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

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

Saturated stabilization and tracking of a nonholonomic mobile robot

Abstract This paper presents a framework to deal with the problem of global stabilization and global tracking control for the kinematic model of a wheeled mobile robot in the presence of input saturations. A model-based control design strategy is developed via a simple application of passivity and normalization. Saturated, Lipschitz continuous, time-varying feedback laws are obtained and illustrated in a number of compelling simulations

Feedback Linearization Techniques for Collaborative Nonholonomic Robots

Collaborative robots performing tasks together have significant advantages over a single robot. Applications can be found in the fields of underwater robotics, air traffic control, intelligent highways, mines and ores detection and tele-surgery. Collaborative wheeled mobile robots can be modeled by a nonlinear system having nonholonomic constraints. Due to these constraints, the collaborative robots arc not stabilizable at a point by continuous time-invariant feedback control laws. Therefore, linear control is ineffective, even locally, and innovative design techniques are needed. One possible design technique is feedback control and the principal interest of this thesis is to evaluate the best feedback control technique. Feedback linearization is one of the possible feedback control techniques. Feedback linearization is a method of transforming a nonlinear system into a linear system using feedback transformation. It differs from conventional Taylor series linearization since it is achieved using exact coordinates transformation rather than by linear approximations of the system. Linearization of the collaborative robots system using Taylor series results in a linear system which is uncontrollable and is thus unsuitable. On the other hand, the feedback linearized control strategies result in a stable system. Feedback linearized control strategies can he designed based on state or input, while both state and input linearization can be achieved using static or dynamic feedback. In this thesis, a kinematic model of the collaborative nonholonomic robots is derived, based on the leader-follower formation. The objective of the kinematic model is to facilitate the design of feedback control strategies that can stabilize the system and Minimize the error between the desired and actual trajectory. The leader-follower formation is used in this research since the collaborative robots are assumed to have communication capabilities only. The kinematic model for the leader-follower formation is simulated using MATLAB/Simulink. A comparative assessment of various feedback control strategies is evaluated. The leader robot model is tested using five feedback control strategies for different trajectories. These feedback control strategies are derived using cascaded system theory, stable tracking method based on linearization of corresponding error model, approximation linearization, nonlinear control design and full state linearization via dynamic feedback. For posture stabilization of the leader robot, time-varying and full state dynamic feedback linearized control strategies are used. For the follower robots using separation bearing and separation-separation formation, the feedback linearized control strategies are derived using input-output via static feedback. Based on the simulation results for the leader robot, it is found that the full state dynamic feedback linearized control strategy improves system performance and minimizes the mean of error more rapidly than the other four feedback control strategies. In addition to stabilizing the system, the full state dynamic feedback linearized control strategy achieves posture stabilization. For the follower robots, the input-output via static feedback linearization control strategies minimize the error between the desired and actual formation. Furthermore, the input-output linearized control strategies allow dynamical change of the formation at run-time and minimize the disturbance of formation change. Thus, for a given feasible trajectory, the full state feedback linearized strategy for the leader robot and input-output feedback linearized strategies for the follower robots are found to be more efficient in stabilizing the system

A Strategy for Multi-Robot Navigation

International audienceThe paper addresses the problem of trajectory regulation of driftless systems such that a stabilizing control input is assumed exists. The perturbed trajectory depends on a regulation control-input which must be designed such that the system's stability is preserved and some undesirable sets belonging to navigation area must be avoided. For the stability and regulation of a multi-robot system a converging attractive set around the target is constructed and a repulsive set around obstacles is emphasized. Taking into account a communication algorithm agents-agents to agents-target, we prove that the proposed regulation control-input preserves the navigation area invariance property and the system's stability. Simulation results illustrate the effectiveness of he proposed control algorithm

Research on a semiautonomous mobile robot for loosely structured environments focused on transporting mail trolleys

In this thesis is presented a novel approach to model, control, and planning the motion of a nonholonomic wheeled mobile robot that applies stable pushes and pulls to a nonholonomic cart (York mail trolley) in a loosely structured environment. The method is based on grasping and ungrasping the nonholonomic cart, as a result, the robot changes its kinematics properties. In consequence, two robot configurations are produced by the task of grasping and ungrasping the load, they are: the single-robot configuration and the robot-trolley configuration. Furthermore, in order to comply with the general planar motion law of rigid bodies and the kinematic constraints imposed by the robot wheels for each configuration, the robot has been provided with two motorized steerable wheels in order to have a flexible platform able to adapt to these restrictions. [Continues.