Elsevier

Control Engineering Practice

Volume 9, Issue 11, November 2001, Pages 1209-1214
Control Engineering Practice

Mobile robot path tracking using a robust PID controller

https://doi.org/10.1016/S0967-0661(01)00066-1Get rights and content

Abstract

This paper presents a simple and effective solution for the path tracking problem of a mobile robot using a PID controller. The proposed method uses a simple linearized model of the mobile robot composed of an integrator and a delay. The synthesis procedure is simple and allows the PID controller to be tuned considering the nominal performance and the robustness as control specifications. Experimental results demonstrate the good performance and robustness of the proposed controller.

Introduction

Although the very first attempts in mobile robotics can be found in the late sixties, it is since the nineties that a great deal of research effort has been focused on this topic. One of the important issues in this field is the path-tracking (PT) problem, which is concerned with the ability to drive a mobile robot autonomously as close as possible to a previously defined reference path. This path is usually specified as either a sequence of consecutive reference points that must be “visited” by the robot or by a set of geometrical primitives such as straight lines or arcs of circumferences.

The study of this problem is well justified not only when the mobile robot navigates through a well known structured environment, where all the obstacle locations and dimensions are known and thus considered in the path planning stage, but also in a more realistic partially structured one, where unexpected fixed or moving obstacles are included in the navigation problem. In this latter case, many navigation approaches use a decoupled strategy, based on a combination of an on-line real-time path planner (RTPP) and path-tracking module. The RTPP modifies the original off-line reference path when an unexpected obstacle is detected with the mobile robot on board sensor system, and subsequently the PT module drives the vehicle through the original or modified path.

Many approaches have been tested for the PT problem and reported in the literature (Thuilot, D’andrea Novel, & Micaellli, 1996; Freund & Mayr, 1997; Egerstedt, Hu, & Stotsky, 1998). Also, predictive control strategies, using either a linear (Normey-Rico, Gómez-Ortega, Alcalcá-Torrego, & Camacho, 1998; Normey-Rico, Gómez-Ortega, & Camacho, 1999) or nonlinear (Gómez-Ortega and Camacho, 1994; Gómez-Ortega and Camacho, 1996) model of the mobile robot kinematics have been proposed as a way of taking advantage of the knowledge of a reference path and also as a natural way of delay compensation.

In this paper, a classical PID approach is proposed for the PT controller, which is the control strategy most frequently used in the industry. A very simple model of the mobile robot kinematics is used and thus a robust PID tuning is necessary. PIDs advantages include simplicity, robustness and their familiarity in the control community. Because of this, a great deal of effort has been spent to find the best choice of PID parameters for different process models. However, studies presented by many authors have shown that a great amount of control problems are caused by inappropriate tuning of the PID parameters (Åström and Hagglund, 1995). The main causes of this are, perhaps, that most of the tuning rules are obtained using advanced control theory difficult to understand for field operators and that they do not consider the robustness as one of the closed loop specifications. It is in this context where a PID tuning method which takes into account these characteristics is of great importance.

One of the most well known methods for tuning PID controllers when the process can be modeled as a first order transfer function with a delay (which is the case of the mobile robot used for the experiments) is the one proposed by Ziegler and Nichols (1942). The main advantage of this method is its simplicity although it has several draw-backs: (a) the obtained closed loop response is, in general, not appropriate for most processes and (b) the responses are very oscillating or very slow when the ratio between the dead time (L) and the equivalent time constant (T) is high or the process has integrative action.

Several new methods have been proposed in the literature for tuning PID controllers looking for a better performance than that obtained by the Ziegler-Nichols method, most of them based on advanced control theory (see for example Rivera, Morari, and Skogestad, 1986; Sung, Lee, and Lee, 1995; Yongho, Park, Lee, and Brosilaw, 1998). In this paper a new PID tuning is proposed, based on basic control tools, which takes into account the robustness of the closed-loop system. This controller has been experimentally tested with a synchro-drive Nomad 200 mobile robot.

The paper is organized as follows: In Section 2, the model considered for the mobile robot kinematics is presented. The description and robustness of the proposed tuning for the PID controller is discussed in Section 3 and the way in which the PID is applied to the PT problem is shown in Section 4. In Section 5, experimental results on a Nomad 200 mobile robot are shown. The paper ends with the conclusions.

Section snippets

The mobile robot path tracking problem

In this paper, the path tracking problem is analyzed using the Nomad 200 mobile robot (see Fig. 1). This robot has a synchro-drive type locomotion system which consists of three drive wheels whose turning speed and orientations vary simultaneously. Fig. 2 shows the synchro-drive configuration and the steering angle δ, with reference to the global axis.

The robot provides a position estimation system based on odometry. It is well known that odometry is a technique which has an accumulative error

Control structure and methodology

As has been analyzed in the previous section, the relation between the steering velocity and its reference can be represented by a simple integrator plus delay model e−Ls/s. The tuning of a PID for this type of processes is not as simple as for the case of stable processes with a delay. The well known tuning rule of Ziegler and Nichols (1942) produces very oscillating responses for this case and even other methods recently developed especially for integrative processes, produce unacceptable

Control structure and implementation

The control structure used for testing the behaviour of the robust tuned PID in the Nomad 200 mobile robot is shown in the block diagram of Fig. 6. In this diagram, two different parts can be distinguished, that are related to the two sections of the controller code programmed in the robot mobile main processor.

In the first part of the algorithm the reference steering angle δr is computed. This computation, represented in the approximation point block, uses the robot position (xg,yg) and the

Experimental results

For the experimental tests the controller parameters have been chosen as follows: the look-ahead λ=0.6 m, the linear velocity V=0.4 m/s (90% of the maximum robot velocity), δ̈max=30°/s2. Fig. 7 shows the performance of the proposed controller for two different real dead times. The initial position for the mobile robot was x0=0.6 m, y0=1.13 m and orientation δ0=0 (parallel to xg axis). Note that the reference path chosen has small curvatures, which makes more difficult to follow the reference. The

Summary and conclusions

A path tracking controller based on a robust PID algorithm has been proposed. The principal advantage of the present methodology is that it uses a very simple model for the mobile robot which allows the tuning of a simple PID controller. The new method for the robust tuning of the PID controller is based on classical concepts and can be applied to integrative process plus a delay.

The synthesis procedure is easy and the obtained rules are similar to the Ziegler–Nichols method for PID

References (15)

  • J. Gómez-Ortega et al.

    Neural network MBPC for mobile robots path tracking

    Robotics and Computer Integrated Manufacturing Journal

    (1994)
  • J.E. Normey-Rico et al.

    A Smith predictor based generalized predictive controller for mobile robot path tracking

    Control Engineering Practice

    (1999)
  • K.J. Åström et al.

    PID controllersTheory, design and tuning

    (1995)
  • I.L. Chien et al.

    Consider imc tuning to improve controller performance

    Industrial Engineering Chemistry Research

    (1990)
  • Egerstedt, M., Hu, H., & Stotsky, A. (1998). Control of car-like robot using a dynamic model. Proceedings of the 1998...
  • E. Freund et al.

    Nonlinear path control in automated vehicle guidance

    IEEE Transaction on Robotics and Automation

    (1997)
  • J. Gómez-Ortega et al.

    Mobile robot navigation in a partially structured static environment, using neural predictive control

    Control Engineering Practice

    (1996)
There are more references available in the full text version of this article.

Cited by (0)

View full text