Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers

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

Formation control of nonholonomic mobile robots using implicit polynomials and elliptic Fourier descriptors

This paper presents a novel method for the formation control of a group of nonholonomic mobile robots using implicit and parametric descriptions of the desired formation shape. The formation control strategy employs implicit polynomial (IP) representations to generate potential fields for achieving the desired formation and the elliptical Fourier descriptors (EFD) to maintain the formation once achieved. Coordination of the robots is modeled by linear springs between each robot and its two nearest neighbors. Advantages of this new method are increased flexibility in the formation shape, scalability to different swarm sizes and easy implementation. The shape formation control is first developed for point particle robots and then extended to nonholonomic mobile robots. Several simulations with robot groups of different sizes are presented to validate our proposed approach

Sliding Mode Control for Trajectory Tracking of a Non-holonomic Mobile Robot using Adaptive Neural Networks

In this work a sliding mode control method for a non-holonomic mobile robot using an adaptive neural network is proposed. Due to this property and restricted mobility, the trajectory tracking of this system has been one of the research topics for the last ten years. The proposed control structure combines a feedback linearization model, based on a nominal kinematic model, and a practical design that combines an indirect neural adaptation technique with sliding mode control to compensate for the dynamics of the robot. A neural sliding mode controller is used to approximate the equivalent control in the neighbourhood of the sliding manifold, using an online adaptation scheme. A sliding control is appended to ensure that the neural sliding mode control can achieve a stable closed-loop system for the trajectory-tracking control of a mobile robot with unknown non-linear dynamics. Also, the proposed control technique can reduce the steady-state error using the online adaptive neural network with sliding mode control; the design is based on Lyapunov’s theory. Experimental results show that the proposed method is effective in controlling mobile robots with large dynamic uncertaintiesFil: Rossomando, Francisco Guido. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Instituto de Automática. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Automática; ArgentinaFil: Soria, Carlos Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Instituto de Automática. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Automática; ArgentinaFil: Carelli Albarracin, Ricardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Instituto de Automática. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Automática; Argentin

Adaptive tracking control of nonholonomic systems: an example

We study an example of an adaptive (state) tracking control problem for a four-wheel mobile robot, as it is an illustrative example of the general adaptive state-feedback tracking control problem. It turns out that formulating the adaptive state-feedback tracking control problem is not straightforward, since specifying the reference state-trajectory can be in conflict with not knowing certain parameters. Our example illustrates this difficulty and we propose a problem formulation for the adaptive state-feedback tracking problem that meets the natural prerequisite that it reduces to the state-feedback tracking problem if the parameters are known. A general methodology for solving the problem is derive

Stabilization Control of the Differential Mobile Robot Using Lyapunov Function and Extended Kalman Filter

This paper presents the design of a control model to navigate the differential mobile robot to reach the desired destination from an arbitrary initial pose. The designed model is divided into two stages: the state estimation and the stabilization control. In the state estimation, an extended Kalman filter is employed to optimally combine the information from the system dynamics and measurements. Two Lyapunov functions are constructed that allow a hybrid feedback control law to execute the robot movements. The asymptotical stability and robustness of the closed loop system are assured. Simulations and experiments are carried out to validate the effectiveness and applicability of the proposed approach.Comment: arXiv admin note: text overlap with arXiv:1611.07112, arXiv:1611.0711