Home > Articles

  • Print
  • + Share This
This chapter is from the book

TimingNavigator Accuracy

The results from testing the preceding code vary greatly. After 30 seconds Trilobot is supposed to return to the point of origin, but in reality it only comes close. I performed a test by dropping a coin on the ground at the point of origin after letting the robot go. Sometimes it came back to within 50 cm, but other times it was off by as much as 90 cm! This sort of discrepancy seems hard to account for, but after performing a few experiments the reason for the inaccuracy is clear. Examine Figure 7–10. This is a small course I set up for Trilobot on carpet by placing a coin at each point. There are five individual vectors to this course, each labeled in Figure 7–10 by a number. The code to make Trilobot follow this course is as follows:

Figure 7-10Figure 7–10 A test course for Trilobot.

	1.	import josx.platform.rcx.*;
	2.	import josx.robotics.*;
	3.	
	4.	class TrilobotMain {
	5.	
	6.	  public static void main(String [] args) {
	7.	   Motor.A.setPower(7);
	8.	   Motor.C.setPower(5);
	9.	   
	10.	   TimingNavigator nav = new TimingNavigator(Motor.C, Motor.A, 5.475f, 4.03f);
	11.	      
	12.	   nav.gotoPoint(75,75);
	13.	   nav.gotoPoint(0,150);
	14.	   nav.gotoPoint(75, 150);
	15.	   nav.gotoPoint(75,0);
	16.	   nav.gotoPoint(0,0);
	17.	  }
	18.	}

This looks like a relatively simple series of movements, but as you can see from Figure 7–11 Trilobot didn't handle it very well. When Trilobot executed the initial 45-degree rotation it didn't quite rotate enough—probably closer to 40 degrees than 45. Not too bad so far. Next comes Vector 2. It executes the 90-degree turn, but once again it underrotated, causing it to wander off drastically to the right. By the time it stops at what it thinks is 0, 150 the orientation of the robot is off by about 15 degrees and the x coordinate is off by about 40 cm. This vector seems to be the worst one of all five. If Vector 2 ended up at 0,150 as it was supposed to, the overall path would be much more accurate. Vectors 3, 4, and 5 are not bad, but their small errors also cause a cumulative effect on the positional estimate. The final position was off by about 15 cm from the point of origin—not bad, considering. Accuracy was probably regained because the errors in the lefthand turns were made up by countererrors in the righthand turns. So what caused all these errors?

Figure 7-11Figure 7–11 Trilobot's interpretation of the course.

Errors fall into two camps by definition. Systematic errors are introduced in the design of the robot and the methodology. This includes errors due to inaccuracies in parameters used in the program and errors caused by the design of the robot itself. Nonsystematic errors are errors that are introduced because of the real world. Errors in this camp include uneven floors, wheel slippage, and cats walking in front of the robot. Let's try to identify the errors that hamper the accuracy of TimingNavigator.

Systematic Errors

The most obvious systematic error introduced into TimingNavigator is the accuracy of the travel and rotate times used in the constructor. Because the whole premise of navigation using timing relies on these, inaccuracies will cumulatively throw off the positioning. For example, the angle parameter requires the time it takes to rotate 360 degrees. If the actual rotation time is 4.2875 seconds and you give a value of 4.4425 seconds it will cause a rotation of 360 degrees to be about 12 degrees off. This disparity will add up quickly after the robot has been traveling for a time.

The biggest problem with accuracy, as we observed, was underrotation. Each time the robot attempted to rotate a discreet angle, it would consistently fall short. How can we explain this, especially after being so careful when timing a complete 360 degree rotation? For an answer we need to look to Newton's first law of motion: objects at rest tend to stay at rest. It takes a certain amount of time and force to overcome the momentum of the stationary robot. So when we tell the robot to rotate right 90 degrees it takes a small amount of time to get moving, in Trilobots case about 0.06 seconds. Because of this factor, larger angles of rotation, such as a 180 degree turn, are likely to be more accurate than smaller rotations, such as a 5-degree turn. This accounts for the observed angle being smaller than the projected angle. As with all systematic errors, it should be possible to correct this through code. Timing by hand with a stopwatch is so inaccurate it is best to start with an estimate for the delay, then refine it with a few trials. Adding the following line of code at line 11 will accomplish this:

nav.setMomentumDelay(60);

The momentum variable (which had been set to 0) will now cause the robot to delay an extra 0.06 seconds for each rotation, giving it enough time to overcome momentum. To refine this, have the robot rotate 90 degrees and stop, then note how accurate it seems. If it rotates too much, decrease this value and if it underrotates, increase the value. Now when the test course is run, accuracy should be improved.

WARNING

If you use the setMomentumDelay() method, the time variable in the Timing Navigator constructor should measure only one full rotation. Do not try to average four rotations otherwise the delay caused by momentum will be divided.

One of the biggest problems with achieving accurate parameters is that the battery slowly loses power, and thus the output speed of the motors changes. I've noticed several times that when the RCX is turned on it may have a charge of 7.6 V, and then by the time the program ends the battery power is at 7.3 V. Then, after shutting down for a few minutes, I turn it on and the voltage once again reads 7.6 V. This change really throws rotations off. The worst part is once you think you have the TimingNavigator parameters honed and the motors balanced, the battery charge lessens and the settings are no longer valid. One way to negate this effect is to use freshly charged batteries.

Nonsystematic Errors

Differences in motor speed between the A motor and the B motor also affect accuracy greatly. One of the noticeable problems encountered in the course just presented is the inability of the robot to drive straight. Just when I thought I had the motors balanced it would start drifting to the right. Then, later in the same run, it would mysteriously straighten up for some stretches! This effect can be attributed to frictional differences in the structure of the robot.

A comparatively minor source of errors likely results from the surface the robot is on. Carpet and rough surfaces are likely to introduce more errors than a smooth floor such as hardwood.

Contact with external objects also introduces error into the positional estimate. When the bumper hits an object it has the potential to turn the robot slightly out of alignment. This can be minimized by slowing down the robot, or by detecting objects before the robot strikes them using a proximity detector (see Chapter 9, "Proximity Detection").

  • + Share This
  • 🔖 Save To Your Account

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

Overview


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information


To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

Newsletters

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information


Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.

Security


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

Children


This site is not directed to children under the age of 13.

Marketing


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information


If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

Choice/Opt-out


Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information


Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents


California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure


Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

Links


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact


Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice


We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020