Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 347410, 12 pages

http://dx.doi.org/10.1155/2015/347410

## Real-Time Inverse Optimal Neural Control for Image Based Visual Servoing with Nonholonomic Mobile Robots

Computer Science Department, CUCEI, University of Guadalajara, 44430 Guadalajara, JAL, Mexico

Received 1 November 2014; Revised 21 January 2015; Accepted 21 January 2015

Academic Editor: Luis Rodolfo Garcia Carrillo

Copyright © 2015 Carlos López-Franco et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We present an inverse optimal neural controller for a nonholonomic mobile robot with parameter uncertainties and unknown external disturbances. The neural controller is based on a discrete-time recurrent high order neural network (RHONN) trained with an extended Kalman filter. The reference velocities for the neural controller are obtained with a visual sensor. The effectiveness of the proposed approach is tested by simulations and real-time experiments.

#### 1. Introduction

Traditionally, robot motion control approaches have feedback provided by a taco-meter or encoder, whose advantages are its easy implementation and its low cost. However, in mobile robotics such information is not accurate due to the appearance of slip phenomenon. One sensor that can be used to overcome these problems is the visual sensor. In this work, we use computer vision techniques to overcome such disadvantages.

Although a visual sensor is more accurate, it can suffer from unknown external disturbances due to the robot motion. In addition, the robot model is inaccurate and it suffers from parameter uncertainties. To overcome such problems, we propose the use of a discrete-time recurrent high order neural network (RHONN) trained with an extended Kalman filter with visual feedback.

The main goal of optimal control theory is to determine the control signals that will force a process to satisfy physical constraints and minimize a performance criterion simultaneously [1]. In optimal control theory, a cost functional is defined as function of the state and the control variables. Unfortunately it requires solving the Hamilton-Jacobi-Bellman (HTB) equation, which is not an easy task. To avoid the solution of a HTB equation an inverse optimal control can be used [2]. In inverse optimal control, we start with the definition of a stabilizing feedback control, and then we have to show that it optimizes a cost functional.

In this work, the input of the inverse optimal control is determined by visual feedback. The visual sensor is responsible of tracking the target and the estimation of the robot velocities to achieve the desired task. In our case the task consists in moving the robot from an initial pose to a desired pose with respect to a target object.

##### 1.1. State of the Art

An extensive class of controllers have been proposed for mobile robots [3–9]. Most of these references present only simulation results and the controllers are implemented in continuous time. A common problem when applying standard control theory is that the required parameters are often either unknown at time or are subject to change during operation. For example, the inertia of a robot as seen at the drive motor has many components, which might include the rotational inertia of the motor rotor, the inertia of gears and shafts, rotational inertia of its tires, the robot’s empty weight, and its payload. Worse yet, there are elements between these components such as bearings, shafts, and belts which may have spring constants and friction loads [10].

##### 1.2. Main Contribution

The paper main contributions are as follows: presenting a controller for mobile robots which includes the robot dynamics and does not need the previous knowledge of robot parameters or model; computing the trajectory references for the controller on real-time using visual data, acquired from a camera mounted on the robot; using visual data the controller drives the nonholonomic robot from its current pose toward a desired one; real-time integration of visual servoing and an inverse optimal neural controller to allow nonholonomic mobile robots to perform autonomous navigation.

The rest of this work is organized as follows. First the problem formulation is presented in Section 2. Then the model of the mobile robot and framework setup is described in Section 3. After that the camera model is presented in Section 4. Later, the visual feedback algorithm is introduced in Section 5. Section 6 provides an introduction to the neural identification. The inverse optimal control approach is presented in Section 7. The neural identification and control of the mobile robot is presented in Section 8. The simulations results are presented in Section 9. The experimental results are presented in Section 10. Finally, the conclusions are given in Section 11.

#### 2. Problem Formulation

The main focus of this work is the navigation of a differential drive robot from its current pose to a desired pose by using visual feedback and a neural controller, Figure 1. The camera is mounted on the robot, and therefore the robot motion induces camera motion. Before the task begins the desired feature is estimated applying a segmentation algorithm to the image of the target. The same process is done in real-time to compute the current future . When the algorithm begins the desired feature and the current feature are compared to compute the error. Then, using this error, the controller estimates the velocities to complete the task.