Displacement errors at a pre-defined trajectory of a mobile robot.

Bitea, Mihai Alin ; Dolga, Valer

1. INTRODUCTION

The subject of this paper is the displacement, and the errors involved, of a mobile robot in an environment with different objects, that are made from different materials. This problem has always been in the attention of scientists. We can define a robot as a machine that senses, thinks, and acts. A mobile robot must have sensors, processing ability that emulates some aspects of cognition, and actuators. (Cox & Wilfrong, 1990). Sensors are needed to obtain information from the environment.

Reactive behaviors (like the stretch reflex in humans) do not require any deep cognitive ability, but on-board intelligence is necessary if the robot is to perform significant tasks autonomously, and actuation is needed to enable the robot to exert forces upon the environment. Generally, these forces will result in motion of the entire robot or one of its elements (such as an arm, a leg, or a wheel). These technological advances have, in term, made possible the automation of new applications: assembly, conveyor-belt following and seam welding are some examples. (Siegwart & Nourbakhsh, 2004)

The mobile robot can be used in indoor (structured environment): transportation and service industries, cleaning, research, surveillance, or outdoor (unstructured environment): military, forest, space, agriculture, air, underwater, mining, fire fighting or construction. Some examples are: the Automatic Guided Vehicle of VOLVO, Helpmate, BR700 Cleaning robot, The Pioneer, The Kepara Robot, Forester Robot, Sojouner, Nomad, The Honda Walking Robot, Stider, Big Dog.

Starting from the premise that coping with uncertainty is the most crucial problem a mobile robot must face, we can conclude that the robot must have the following basic capabilities:

Sensory interpretation: The robot must be able to determine its relationship to the environment by sensing (Bekey, 2005). Reasoning: The robot must be able to decide what actions are required to achieve its goal(s) in a given environment. This may involve decisions ranging from what paths to take to what sensors to use. (Ramos Arreguin, 2008)

This paper is trying, using an analytical method for displacement errors, based on the measurements values that are taken using sensors on different trajectories, to obtain a mathematical model for displacement coordination. The measurements are taken using a compass module.

2. EXPERIMENTAL DESCRIPTION

2.1 Describe of the experiment

In order to be able to analyze the displacement errors using the Hitachi HM55B Compass Module, I developed an environment where the mobile robot must leave the START point and reach the STOP point. I developed 3 different trajectories to reach the same goal (Fig. 1).

[FIGURE 1 OMITTED]

The mobile robot used a BASIC Stamp board and microcontroller. The locomotion system is composed by 3 wheels and a special device to trace the path (attached to the front of the robot). Two wheels are in front and each of them is commanded by a servo motor of 5V. The third one is in the back and it is only used for keeping the balance of the robot. The two servo motors are being commanded using pulses, IN and OUT. Because of this the speed of the robot from the START point to the STOP point is constant.

The mobile robot is equipped with a compass module and an LCD display, because all the measurements have been taken in real time and depending on the Earth's magnetic field.

2.2 Compass Module

The Hitachi HM55B Compass module measures direction. If it is used along with a BASIC Stamp, Board of Education, and Serial LCD we obtain a digital compass that works as shown in Fig.2. The module's Hitachi HM55B chip is an increasingly common feature in automobile electronics, providing a compass heading for the driver.

The microcontroller connected to the HM55B must control its enable and clock inputs and use synchronous serial communication to get the axis measurements from its data input and data output pins.

In order to be able to read the data, the Compass Module used a program that follows a subroutine named Compass_Get_Axes (Lidsay, 2006) that returns the x and y magnetic field strength values. The program is written in the Basic Stamp 2.2. language.

The value of x is the component of the Earth's magnetic field acting on the sensor's xm axis as shown in Fig.2. The value of y is the negative of the Earth's magnetic field acting on the ym axis. If N is the value reported by x or y when it is aligned with the Earth's magnetic field, then the value of x at some angle [theta] will be Ncos[theta], and the value of y will be --Nsinf[theta].

[FIGURE 2 OMITTED]

Using these facts and a couple of trigonometry identities, it turns out that the angle 9 is the arctangent of -y/x.

The mathematical equation between these values is:

tg[theta] = -y/x (1)

[tg.sup.-1] (tg[theta]t = [tg.sup.-1] (-y/x) (2)

[theta] = [tg.sup.-1] (-y/x) (3)

Regarding the program, I will present below a sequence of the subroutine Compass_Get_Axes.

 HIGH En: LOW En
 SHIFTOUT DinDout,clk,MSBFIRST,[Reset\4]
 HIGH En: LOW En
 SHIFTOUT DinDout,clk,MSBFIRST,[Measure\4]
 status = 0
DO
 HIGH En: LOW En
 SHIFTOUT DinDout,clk,MSBFIRST,[Report\4]
 SHIFTIN DinDout,clk,MSBPOST,[Status\4] LOOP
UNTIL status = Ready

 SHIFTIN DinDout,clk,MSBPOST,[x\11,y\11]
 HIGH En

 IF (y.BIT10 = 1) THEN y = y | NegMask
 IF (x.BIT10 = 1) THEN x = x | NegMask
RETURN

This subroutine works in a Loop concept, first the program reset the Compass Module, and after that it starts the measuring command. Also at this step the program clears all the previous flags (status=0). At this point we have another LOOP. The program loops until the module gives the OK signal (LOOP UNTIL status = Ready). The next step is to get the x and y values and once recorded, the module stops until the values are displayed on the LCD module. Once this step is complete, the loop begins again.

This subroutine is part of the main program and is combined with other subroutines that made the displacement of the mobile robot possible.

3. RESULTS

For each of the planned trajectories 5 tests have been made.

[FIGURE 3 OMITTED]

Each time the values for angle were recorded. For trajectory no.1 the measurements were taken in 8 points, along the path of the mobile robot.

For trajectory no. 2 and 3, the measurements were taken in 11 points.

Based on the result of these tests it was possible to determine the optimal path for each of the trajectories.

I made an average of the 5 values for each point where the measurement was recorded. There for it was possible to determine the optimal path for each trajectory.

Once we had the optimal path, the next problem was to obtain the angle deviations from the path that will result in an evolution graphic of the deviation (Fig.3).

4. CONCLUSIONS

After the values were analyzed it is clear that we have deviations for each trajectory. These deviations can be caused by a number of facts, and can be included in the displacement errors category.

By using the Compass Module, it has been possible to observe and record the deviations from the perspective of angle components values. In the graphic above we are able to observe the main changes of the trajectories of the mobile robot (like curves) and also we are able to detect the deviations for a predefined trajectory.

This way we are able to improve the locomotion systems of the mobile autonomous robots.

The compass module is also a great tool for mobile robots, giving them a sense of direction which can make a tremendous difference in robot team sports, as well as mazes.

Also the mobile robot will also have an accelerometer module attached, for a better identification of the displacement errors.

In the future the mobile robots can use the earth's magnetic field for navigation, mapping localization or measuring different aspects from displacement of the robots area.

5. REFERENCES

Bekey, G.A (2005). Autonomous Robots, MIT Press, ISBN-10: 0-262-02578-7, Massachusetts

Cox, J.J & Wilfrong, G.T. (eds.)(1990). Autonomous Robot Vehicles, Springer-Verlag, ISBN: 0387972404, New York

Lindsay, A. (2006). Smart sensors and application, Parallax Inc., ISBN 1-928982-39-5, Rocklin-California.

Ramos Arreguin, I. (2008). Automation and Robotics, I-Tech Education and Publishing, ISBN 978-3-902613-41-7, Croatia

Siegwart, R. & Nourbakhsh, I. (2004). Introduction to Autonomous Robot, MIT Press, ISBN 0-262-19502-X, Massachusetts