instagram

Thursday, May 7, 2015

Tau Labs and CyPhy "Level Up"

It was exciting to see another player adopting Tau Labs at their core with the announcement of the CyPhy LVL 1 kickstarter. This is a really neat drone project that removes the need for a gimbal while flying by being able to navigate around and remain level. This is a neat idea but traditionally multirotors fly by tilting to generate lateral acceleration. While they are using Tau Labs, they haven't yet released any code, so we can't look there. So how do they do it?

Note: I am affiliated with Tau Labs not CyPhy or LVL1 so this is all inferred from their press information.

My vectored thrust hexcopter
Figuring this out seemed like a fun evening challenge, and also highlights that Tau Labs is flexible enough to really make things like this easy. The best way to understand something is to replicate it, so let's dive in.

Traditional system

So a traditional quadcopter has four motors. The speeds of these four motors are computed based on four inputs: roll torque, pitch torque, yaw torque, and finally total thrust. This is a fully constrained system and has no possible other inputs. There are some ways to permanently alter it. For example many people are experimenting with tilted motors to generate horizontal force while staying closer to level. This allows faster FPV flights while keeping the camera more level (e.g. TBS Gemini, which also uses Tau Labs).

You can also make this more flexible but tilting the motors dyamically using a tilt mechanism. For example I put this on TriBlivion, which allows you to fly forward controllably while staying level.

Once you go to a hexcopter, you have an overactuated system: where you have more control outputs than you have desired inputs. For a traditional arrangement of motors (all horizontal, such as Y6 or flat 6) there is no way to use a different mixer and generate more forces. This can be written more formally: there is a matrix that translates from motor RPMs to torques (3 rotation directions) and thrusts (in 3 directions, forward, leftward, and upward) and they cannot be dissociated.

A more controllable hex

This does not have to be the case. If we do not have all the motors parallel, then is it possible to separately control thrust forward (like with tilted motor racing quads) separately from the thrust upward. I saw this image online:


Which shows the side profile in a more informative manner. You can see the front motor is tilted back and the middle motor is tilted forward. If you were to speed up the middle motor while slowing down the back and front motor, you would create no net rotational force while generating a forward force. If you speed up the front and slow down the back motor while speeding up the front motor, you would create a pitching upward torque. If you speed up all three, you create an upward force. So for these three motors you can separate forward force, vertical force, and pitching torque.

TL;DR: 6 motors means 6 controls!

As an aside, basically anyone that has been flying a V-tail has been doing this type of vectored thrust for years. With a V-tail you have two motors at the back that are angled and fighting each other. Combined they create a pitch force. Their difference creates a yaw force. However this is not an over-actuated system -- it has four motors and four controls.

Let's math it

Now let's try and extend this to a general solution with 6 motors and also while at it solve for the mixer that would allow us to control things.

Each motor will have a position -- in this case spaces at 60 degrees along a unit circle (although since this is a general solution we can change this later and re-derive it). The front two motors will be tilted backward and slightly outward (adding some yaw and lateral maneuvering). The middle is tilted inward and force, and the back are only tilted inward.

Put these into quaternion notation, we can then do a little bit of math to convert their thrust into the frame reference plane:

for i = 1:N
    q(i,:) = RPY2Quaternion([mot_r(i), mot_p(i), 0]);
    
    % the last column of the matrix that rotates from the body (motor)
    % to the earth (hexcopter) reference frame gives the force it generates
    % in each axis
    Rbe = Q2Rbe(q(i,:));
    force(i,:) = Rbe(:,3)';
end

Now those thrusts can be used to compute the lateral forces. However, they also create torques on the frame which we want to solve for. The yaw force from each motor is a mixture of two components. the first is from the drag of the blade on the air creating a rotation force on the frame that will be proportional to the Z force. the second and larger will be the cross product of the position of that motor relative to the center of mass. Since I plan to use this with tiny props, the thrust component of the yaw will be dominant and I will ignore the drag.

k1 = 0.0; % the drag component
k2 = 1;
for i = 1:N
    torques(i,:) = cross(force(i,1:3)', pos(i,:)');
    torques(i,3) = k2 * torques(i,3) + k1 * CW(i) * force(i,3);
end

We can visualize these forces and torques in 3D:

From this, we can generate a matrix that takes the set of motor RPMs and computes the torques and accelerations:

k1 = 0.0; % the drag component
% W maps from 6 motors to six control outputs
% roll, pitch, yaw, forward, sideways, up
W = [torques'; ...
     force'];

Then finally using the pseudo-inverse (or since this is 6x6 we can use true inverse) we can calculate mixer matrix that will let us take the desired roll, pitch, yaw rates, and forward, sideways acceleration and solve for the motor settings.

k1 = 0.0; % the drag component
M = W'*(W*W')^-1;

The result gives us a nice sensible mixer matrix
k1 = 0.0; % the drag component
M =

    0.0068    0.0034    0.0084   -0.6356   -0.9976    0.1764
   -0.0068    0.0034   -0.0084   -0.6356    0.9976    0.1764
   -0.0060    0.0034    0.0101    1.2963   -0.0296    0.1764
    0.0011   -0.0068   -0.0115   -0.6433   -0.9510    0.1785
   -0.0011   -0.0068    0.0115   -0.6433    0.9510    0.1785
    0.0060    0.0034   -0.0101    1.2963    0.0296    0.1764

So basically we multiply this matrix by the desired behavior (roll, accel, etc) and get the motor speeds. BTW as a sanity check, if we remove the tilts the result says singular matrix and makes no sense. That's because a traditional (non-tilted hex) cannot do this.

Let's build it!

Ok, so now we know these motor positions create a controllable system, let's build it! I went ahead and whipped this up in no time in OpenSCAD. You can download your own (or change the motor parameters) on Thingiverse.


Ninety minutes of printing later, I had my motors in position. Luckily I'd be planning on making a hex version of BrushedSparky using a 3d printed attachment and already have the 6 necessary brushed outputs. So let's go ahead and mount this.



Flight!

Next we use the custom mixer calculated in matlab with arbitrary scales applied to get normal ranges. This scaling is equivalent to changing the PIDs and we will autotune this at the end to get it better. At this point, it should not have as much unrequested forward and sidways motion. However, this isn't fun yet! We are still flying like a traditional system.

I then set up the slider on my transmitter to map to Accessory0 and added the entries into the mixer so that controlled forward thrust. Later if this starts flying really well I can actually make the slider provide roll and pitch and use the roll and pitch sticks on Accessory0,1 to fly around purely level.


At this point there was no more excuse to not fly :). It still can do with some tuning, but here are the initial flights. Here I'm using Brushed Sparky's native OpenLRS support. It has a tiny chip antenna mounted which is convenient for keeping it low profile.


You can see when I enable forward mode, there is a tendency to climb. At this point I think I'm hitting issues because of the linearization of the mixer. For small changes where the motors are nearly running at the same speed this is appropriate. However, for large forward inputs that makes the middle motor run quite high (which creates excessive thrust because that is super-linear with input) and the decrease in the front and back motors is not sufficient. This might be fixable with some static non-linearities in the mixer (e.g. sqrt) or could require a more sophisticated controller.

A second issue that is related but probably more about weight-to-thrust is that as when I generate enough forward thrust to be entertaining, it starts rocking in pitch a bit. I need to get some logs to confirm this, but I'm pretty sure the middle motor is running and practically shutting off the front and back motors.

Anyway, it doesn't fly wonderfully yet - but this is 12 hours after I got the idea ;-). I think it is a pretty solid demonstration of how you can take funny motor positions and generate a mixer to get new control dimensions, and a pretty nice proof of principle.

Conclusion

CyPhy have a really cool frame design, and it really shows off the versatility of Tau Labs that we can control airframes like this that weren't conceived of when we wrote the code. I definitely need to play with mine more to get it better tuned in and explore doing some level FPV flying. It might be that something a bit more substantive with brushless motors might be required to have sufficient thrust. I'll also be interested to see about flight times and efficiency. Having the motors fight each other (some pushing forward and some backward) is definitely burning batteries.

Speaking of thrust, I will be really really curious to see more videos of their frame flying in windy conditions. By using thrust vectoring like this to maneuver, the maximal amount of forward thrust is much less than traditional hexcopter navigation. For example, with a whole hex tilted at 30 degrees you get essentially 0.5 * gravity acceleration forward. On a vectored design like this for max forward thrust (while keeping the thing level) is substantially less than that.

Also behavior in wind will be interesting. An advantage of a gimbal is you have a relatively small mass that simply has to not rotate (it's natural state). For example I took this video at the beach in extremely stable conditions with Sparky Brushless Gimbal Controller:


Even though it is getting hammered by wind, the video is rock solid. I'm not sure you can ever get a stabilization controller so tight that you won't have wind moving it, so lacking that gimbal to isolate the motion might be tough.

I'm sure there are some clever tricks that CyPhy developed to get really nice performance. The clips in their demo reel look really nice. Tau Labs is GPL, so hopefully they will release their code changes at some point so we can see what they were!

Future!

So as much as vectored thrust is fun, I really like traditional flying. The control authority of pointing the motors in the direction you want to haul ass is huge. However, this motivated me to work out something I've wanted forever: how to take an arbitrary set of motor positions and angles and calculate the mixer

This is useful for some simple reasons: got your custom shaped frame, weird H, V tail, etc? Now we can solve for the mixer. Even more excitingly, this is exactly what is required to recompute the mixer on the fly for something like a tilt rotor airframe :). TriBlivion might be getting pulled back out of storage.

219 comments:

  1. That's some great stuff man - just putting together a brain controller now but eager to jump on the sparky platform.

    ReplyDelete
  2. Wow that takes off like a rocket :) Very interesting project James.

    ReplyDelete
  3. Wow that takes off like a rocket :) Very interesting project James.

    ReplyDelete
  4. Thats just brilliant James nicely done.

    ReplyDelete
  5. Very awesome mate! Thanks for sharing. Looked like you were using some type of state space control based upon forces. Issue is, how can you calculate the forces without knowing the speed of the motors/propellers? Just varying pwm / current to the motors I would think would have a non linear effect on speed which would likewise make your force responses abit odd as well.

    ReplyDelete
  6. All Assignment Help is a web portal where students get help in making assignments for all the subjects, with the help of our experts. You will get 100% plagiarism free assignment. Expertes consultation is also available for students. If they have any query they can contact with our experts anytime

    ReplyDelete
  7. I found this one pretty fascinating and it should go into my collection. Very good work! I am Impressed. We appreciate that please keep going to write
    more content. We are the assignment helper, we provide services all over the globe. We are best in these services:-

    ReplyDelete

  8. Thanks for sharing this information. I have shared this link with others keep posting such information. to provide best in class law assignment help online at very affordable prices.

    "Assignment Help
    "
    "Assignment Helper
    "
    "Essay writing
    "
    "Essay writing service
    "
    "Dissertation help
    "
    "Thesis writing help
    "
    "Write My Essay
    "
    "Do My Essay
    "
    "Hire Cheap Essay Writer
    "
    "College Essay Help
    "

    ReplyDelete
  9. Initially, I did not even know what is R programming. However, I had always been given a lot of such assignments. so, whenever I searched for essay help, I could not judge whether a firm is suitable or not. But this blog not only gave me an idea essay services, but also made me aware about the things which I must look for in a company that would provide me with Essay Writing Help.

    Now, as I am fully acquainted with both essay services, I can very well judge how erudite the experts of TutorVersal are. The experts have made my life a lot easier now.

    ReplyDelete
  10. Essayassignmenthelp in Australia is undoubtedly one of the most prestigious places for students to get quality academic help online.

    ReplyDelete
  11. Are you stuck up with your assignment writing in various subjects such as Financial Accounting, Audit, Managerial Accounting, Finance, Economics, Marketing, Statistics, Law, Taxation, Human Resource Management, Operations etc ? You are in the right place. Its high time to beat your competitors and score high grades in our guidance. We help students in media assignment help.

    ReplyDelete
  12. It’s good to know about your blog and its post. You have done pretty impressive work on this blog and it posts, Keep up doing well. business law case study assignment example

    ReplyDelete
  13. It can be well explained by taking the example of a giant coffee company “Starbucks” in the following discussions.
    https://myassignmenthelp.com/free-samples/outsourcing-in-starbucks

    ReplyDelete
  14. Very helpful advice in this particular post! It’s the little changes that make the largest changes. Strategic Issues And Options For Sainsbury

    ReplyDelete

  15. I am really satisfied by the great approach is visible in this post and thanks a lot for using the great info is visible in this post.
    cdr sample
    acs rpl sample

    ReplyDelete

  16. Thanks for your marvelous posting! I definitely enjoyed reading it, you could be a great author.
    I will remember to bookmark your post and definitely will come
    back later in life. I want to encourage one to continue your great writing, have
    a nice evening
    cdr sample
    chemical engineer anzsco

    ReplyDelete
  17. Writing a thesis is such an tedious task, but it is too important to for any Doctorate degree aspirant, if you also feeling tiresome come to myassignmenthelp.com and ask for ask for help me with thesis.

    ReplyDelete
  18. Looking for essay writers? Well get online essay help from the best services of my assignment help.

    ReplyDelete
  19. I enjoyed by reading your blog post. Your blog gives us information that is very useful for us, I got good ideas from this amazing quantum realm jacket blog. I am always searching like this type blog post. I hope I will see again. You can use this for any kind of academic writing work.

    ReplyDelete
  20. we are providing english Homework help by World-class native English-speaking writers with advanced degrees at elite universities. So connect MyAssignmentHelp on and get the services

    ReplyDelete
  21. Nice blog post with amazing information. keep sharing the blog like this.

    Math Assignment Help

    ReplyDelete

  22. It is very great to use gaming quadcopter and I found on Kmart promos 2019 with huge discount and it is was much
    impressive.

    ReplyDelete
  23. Ohhh great to read this and thanks for informing us such a great blog which is including all kind of information
    Kmart Coupon Code 2019
    Thanks for sharing.

    ReplyDelete
  24. Extremely authentic and originStrategy Planning Helpal content is what we guarantee. The strategy and planning assignment help provided by our experts is very reliable.

    When we say our services are reliable, we mean it. You will need not worry about anything once you trust our strategy and planning assignment help.

    Email:- ozpaperhelp@gmail.com

    https://www.ozpaperhelp.com/

    https://www.cheapassignmenthelp.co.uk

    https://www.freeassignmenthelp.com
    https://cheapassignmenthelp.blogspot.com/
    Whatsapp :+61-451442632.+91-7503070001,+44-7437875635


    ReplyDelete
  25. Great post I would like to thank you for the efforts you have made in writing this interesting and knowledgeable article.
    norton com/setup
    norton com/setup

    ReplyDelete
  26. You can say this is the best free logo maker app 2019 to create online logo. By the way, there are many logos making apps on the store, but our team has introduced the best app to create online logo, which is not only the 3D logo builder app it also makes visiting cards, its generates beautiful post and create online logo with Free Logo Maker best app.

    ReplyDelete
  27. Arts and architecture
    is nearly as old as the human civilisation itself. It is one of the most beautiful and fascinating program in our educational system. Arts has a history which is not properly known even today, it is existing since time immemorial whereas, architecture is a delineate and planned arrangement. Arts and architecture is the part of philosophical branch which is called aesthetics.

    Arts
    Arts
    is in practice since the existence of human beings. Arts is no longer confined to the closed walls of galleries and museums, it has reached every facet of mankind in advanced forms. Digital art and installation art are two such example of advanced art form.
    You can reach us at-

    Email:- ozpaperhelp@gmail.com

    https://www.ozpaperhelp.com/

    https://www.cheapassignmenthelp.co.uk

    https://www.freeassignmenthelp.com
    https://cheapassignmenthelp.blogspot.com/
    Whatsapp :+61-451442632.+91-7503070001,+44-7437875635


    ReplyDelete
  28. Turkiye'nin ilk ozel televizyon kanalı 1989 yilinda kurulmustur. Dogus Yayın Grubu uzerinden yayın yapmakta olan kanal star tv canlı ismi ile gunumuzde yayınlanmaktadir.Haber bultenleri, cesitli diziler, filmler ve yarisma programlarina star tv izle ekranlarindan ulasabilirsiniz.

    ReplyDelete
  29. This comment has been removed by the author.

    ReplyDelete
  30. Thanks for sharing this information. I have shared this link with other keep posting such information to provide best in class law assignment help online at very affordable prices.

    Online Assignment Help Australia
    5 effective database assignment ideas
    psychology assignment help
    6 Benefits of Meditation to Students
    Best Statics Assignment Help
    Best Assignment Help
    Top Assignment Help

    ReplyDelete



  31. Jaipur Escort Service will not going to get over from you till the time you didn't tell her to do that and will love.Independent Call Girls Jaipur Escorts Service.Escort service in Jaipur we supply that funny exquisite & pleasing nature woman that shall he up a number of pains of life
    Chandigarh call girls
    Chandigarh Escort Service
    call girls in Chandigarh


    Jaipur call girls
    Jaipur escort service
    escort service in Jaipur

    ReplyDelete

  32. My Assignment help is one of the most successful homework help providers on the internet as most experienced writers are associated with them who complete the orders of students within the deadlines. Interestingly, our company has been helping students reach their academic goals with confidence, over 10 years now. And if you also want the same when you look for pay to do my homework, our academic writers can provide you with the necessary homeworks as per your request.

    ReplyDelete
  33. We are Assistance for All Apple Product, a highly rated and reliable apple support agency. You can dial 18003823046, our toll free number to get in touch with our apple support number.

    ReplyDelete
  34. Microsoft Office PC Setup Office Remote turns your phone into a smart remote that interacts with Microsoft Office on your PC. The app lets you control Word,
    Excel, and PowerPoint, Outlook from across the room, so you can walk around freely during presentations.



    Need Help Click Here. www.office.com/setup.

    Get yourself safe from a huge financial loss just be contacting a regular and experienced antivirus
    software service provider. Wiz Customer Service is the name you would be looking for in such conditions which can resolve
    the issues of antivirus scanning.

    Need Help Click Here. www.norton.com/setup

    ReplyDelete
  35. This article you have shared here is perfect. Very good Information in it. I love to read this type of article. Thank you very much for sharing - Monty Singh

    Replica watches india

    first copy watches india

    AAA copy watches

    ReplyDelete
  36. At Best CDR Writing, we are providing the best CDR and RPL report Writing services at an affordable cost. We will deliver 100% plagiarism free and best quality work. Feel free to contact us at https://bestcdrwriting.com/

    ReplyDelete
  37. Webroot Safe is the antivirus which gives total protection and 100% security. All the devices like PC's, Laptops, Mac, Ios, and Android Phones in which we use internet www.webroot.com/safe connection are safe with the use of Webroot Antivirus.

    ReplyDelete
  38. After you buy Norton Antivirus visit norton install with product key sign in to norton account then enter norton product for Norton Setup or Install Norton Antivirus

    ReplyDelete
  39. nortoncom-norton.com download, establishment and enactment. install norton security setup with product key
    The web slanted world structures the need of an antivirus that can verify your data and besides ensure safe taking a gander at and what's more guaranteed trades over the web

    ReplyDelete
  40. Roku.com/link - Steps to interface your Player to your TV. enter activation code roku Roku activate device is the easiest method to stream stimulation to your TV. visit for roku .

    ReplyDelete

  41. To enact the Norton setup, select the Activate Now option at the base. To recharge the membership for Norton, select the Help choice and snap on Enter item key. Cautiously type the right Norton item key in the clear. norton.com/setup Snap on the Next catch.Go through with for more details.

    ReplyDelete


  42. Webroot Antivirus Software Installation Requirements As we realize that Webroot is security programming and antivirus that give a webroot safe high-class insurance to both individual and expert

    ReplyDelete

  43. A progressing Microsoft statement gives some comprehension of how the association designs the landing of new Office 365 ProPlus features. office.com/setup Microsoft uses the equivalent "channels" language for MS Office 365 ProPlus incorporates revives as it does with Windows 10 feature invigorates.

    ReplyDelete
  44. office setup is the best software which is widely used in globe .It is a powerful service that helps you unleash your best ideas ,
    www.office.com/setup get things done, and stay connected on the go.for more details visit:

    ReplyDelete

  45. Webroot Safe is the antivirus which gives total protection and 100% security. All the devices like PC's, Laptops, Mac, www.webroot.com/safe Ios, and Android Phones in which we use internet connection are safe with the use of Webroot Antivirus.

    ReplyDelete
  46. Visit Roku.com/link roku link code to enter Roku activation code and activate your roku device on Tv.Contact for Support if facing any problem

    ReplyDelete
  47. Norton.com/Setup allows you to deploy your Norton setup effectively norton setup . Learn the basics to download, install and activate Norton Setup without any error.

    ReplyDelete
  48. setup & Activate roku.com/link roku link code Streaming device. Get exhaustive guidelines to Enter Roku Code in Roku account from the experts at roku link

    ReplyDelete
  49. office.com/setup - Here you can download latest version of Office office setup the link says 2016 but the version is most updated just visit office setup.

    ReplyDelete
  50. McAfee.com/activate - Find the process for downloading mcafee activation , installing, and activation McAfee products on PC, Mac, Android, and iOS. To activate the product, visit mcafee activate.

    ReplyDelete
  51. The simpletest way to enjoy the large variety of streaming channels on your TV can be available at roku link code . Roku provide great and large variety of streaming channels and other features at its best.

    ReplyDelete
  52. To protect your device from being damaged and hacked mcafee activation , user is advised to use mcafee antivirus. Get started with mcafee today at mcafee.com/activate.

    ReplyDelete
  53. Norton antivirus a family of client software norton setup , server software and services through this you can create professsional looking documents , charts , calculations, reports, and presentation in high speed and accuracy.if you want to install it then visit our site.

    ReplyDelete
  54. I am an academic writer at My Assignment Help. I love the way you have written this, I found it very intriguing and instructive. I am here to inform the readers that we (My Assignment Help) is an  Fast essay writing service  who is known popularly for its assistance to undergraduate, graduate and postgraduate students. We all knew how difficult is to manage and complete university’s tasks like assignment, PPTs, Videos presentation, online exams, online quizzes etc. Keeping this in mind, we are here with civil engineering assignment help for such students who are facing difficulties in their assignment. We have a team of talented, capable and experienced writers to look into your concern and provide a proper and accurate solution. My Assignment Help is a firm offering gpa calculator  in countries like the UK, Australia, USA, South Africa, Canada, Singapore etc.

    ReplyDelete
  55. Excellent information Providing by your Article, thank you for taking the time to share with us such a nice article. Amazing insight you have on this, it's nice to find a website that details so much information about different artists. Kindly visit livewebtutors website we providing the best assignment help services in Australia.
    Read more now :- Assignment Help Sydney

    ReplyDelete
  56. Where can you get assignment help which is remarkably affordable, packed with perfection and done by the real subject experts, which are very hard to find easily these days? We know the answer. The place is UK Assignment Help and you can very easily find them just a click away!

    ReplyDelete
  57. I am a freelancer and have been helping a lot of students in providing assistance to students who frequently gets worried about their assessment tasks and went online to search for Australian Assignment Help terms.
    We at My Assignment Services have potentially recognized the need way back and started what we are an enlarged version of then. With many assignment helper companies in the market, no one has quite able to match the standard that we follow. We give utmost priority to students by strictly adhering to the assignment requirements as well as marking rubrics to score high grades. Our Programming Assignment Help writers are well-proficient in not only comprehending your assessment tasks but also to give an expert finish to it.
    Provided a well-written assignment suitable to your needs, your search for Essay Assignment Help will now end with My Assignment Services. You just have to visit our website for more information.

    ReplyDelete
  58. I suggest all members choose Humanities Assignment Help Australia for the best guideline in your academia. The perfect and expert assistant your requirement and learning assignment project by the university.

    ReplyDelete
  59. Office Installation is easy and yet the most complex thing for some. Here we are to guide you through some easy ways to Install office setup with product key and Setup Office.

    ReplyDelete
  60. Roku Streaming is a hassle-free, latest technology and very economical to watch T/V, Only require to connect roku activation link code Roku device into t/v. The user needs to set up a Roku account, after that user only needs to Activate Roku device.

    ReplyDelete
  61. Office is one of the best software office setup and enter product key available right now. The productivity suite is one of the best and the biggest software available right now.

    ReplyDelete
  62. AVG Support resolves issues using remote access technology install avg with license number you just need to sit back relax and let the technician do their work.

    ReplyDelete
  63. For Office Setup and Installation go to website install office 365 with product key and get started with Installation.

    ReplyDelete
  64. Office has the cloud support integrated and can be used where you want. Office 365 is solely based on the office setup and enter 25 character cloud and won’t take up your device space. You can save documents via the cloud too.

    ReplyDelete
  65. If you seek proper Norton Antivirus installation, the simpler way is to use the norton install with product key In addition to protecting a device after installation, Norton also blocks unauthorized access during installation as well.

    ReplyDelete
  66. Webroot is quick and easy to download, install, and run. Plus, updates are automatic so you always have the most current protection. Clicking webroot install with key code will trigger an automatic download accompanied by instructions for activating your protection.

    ReplyDelete
  67. Avg is a well- known name in the field of virus protection. The reason for which this name is common among all end users is its free install avg with license number antivirus and malware protection.It not only sounds avg.com/retail free but it provides a lot more with no money. It scans for virus and malware

    ReplyDelete
  68. Accomplish more with OneDrive and Office 365 Create cleaned reports, open bits of knowledge, present withinstall office 365 personal with product keyr lucidity, and work together continuously utilizing Office 365

    ReplyDelete
  69. norton web security is generally utilized antivirus gives the least demanding to utilize and most intutive assurance for your PC and your mobiles .introduce it norton antivirus and disregard viruses,spyware,root-units, hackers.for more subtleties visit: norton.com/setup today

    ReplyDelete
  70. norton setup offers a fee-based suite of antivirus products which provide various malware detection method. User can protect their norton com setup devices by regularly scanning the computer with Norton antivirus. norton.com/setup anti-virus suite uses virus definitions, suspicious behavior, emulation and the sandbox method to detect viruses

    ReplyDelete
  71. Webroot SecureAnywhere AntiVirus is a powerful antivirus that has been created to fight against malwares and other threats. Visit : webroot product key for installing webroot

    ReplyDelete
  72. Download and istall Webroot Software and Webroot Secure Anywhere AntiVirus webroot download which affect your computer and laptop

    ReplyDelete
  73. After you buy Norton Antivirus visit norton.com/setup, sign in to norton account then enter www norton com setup norton product for Norton Setup or Install Norton Antivirus

    ReplyDelete
  74. Roku provides the simplest way to stream entertainment to your TV. With thousands of available channelsvisit here for more details roku activation enter link code

    ReplyDelete
  75. Webroot Mobile Security is a multi client permit enabling you to utilize your permit on up to 3 gadgets. On the off chance that you are webroot account utilizing the most extreme number of gadgets you should uninstall from the old gadget preceding introducing on the new gadget

    ReplyDelete
  76. Introduce Mcafee antivirus to shield your PC or PC from infection assaults nd ensure ur data. Mcafee Activate Visit there mcafee installation with product key to initiate mcafee antivirus with enactment code that is

    ReplyDelete
  77. To enact Hulu Plus on your gadget, either utilize the on-screen console to enter your Hulu sign in data or go to and enter the gadget initiation code. Both of these strategies will enable you to create hulu account utilize Hulu on any Hulu-upheld gadget

    ReplyDelete
  78. You can utilize Certutil.exe to dump and show confirmation authority (CA) arrangement data, design Certificate Services, reinforcement and reestablish CA parts, and check testaments, key matches, and verifies key declaration chains

    ReplyDelete
  79. Get a champion among the best Office setup support! We offer MS Office 365 setup and MS Office 2016 setup organizations. Besides, our point is to empty all enter your product key 25 character of the issues of your pc , PC, etc you can our site for more information click here for more subtleties

    ReplyDelete
  80. mcafee antivirus is commonly used aantivirus distinguishes and kill PC contamination, the mail worms,the trojan programs,and in like manner empowers your structure mcafee activate download and activate to free of disease and other malware is a noteworthy consistently challenge. for more nuances visit : here for more subtleties

    ReplyDelete
  81. Microsoft Office is an application software. It is used in most of the businesses and organizations Install office setup on your office setup and enter 25 product key Pc's to get best advantage of it. mostly used tasks are ms-word, Ms-excel and Ms-powerpoint

    ReplyDelete
  82. mcafee antivirus is generally utilized aantivirus recognizes and kill PC infection, the mail worms,the trojan programs,and likewise enables enter mcafee activation code your framework to free of infection and other malware is a significant day by day challenge. for more subtleties visit:

    ReplyDelete
  83. I am overwhelmed by your post with such a nice topic. they mainly provide assignment help Australia in universities and college at myassignmenthelpAu.com. we offer pocket-friendly services and write tailored assignments at Affordable Price. They are capable to write the premium quality of assignments according to the requirements of students and university norms.

    ReplyDelete
  84. Create or log into your Webroot account office setup with product key here. Manage your security across multiple devices, with any Webroot product. Get started today!

    ReplyDelete
  85. Find the easy way to download, install and activate McAfee Antivirus, type the 25-digit product key at mcafee installation with product key here.

    ReplyDelete
  86. AVG is the one of best antivirus which protects your computer

    and network from bad infection and threats. AVG now includes

    real-time security updates, scans for both malware and

    performance issues, and even catches malicious downloads before

    they reach your PC. User can Install AVG Antivirus on their

    computer to protect thier computer and network...
    www.avg.com/retail

    ReplyDelete
  87. Do you need How to start an essay? So don't worry, students 360assignments.com have many essay experts. Who assists you in your essay writing problems and guide how to start an essay.

    ReplyDelete
  88. It may not easy for every student to gather all essential information to write their project management assignments. If you are the one, then choose professionals’ guidance using Project Management Assignment Help
    services.
    Project Management Homework Help

    ReplyDelete
  89. Are you looking for assignment expert justquestionanswer.com is providing college homework in the USA from the qualified expert. Our 3000+ experts are available 24x7 to help the USA students and bring forth the peerless Science end of the day without asking an amount that exceeds the budget.

    ReplyDelete
  90. Behavior therapy, for instance, makes it possible for individuals living with ADHD to improve social skills such as sharing and interacting more with peers. cheap assignment help

    ReplyDelete
  91. This post was awesome thank you for sharing. GIS (Geographical Information System) are basically systems of computers that are designed to collect, analyze, manage and share geographical and spatial data. Remarkably, almost all environmental applications today utilize GIS. In other words, GIS has gained wide applications in both research, management of wildlife, tracking specific species, informing agricultural practices among a tone of other different uses. Learn more from GIS Assignment Help

    ReplyDelete
  92. Nice blog and raise brilliant content for torque.You have give sufficient knowledge of torque and motor.Nice to read the blog i will come here again to read new article posted by you.
    Webroot Download

    Garmin Express

    ReplyDelete
  93. This comment has been removed by the author.

    ReplyDelete
  94. My assignment help is the most preferred place to get assignment help Australia services where we offer 100% plagiarism free and money back guarantee ensuring complete satisfaction of students with every order. Our subject-specific experts are available 24x7 to provide properly formatted and referenced solutions in any subject from any level in Australian universities.

    ReplyDelete
  95. Get affordable and impressive biology assignment help from Phd holders in biology. Every student is welcome at abc assignment help, can request for any assignment any time. We will provide you 100% plagiarism free content, which will help you to get top grades in academics

    ReplyDelete
  96. My Assignment Help services online is a premium academic writing service offering professional assistance in every course and subject of your choice. You come up with any topic and our tutors will guide you through identifying expert answers with proper arguments and references. We offer expert writing service for assignments, essays, coursework, report writing, case study, research paper and thesis within your budget.

    ReplyDelete
  97. It is a great chance I had to read your amazing article for sure I have cached for future reading. A geographic information system is a computer system that captures, stores, checks, and displays data related to locations on the Earth’s surface. GIS relates unrelated data to help individuals and organizations develop a better understanding of spatial patterns and relationships. Read more from GIS Assignment Help .

    ReplyDelete
  98. The most challenging thing in student life is when you run out of money and it’s the start or middle of the running month and you have to do a lot of things related to your studies especially when you have to hire do my assignment writing service provider for your academic writing. Keeping this in mind our Academic Writing Experts provides the best rates in Australia.

    ReplyDelete
  99. Fluid mechanics assignment help : Your service helped me to solve the engineering assignment in a timely manner. I appreciate your professional approach that adds a taste of difference. I tried many writing services before. However, you proved to be the best in technical disciplines. I will recommend your best offers to my college friends. Many thanks! or fother information visit here :Exercise Physiology Assignment Help

    ReplyDelete
  100. This comment has been removed by the author.

    ReplyDelete
  101. At Best CDR Writing, we are providing the best CDR Writing services at an affordable cost. We have a team of professionals which will deliver the best quality work

    ReplyDelete
  102. very professional approach. like the way you have make it clear to me.
    Custom boxes provides you the services in same manner including Custom tissue paper and many more to save your time and money.

    ReplyDelete

  103. After the launching of "Kids & Family" section on Roku channel, Roku is also adding new features to give more control to parents over the channel, what their kids can watch when accessing Roku channels.

    roku.com/link

    ReplyDelete
  104. To install the MS office setup and enter product key, make sure that user have a good internet connection. Now to install office on the device, open the folder where you have downloaded the file.

    install office home and student


    ReplyDelete
  105. Thank you for predicting our needs and writing great and informative article. Shade nets are the upcoming synthetic fibers materials that are nowadays preferred in the construction of net houses, greenhouses and preparing seed nurseries. They are mostly used in a broad variety of crops like blackberries, chives, and tomatoes. Visit Shade Nets Purchase and Installation

    ReplyDelete
  106. Thank you for posting such a great blog! I found your website perfect for my needs. It contains wonderful and helpful posts. Keep up the good work. Thank you for this wonderful Blog! Read more: statistics assignment help online

    ReplyDelete
  107. Thank you for sharing this useful information, I will regularly follow your blog. Get the best website design, mobile app development, SEO, PPC advertising company

    ReplyDelete
  108. I was very impressed by this post, this site has always been pleasant news Thank you very much for such an interesting post, and I meet them more often then I visited this site.
    Drive Jacket

    ReplyDelete
  109. Such an interesting article here.I was searching for something like that for quite a long time and at last I have found it here. Brown Leather Bomber Jacket

    ReplyDelete
  110. Create Backlinks to Publish Your Blogs & Articles! Whether you'd like to share your knowledge, experiences or the latest news. And free update Blogs & Articles here.
    top blog platforms in UK
    top blog platforms in USA

    ReplyDelete
  111. At Infotrench SEO Company - Innovation, quality, creativity, and promptness are the main mantras of Infotrench Technologies and we imbibe these mantras in our work, to the core.
    ppc advertising company in Moradabad
    ppc advertising company in Lucknow

    ReplyDelete
  112. Our the purpose is to share the reviews about the latest Jackets,Coats and Vests also share the related Movies, Gaming, Casual,Faux Leather and Leather materials available Tiger King Jacket

    ReplyDelete
  113. Why my printer HP showing error code 79?
    HP printers are in use for a long time, and it provides best-in-class services to its users, but sometimes the case may be different. The HP printer error code 79 is one of the cases, and this occurs because of some corrupter or interrupting printing job. The other reason may be the lack of communication between the spooler and the printer and that too because of the outdated version of the firmware.

    ReplyDelete


  114. Norton.com/setup can only work when it has been activated. To activate your Norton Setup, the user is required to Enter 25 digit Norton Product Key.n install with product key click here for subtleties.

    norton.com/enroll

    ReplyDelete
  115. Everyone searching for some new and innovative ideas from anywhere Political Science Assignment Help. If you have some useful and informative then, peoples are loves for that. Really I am very thankful for this article to share high value with us.

    ReplyDelete
  116. Everyone searching for some new and innovative ideas from anywhere Political Science Assignment Help. If you have some useful and informative then, peoples are loves for that. Really I am very thankful for this article to share high value with us.

    ReplyDelete
  117. Create Backlinks to Publish Your Blogs & Articles! Whether you'd like to share your knowledge, experiences or the latest news. And free update Blogs & Articles here.
    guest posting sites in USA
    guest posting sites in UK

    ReplyDelete
  118. At Infotrench SEO Company - Innovation, quality, creativity, and promptness are the main mantras of Infotrench Technologies and we imbibe these mantras in our work, to the core.
    Search Engine Optimization Company in Pune
    Search Engine Optimization Company in Chandigarh

    ReplyDelete
  119. Thank you because of this informative blog since it's really assistance, I like blog. Wonderful! Thank you for sharing an informative information! If you are planning to upgrade your older TV to Smart TV, then you must purchase Roku instead. Roku is a budget-friendly streaming media player. They are available 24X7 to pick up your phone call. Post click here Roku com/link!

    ReplyDelete
  120. Great Info, Your blog is very informative and interesting, your all post are amazing, keep sharing more interesting topics.
    roku application for pc windows mac
    roku App install

    ReplyDelete
  121. I like your post. Pro Assignment Help provide top quality assignment services and we have never at any point traded off with the reliability. This is the reason a considerable lot of us have had the option to have the option to help students with accomplishing engaging evaluations, everytime they seek for online essay writing help,homework help online,coursework help,research writing help onilne,thesis writing help online,from us.

    ReplyDelete
  122. Usually, I do not learn post on blogs, however, I would like to say that this write-up very forced me to check out and do so!

    Jodhpur Sightseeing Tour

    ReplyDelete
  123. Great Job here on your blog. I read a lot of blog posts and i never heard of a topic like this. I love this topic you made. you can also enjoy my blog shayariguide - check links

    Shayari Guide
    ShayariGuide
    Shayari

    Attitude Shayari
    Attitude Shayari for boys
    Attitude Shayari for Girls
    Attitude Shayari In Hindi
    Attitude Shayari In English

    ReplyDelete
  124. Great Job here on your blog. I read a lot of blog posts and i never heard of a topic like this. I love this topic you made. you can also enjoy my blog shayariguide - check links

    Shayari Guide
    ShayariGuide
    Shayari

    Attitude Shayari
    Attitude Shayari for boys
    Attitude Shayari for Girls
    Attitude Shayari In Hindi
    Attitude Shayari In English

    ReplyDelete
  125. Usually I never comment on blogs but your article is so convincing that I never stop myself to say something about it. You’re doing a great job Man,Keep it up.you can also enjoy my blog shayariguide - check links
    Shayari Guide
    ShayariGuide
    Shayari

    ReplyDelete
  126. Great content comes from great writers. Most institutions of higher learning across the globe have made it compulsory for students to have a capstone experience as part of their graduation requirements. In other words, chances are that you will have to work on a capstone research project in order for you to graduate. Read more on Capstone Writing Services

    ReplyDelete





  127. Roku is a streaming device, which provides the simplest way to stream entertainment channel to your TV. On your terms. You can access more than 500000+ movies and TV episodes across free and pay on Roku. Also, you will get the best quality video streaming with it. You can watch shows, movies, an entertainment channel, web series, etc. For the activation of the Roku device, Go to URL:
    roku.com/link

    ReplyDelete
  128. Read about best smartphone news reviews, price and specifications and much more features
    Done
    Done
    Done
    Done

    ReplyDelete

  129. Roku streaming device that is very popular in the United States all over the world. Roku provides users with the best entertainment they have ever wanted.

    roku.com/link

    ReplyDelete
  130. Create Backlinks to Publish Your Blogs & Articles! Whether you'd like to share your knowledge, experiences or the latest news. And free update Blogs & Articles here.
    free blog sites in USA
    free blog sites in UK

    ReplyDelete
  131. Now, if you are confused about the guidelines to be followed in Vancouver style citation, don’t worry. We, at MyAssignmentHelp, have created a citation generator to help students with vancouver referencing example.

    ReplyDelete
  132. I ejoyed surfing your blog,I just found what i needed in this site
    meta description writing services

    .

    ReplyDelete
  133. I have had so many disappointments online. I have found it so hard to trust anyone online. I am giving it a last go with you. I want economics assignment help which must be delivered in 48 hours. If it is not possible just be frank and say it is not. More to that I would like to see your economics homework help samples to ascertain that I am hiring the right person. I just hope I won’t be disappointed this time around.

    ReplyDelete
  134. Excellently written article. Great info. Thanks.
    Elite Academic Broker

    ReplyDelete
  135. How do you treat urgent assignments? I need an economics assignment help expert in a position to deliver my order in 5 hours. It is very urgent and I am willing to pay extra cash if you are ready to deliver on time. I also want you to concentrate on quality too. If you can deliver it then reach out to me. Let me also know how much you charge for economics homework help.

    ReplyDelete
  136. Acharya, Maharaj pulak sagarji, chinmay sagar ji, tarun sagar ji, gyan sagar ji, Shiv Muni Ji, Mahashraman Ji, Subhadra Muni Ji, Pranamya sagar ji, Swasti Bhushan, Gyan mati mata ji, Praman sagar ji, vidyasagar, jain muni, shwetambar saints ke vachano se apni life change kijiye.
    tarun sagar ji maharaj
    Kadve Pravachan
    gyan sagar ji maharaj

    ReplyDelete
  137. McAfee Antivirus Tools are developed by Symantec Corporation, provides a complete Anti-Virus suite for PCs.o to your McAfee Antivirus software and Open it. · Enter the 25 digits alpha-numeric product key that was mailed to you
    www.mcafee.com/activate
    mcafee.com.com/activate"
    <a href="https://mcafee-mcafeeactivate.com/>mcafee activation</a>

    ReplyDelete
  138. The substantial growth of the key end-use industries is expected to be one of the prime factors for Chlorine Trifluoride Market growth during the forecast period. Chlorine trifluoride is extensively used in the semiconductor industry for the application of cleaning chemical vapor deposition chambers. Chlorine trifluoride has the advantages that it can remove solid residues from the wall of the chamber without disassembling chambers. The application of chlorine trifluoride also allows cleaning to be accomplished at relatively low temperatures.

    ReplyDelete
  139. This is an amazing blog. Your blog is really good and your blog has always good thank you for information. AWS certified partner media live.

    ReplyDelete
  140. Exactly what i was looking for. It is no secret that people are often charged with more responsibility than what they signed up for in an organisation. At such a time, one cannot argue over the fact that they did not sign up for this. Consequently, universities prepare the students to work with a greater knowledge of Petroleum Engineering. For that, the assignments are targeted in a way that makes students go beyond the classroom knowledge. Get Petroleum Engineering Tutors

    ReplyDelete
  141. Ice Bongs: Buy the best quality ice bongs online in wholesale in Germany, Netherland, Spain and Europe on metierwholesale.com. Order now!
    ice bongs, wholesale water pipes

    ReplyDelete
  142. thank you for sharing Custom hair packaging boxes at wholesale that's great job.

    ReplyDelete
  143. Wonderful article. Very interesting to read this article. Printer Helpers is a US based printer master affiliation that is striking for its reasonable system.
    Printer Helpers
    printerhelpers.com

    ReplyDelete
  144. Very interesting articles. I’ve really loved surfing around your website many subjects. Thank you so much admin like this info sharing to us and I’m hoping you write again soon! Assignment Help Adelaide -
    Assignment Help Australia -
    Assignment Help Melbourne

    ReplyDelete
  145. Audience goes ahead to a point of making their own conclusion basing their grounds on conversations and events that takes place throughout the narrative.article writer

    ReplyDelete
  146. Roku activation code is a code meant to activate the software and confirm that when you are finished with the Roku activation process, you can add multiple streaming services like Netflix, HBO, NBC and many more .

    roku.com/link

    ReplyDelete
  147. I am Irene Garcia, a Corporate Sales Specialist operating in the Latin American region. We are experts in Market Research (Mercado de Vehículo Eléctrico Híbrido de México ). We provide market reports across various industry verticals and also help with procurement and supply chain intelligence. By giving you better insights, we help you make informed business decisions.

    ReplyDelete
  148. Very nice information providing by your post, thankyou so much for taking the time to share such an excellent post. I am a professional assignment writing expert and offering the best Need Assignment Help to students worldwide.

    For more info: Mechanical Engineering Assignment Help Australia

    ReplyDelete
  149. Ceramic Bongs: Buy ceramic bongs online in wholesale in Germany, Netherland, Spain & Europe on metierwholesale.com. Easy shipping.
    ceramic bongs
    acrylic bongs
    glass bong wholesale

    ReplyDelete
  150. amazing website, this is really some good quality content. loved the way you explained through words keep writing the best articleNEWS

    ReplyDelete
  151. amazing website, this is really some good quality content. loved the way you explained through words keep writing the best article
    Readerscook

    ReplyDelete
  152. My Assignment Help always give you error free Professional Finance Assignment Help in time. In case if you are not satisfied with our help. Our writer can change your assignment. You can take an unlimited revision of your assignment Studies.

    ReplyDelete
  153. To complete online activation process, user should have Office Account along with product key. Then after we will be able to activate office product. Here are some steps listed below to complete process.

    Office home student 2019

    ReplyDelete



  154. Office.com/setup Home student 2019 is a collection of all Microsoft application software. In this, Word, Excel, PowerPoint, Outlook, and One Note are all included.

    Office.com/setup home & student 2019

    ReplyDelete
  155. Having problem of write my thesis online for the student. Another problem that students face is the ability of not able to understand the thesis. For that student ask for assistance from the thesis experts, experts give them precise and accurate answers for all the doubts that are asked by the students.

    ReplyDelete
  156. Gotoassignmenthelp is team of leading professional writers for Essay Help Writing Services to students all around the world. Contact us today for Best Research Paper Help at very affordable price. Under GotoAssignmentHelp we provide many types of help to the students. We are the most reliable assignment helpers. We have gained our specialization after spending most of our times in making ourselves perfect. We providing 100% plagiarism free Assignment Help. At the point when you pick our Case Study Help assistance, our faculty will consider the quality and your evaluation criteria.

    ReplyDelete
  157. "mcafee is an antivirus software providers that secure your computer for virus , worms ,trojens and other mailcious program .it provides full range of
    security product like antivirus , firewall etc .you have to do mcafee antivirus download "

    ReplyDelete
  158. Best Assignment Experts offers outstanding assignment help to students who are struggling with assignment writings. Our subject matter experts, scholars, and professors are 24*7 hours available for all learners. We offer a well-prepared and 100 % plagiarism-free solution that guarantees an A+ grade. Communicate Best Assignment Experts now! All Assignment Help

    ReplyDelete
  159. The best Assignment Experts team is very much dedicated responsible and takes care of yourMYOB Assignment Help . Well-versed, Ph.D. professors, MYOB experts write flawless, andwell-written, customized, and 100 % plagiarism-free MYOB Assignments. 24*7 hours assistance and on-time delivery is guaranteed to all accountant students at an affordable price.

    ReplyDelete
  160. The great website and information shared are also very appreciable.
    Knight Rider Leather Jacket

    ReplyDelete
  161. The contents of this blog are always very interesting, educative and informative, I must commend you for the good work you are doing here, keep it up. futo cut off mark for medicine and surgery

    ReplyDelete
  162. Hi, I am Linnea! If you need help with your assignment, I recommend you get online assistance. The Best assignment help we provide gives them good grades. Before paying for an assignment help service, feel free to get a free sample from our assignment helper. If you run into any issues, I am available to assist you.

    ReplyDelete
  163. The great website and information shared are also very appreciable. Sons of Anarchy Leather Vest

    ReplyDelete
  164. Thank you for Such a Informative Blog, We proudly provide services that keep our community moving, with expertise in constructing hardstands, carparks, roads and driveways. We primarily service Melbourne metro, Geelong, Ballarat, Bendigo, Warragul and Mornington regions.
    READ MORE :- Asphalt Driveways

    ReplyDelete