic car-like robot in a dynamic environment consists of two layers is described: a Sugeno-type fuzzy motion planner; and a modified proportional navigation based fuzzy controller. The system philosophy is inspired by human routing when moving between obstacles based on visual information including right and left views to identify the next step to the goal. A Sugeno-type fuzzy motion planner of four inputs one output is introduced to give a clear direction to the robot controller. The second stage is a modified proportional navigation based fuzzy controller based on the proportional navigation guidance law and able to optimize the robot's behavior in real time, i.e. to avoid stationary and moving obstacles in its local environment obeying kinematics constraints. The system has an intelligent combination of two behaviors to cope with obstacle avoidance as well as approaching a target using a proportional navigation path. The system was simulated and tested on different environments with various obstacle distributions. The simulation reveals that the system gives good results for various simple environments

Stabilization of non-admissible curves for a class of nonholonomic systems

The problem of tracking an arbitrary curve in the state space is considered for underactuated driftless control-affine systems. This problem is formulated as the stabilization of a time-varying family of sets associated with a neighborhood of the reference curve. An explicit control design scheme is proposed for the class of controllable systems whose degree of nonholonomy is equal to 1. It is shown that the trajectories of the closed-loop system converge exponentially to any given neighborhood of the reference curve provided that the solutions are defined in the sense of sampling. This convergence property is also illustrated numerically by several examples of nonholonomic systems of degrees 1 and 2.Comment: This is the author's version of the manuscript accepted for publication in the Proceedings of the 2019 European Control Conference (ECC'19

Mobile Formation Coordination and Tracking Control for Multiple Non-holonomic Vehicles

This paper addresses forward motion control for trajectory tracking and mobile formation coordination for a group of non-holonomic vehicles on SE(2). Firstly, by constructing an intermediate attitude variable which involves vehicles' position information and desired attitude, the translational and rotational control inputs are designed in two stages to solve the trajectory tracking problem. Secondly, the coordination relationships of relative positions and headings are explored thoroughly for a group of non-holonomic vehicles to maintain a mobile formation with rigid body motion constraints. We prove that, except for the cases of parallel formation and translational straight line formation, a mobile formation with strict rigid-body motion can be achieved if and only if the ratios of linear speed to angular speed for each individual vehicle are constants. Motion properties for mobile formation with weak rigid-body motion are also demonstrated. Thereafter, based on the proposed trajectory tracking approach, a distributed mobile formation control law is designed under a directed tree graph. The performance of the proposed controllers is validated by both numerical simulations and experiments