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

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

Stochastic Asymptotic Stabilizers for Deterministic Input-Affine Systems based on Stochastic Control Lyapunov Functions

In this paper, a stochastic asymptotic stabilization method is proposed for deterministic input-affine control systems, which are randomized by including Gaussian white noises in control inputs. The sufficient condition is derived for the diffucion coefficients so that there exist stochastic control Lyapunov functions for the systems. To illustrate the usefulness of the sufficient condition, the authors propose the stochastic continuous feedback law, which makes the origin of the Brockett integrator become globally asymptotically stable in probability.Comment: A preliminary version of this paper appeared in the Proceedings of the 48th Annual IEEE Conference on Decision and Control [14

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

Control Of Nonh=holonomic Systems

Many real-world electrical and mechanical systems have velocity-dependent constraints in their dynamic models. For example, car-like robots, unmanned aerial vehicles, autonomous underwater vehicles and hopping robots, etc. Most of these systems can be transformed into a chained form, which is considered as a canonical form of these nonholonomic systems. Hence, study of chained systems ensure their wide applicability. This thesis studied the problem of continuous feed-back control of the chained systems while pursuing inverse optimality and exponential convergence rates, as well as the feed-back stabilization problem under input saturation constraints. These studies are based on global singularity-free state transformations and controls are synthesized from resulting linear systems. Then, the application of optimal motion planning and dynamic tracking control of nonholonomic autonomous underwater vehicles is considered. The obtained trajectories satisfy the boundary conditions and the vehicles\u27 kinematic model, hence it is smooth and feasible. A collision avoidance criteria is set up to handle the dynamic environments. The resulting controls are in closed forms and suitable for real-time implementations. Further, dynamic tracking controls are developed through the Lyapunov second method and back-stepping technique based on a NPS AUV II model. In what follows, the application of cooperative surveillance and formation control of a group of nonholonomic robots is investigated. A designing scheme is proposed to achieves a rigid formation along a circular trajectory or any arbitrary trajectories. The controllers are decentralized and are able to avoid internal and external collisions. Computer simulations are provided to verify the effectiveness of these designs