Gustavo Scaglia

Trajectory Tracking of Underactuated Surface Vessels: A Linear Algebra Approach

This brief presents the design of a controller that allows an underactuated vessel to track a reference trajectory in the x-y plane. A trajectory tracking controller designed originally for robotic systems is applied for underactuated surface ships. Such a model is represented by numerical methods and, from this approach, the control actions for an optimal operation of the system are obtained. Its main advantage is that the condition for the tracking error tends to zero, and the calculation of control actions are obtained solving a system of linear equations. The proofs of convergence to zero of the tracking error are presented here and complete the previous work of the authors. Simulation results show the good performance of the proposed control system.

Trajectory Tracking Controller Design for Unmanned Vehicles: A New Methodology

A major issue in the automatic guidance of vehicles is the design of control laws dedicated to the specific mobile platform used. Thus, if the model associated with the mobile platform or its constraints change, a new control law must be designed. In this paper, the problem of designing trajectory tracking controllers for unmanned vehicles is addressed. The methodology proposed here is an algebraic approach for obtaining optimum and stable trajectory tracking controllers for nonholonomic vehicles. Such an algebraic formulation makes the proposal suitable for embedded applications. The stability and optimality of the proposed controllers design method is theoretically proven for both bicycle-type and unicycle-type mobile robots, although the methodology can be extended to other types of unmanned vehicles. Four tests were carried out in this work in order to show the advantages of the proposal: the step discontinuity test, the curvature test, the real world test, and navigation under disturbances in the control actions. The results obtained were compared with four trajectory tracking controllers previously published in the literature. Additionally, an agricultural application is included in order to show the performance of the proposed controller when applied to a service unit within an agricultural environment. Field experiments demonstrating the capabilities of our proposal are also reported and discussed.

Numerical methods based controller design for mobile robots

This paper presents the design of four controllers for a mobile robot such that the system may follow a preestablished trajectory. To reach this aim, the kinematic model of a mobile robot is approximated using numerical methods. Then, from such approximation, the control actions to get a minimal tracking error are calculated. Both simulation and experimental results on a PIONEER 2DX mobile robot are presented, showing a good performance of the four proposed mobile robot controllers. Also, an application of the proposed controllers to a leader robot following problem is shown; in it, the relative position between robots is obtained through a laser.

Trajectory tracking of mobile robots in dynamic environments: A linear algebra approach

A new approach for navigation of mobile robots in dynamic environments by using Linear Algebra Theory, Numerical Methods, and a modification of the Force Field Method is presented in this paper. The controller design is based on the dynamic model of a unicycle-like nonholonomic mobile robot. Previous studies very often ignore the dynamics of mobile robots and suffer from algorithmic singularities. Simulation and experimentation results confirm the feasibility and the effectiveness of the proposed controller and the advantages of the dynamic model use. By using this new strategy, the robot is able to adapt its behavior at the available knowing level and it can navigate in a safe way, minimizing the tracking error.

Formation control and trajectory tracking of mobile robotic systems – a linear algebra approach

A novel approach for trajectory tracking of a mobile-robots formation by using linear algebra theory and numerical methods is presented in this paper. The formation controller design is based on the formation states concept and the dynamic model of a unicycle-like nonholonomic mobile robot. The proposed control law designed is decentralized and scalable. Simulations and experimental results confirm the feasibility and the effectiveness of the proposed controller and the advantages of using the dynamic model of the mobile robot. By using this new strategy, the formation of mobile robots is able to change its configuration (shape and size) and follow different trajectories in a precise way, minimizing the tracking and formation errors.

Tracking control of concentration profiles in a fed-batch bioreactor using a linear algebra methodology

Based on a linear algebra approach, this paper aims at developing a novel control law able to track reference profiles that were previously-determined in the literature. A main advantage of the proposed strategy is that the control actions are obtained by solving a system of linear equations. The optimal controller parameters are selected through Monte Carlo Randomized Algorithm in order to minimize a proposed cost index. The controller performance is evaluated through several tests, and compared with other controller reported in the literature. Finally, a Monte Carlo Randomized Algorithm is conducted to assess the performance of the proposed controller.

Towards features updating selection based on the covariance matrix of the slam system state

This paper addresses the problem of a features selection criterion for a simultaneous localization and mapping (SLAM) algorithm implemented on a mobile robot. This SLAM algorithm is a sequential extended Kalman filter (EKF) implementation that extracts corners and lines from the environment. The selection procedure is made according to the convergence theorem of the EKF-based SLAM. Thus, only those features that contribute the most to the decreasing of the uncertainty ellipsoid volume of the SLAM system state will be chosen for the correction stage of the algorithm. The proposed features selection procedure restricts the number of features to be updated during the SLAM process, thus allowing real time implementations with non-reactive mobile robot navigation controllers. In addition, a Monte Carlo experiment is carried out in order to show the map reconstruction precision according to the Kullback–Leibler divergence curves. Consistency analysis of the proposed SLAM algorithm and experimental results in real environments are also shown in this work.

Feature Selection Criteria for Real Time EKF-SLAM Algorithm

This paper presents a seletion procedure for environmet features for the correction stage of a SLAM (Simultaneous Localization and Mapping) algorithm based on an Extended Kalman Filter (EKF). This approach decreases the computational time of the correction stage which allows for real and constant-time implementations of the SLAM. The selection procedure consists in chosing the features the SLAM system state covariance is more sensible to. The entire system is implemented on a mobile robot equipped with a range sensor laser. The features extracted from the environment correspond to lines and corners. Experimental results of the real time SLAM algorithm and an analysis of the processing-time consumed by the SLAM with the feature selection procedure proposed are shown. A comparison between the feature selection approach proposed and the classical sequential EKF-SLAM along with an entropy feature selection approach is also performed.

Controller Designed by Means of Numeric Methods for a Benchmark Problem: RTAC (Rotational Translational Actuator)

A nonlinear benchmark problem, very interesting due to interaction between translational and rotational movements is the RTAC system (also called TORA). Diverse control techniques in several previous papers have been dedicated to it. The present work proposes, by means of a straightforward procedure, a controller design based on an approach of RTAC system, using numerical methods, so that the system tends to origin after being displaced of this position. The control signal is calculated through the resolution of a linear equations system. Computer simulations show that the performance is comparable and in some aspects better than the one obtained with more complicated controllers

Trajectory tracking of a mini four-rotor helicopter in dynamic environments - a linear algebra approach

This paper presents the design of a controller that allows a four-rotor helicopter to track a desired trajectory in 3D space. To this aim, a dynamic model obtained from Euler-Lagrange equations describes the robot. This model is represented by numerical methods, with which the control actions for the operation of the system are obtained. The proposed controller is simple and presents good performance in face of uncertainties in the model of the system to be controlled. Zeroconvergence proof is included, and simulation results show a good performance of the control system.