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.

101 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. Assignmenthelp.us has come up with the perfect chemistry assignment help service to serve students best with their academic works.

    ReplyDelete
  8. The word ‘effect’ implies of a greater action than ‘affect’. Thus, when you use affect and effect, the whole meaning of the sentence is dependent on that particular word.

    ReplyDelete
  9. This post is not just informative but impressive also. The post is so convincing that it created an urge to choose Assignment Help services. You can email us at Info@Myassignmenthelpau.Com or Phone Number: +61-2-8005-8227

    ReplyDelete
  10. 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
  11. Many of the people are depressed about the problems of essay writing. Well, don’t worry about that because we are providing this service at a very reasonable price.
    "Essay writing
    "
    "Essay Writer
    "
    "Article rewriter
    "
    "Essay writing service
    "
    "Essay writing help
    "
    "Write My Essay
    "
    "Write My Article
    "
    "Essay Helps
    "
    "Write my essay cheap
    "
    "Do my essay cheap
    "

    ReplyDelete
  12. 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:-

    Digital Markrting Blog
    SEO Blog
    Social Media Blog
    Email Marketeting Blog
    Online marketing Blog

    ReplyDelete
  13. Many of the people are depressed about the problems of essay writing. Well, don’t worry about that because we are providing this service at a very reasonable price.
    "Assignment Help
    "
    "Assignment Helper
    "
    "Essay writing
    "
    "Essay writing service
    "
    "Dissertation help
    "
    "Thesis writing help
    "
    "Write My Essay
    "
    "Computer Science Assignment Help
    "
    "Assignment Help Soth Africa
    "
    "Assignment Writing Service
    "

    ReplyDelete
  14. 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:-


    "Assignment help NZ
    "
    "Assignment help NZ
    "
    "Assignment help UK
    "
    "Assignment help US
    "
    "Assignment help Australia
    "
    "Assignment help Canada
    "
    "Assignment helper
    "
    "Assignment help
    "
    "Writing Assignment Help
    "
    "Help For Assignment
    "
    "Write my assignment help
    "

    ReplyDelete

  15. 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
  16. The above information you shared give me a new look at this topic. I am working as a full-time academic writer in myassignmentHelpsg providing Assignment Help Singapore services to college students.

    ReplyDelete
  17. Thanks for this informative content. It’s really good. Actually, I want to share some thoughts and reviews about an assignment help company in Australia and the brand name is SAMPLE ASSIGNMENT. Here, I am working as an Academic Expert. To look at our online academic assistants who provide reference assignment including Accounting, Management, Finance, IT, Economics, Computer Science, Nursing, Marketing; all Academic subjects to University Students all over the Australia or even worldwide, Here is a big online assignment help providers who help students to get HD grades according to assessment guidelines and instructions. Those who are searching for assignment provider in Melbourne, Perth, Brisbane, Adelaide etc. get a touch with Sample Assignment - the No.1 Assignment provider. Any student really wants to buy an assignment at the cheapest price goes to our branded website and has a look and opts our amazing and informative services, you can avail of our convenient online assignment help and samples available on our website for free. You can download it if you want. Are you ready to get 100 out of 100 in your university assessment? We assign the best writer according to the subject for your academic problems and provide support in assignment writing services. Our Customer Care Executives are available 24*7 hours to assist you in the best possible manner. Phone calls and emails are the best methods used by online assignment help providers.

    ReplyDelete
  18. Those who are roaming around, website to website in search of the right "my assignment help Australia” Package that found a website. Who never imagined there existed more accurate and genuine assignment help services. Many websites claim to be the number one, but my vote, undoubtedly lands into your account. After getting cheated by several other assignment providing companies, you know for sure, you buy assignment online or you can also found related topics assignment like cdr writing services from sample assignment.

    ReplyDelete
  19. 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
  20. A lot of valuable information can be derived from the post. Certainly, this compelling post will encourage readers to choose Assignment Help Australia services. You can email us at info@firstassignmenthelp.com.

    ReplyDelete
  21. For nursing students, it gets a bit difficult to even make time to content an online assignment help providing company for nursing assignment help. Which is why, we, at Online Assignment Expert have extended our assignment help services which only exist in order to make it more convenient for the nursing students to fetch assignment solutions from an online assignment help company. Therefore, in order to avail our nursing assignment help offering no plagiarism, Free Turnitin, Partial Payment, Unlimited Revisions, etc. You can contact our team of highly professional, experienced, PhD experts to avail the discounted services!

    ReplyDelete
  22. For nursing students, it gets a bit difficult to even make time to content an online assignment help providing company for nursing assignment help. Which is why, we, at Online Assignment Expert have extended our assignment help services which only exist in order to make it more convenient for the nursing students to fetch assignment solutions from an online assignment help company. Therefore, in order to avail our nursing assignment help offering no plagiarism, Free Turnitin, Partial Payment, Unlimited Revisions, etc. You can contact our team of highly professional, experienced, PhD experts to avail the discounted services!

    ReplyDelete
  23. Students are given assignments, such as an essay, on a regular or periodic basis by their professors. These are mandatory and students are graded on the basis of the quality of work done by them. Essay writing may be a great opportunity to score the top grades but they come along with challenges as well. To overcome them, the best way is to consult an online academic helper who provides essay help. TutorVersal has a dedicated team of qualified essay and homework help experts who assist students with their assignment tasks. This not allows students to submit their work on time but also lets them score excellent grades in them!

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

    ReplyDelete
  25. 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
  26. 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
  27. Thank you for your informative content. I really appreciate it. However, I would like to recommend every single student that is facing any kind of challenges in their academic assignment, about highly accurate assignment writing services that are being offered by Industry best assignment help provider My Assignment Help Oz.
    I could recall an event where I once urgently needed professional assignment writing service to help me make a perfectly structured essay in 2hours. This is when the best assignment writing services offered me a chance to avail their professional services and in a couple of days, I was rewarded with a huge round of applause for preparing the best assignment in front of the whole batch.

    ReplyDelete
  28. Hey, great article you have there. I am sure that the students looking for assignment helpand ways to write their assignment got to learn a lot of things that were not clear before. The students who need guidance on how to write an assignment, I am also an academic expert who provide online assignment help to the university going students in their academic tasks at My Assignment Services. We are a team of professional experts who are all either a Master’s degree holder or a PhD scholar. For years, we have aided students who are busy in their part time jobs or cannot take out sufficient time for assignment writing. Their can you do my assignment questions are successfully addressed at My Assignment Services.

    ReplyDelete
  29. This post is a pool of information. The readers are quite impressed after reading this impressive post. This impressive post certainly encourages to choose Assignment Help Australia Services. You can email us at cs@Myassignmenthelpau.Com or Phone Number: +61-2-8005-8227

    ReplyDelete
  30. 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.
    cheap assignment help Australia

    ReplyDelete
  31. 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
  32. Thanks for sharing this information. We need such information to create CDR Reports. You can get complete CDR Report Writing Service from us. We also provide CDR Reports in Australia, Summary Statement Writing and Career Episode Writing.
    Thanks for sharing this information. We need such information to create CDR Reports. You can get complete CDR Report Writing Service from us. We also provide CDR Reports in Australia, Summary Statement Writing and Career Episode Writing.

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

    ReplyDelete
  34. Excellent information on 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. Assignment Help

    ReplyDelete
  35. I really like your post. Get CDR Report Help by a team of professionals. Our Services consists of a wide range of CDR Reports. Our services include CDR Preparation, Complete CDR Writing service, career episode writing, Summary Statement Writing, and RPL report writing as well.

    ReplyDelete
  36. 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.
    Assignment help
    Assignment help
    Assignment help
    Python Programming Assignment
    Programming Assignment Experts
    Assignment help tutors
    Assignment help

    ReplyDelete

  37. 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

  38. 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
  39. 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
  40. Excellent and nice post. It will beneficial for everyone. Thanks for sharing such a wonderful post. Avail No 1 Essay writing Services UK from certified PhD writers. It is extremely helpful for me. You can email us at info@ukdissertationhelp.co.uk or Phone Number - 020 8144 9988

    ReplyDelete
  41. Much obliged to you for such an enlightening bit of work. It, without a doubt, is really educational! In any case, this is to illuminate the reader about My Assignment Services, an Australian nursing assignment help service provider. The brand has around 100+ nursing academic writers. I am one of those helping students who search “is there someone who can do my assignment?” . When you do examine our site, the academic experts would begin preparing your assignment necessity with the best quality. For the students, searching for assignment writer in Australia, My Assignment Services has been the essential decision with regards to online assignment help in Australia and abroad. With a top to bottom research going into every single task we give, the nature of our assignment help online has set industry breaking measures. So as to get in touch with us, the most advantageous way that is available, we have obliged a speedy structure and email to make our online task help Australia bound administrations in a jiffy.

    ReplyDelete
  42. Are you in search of MATLAB Assignment Help or any assistance with MATLAB Project Help Services?? Nothing to worry when MATLAB Solutions team is here. Leave all your Matlab Programming problems on us

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

    ReplyDelete
  44. 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
  45. 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

  46. I would like say thanks for this post. Here are some useful links for stdudents all across the globe. If you are looking for assignment help, we are the best providers for you. We have our services which include :
    Python Assignment Help
    Electrical Engineering Assignment Help
    Programming Assignment Help

    ReplyDelete

  47. Are you in search of MATLAB Assignment Help or any assistance with MATLAB Project Help Services?? Nothing to worry when MATLAB Solutions team is here. Leave all your Matlab Programming problems on us.

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

    Math Assignment Help

    ReplyDelete

  49. 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
  50. Really great information. I always love to read and spread this kind of information that is unique and really informative. Keep up the good work.
    Regards,
    The Soft Logix

    ReplyDelete
  51. Thanks for sharing great information. I always love to read and spread this kind of information that is unique and really informative Flip Flop Direct

    ReplyDelete
  52. 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
  53. Thanks for sharing this valuable information, I am here to share some benificial information for stduents looking for cdr report help. We are cdr report service providers providing , ka02 writing services, career episode writing and rpl report writing.

    ReplyDelete
  54. 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
  55. 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

  56. Here I am sharing a very useful resource for students looking for assignment help. ProAssignmentHelp providing all sort of assignment writing in various subjects like as : Electrical engineering assignment help , electronics assignment help , MATLAB assignment help , management assignment help , etc.

    ReplyDelete
  57. 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
  58. 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
  59. Thank you for making me understand about how important is the subject of marketing for students pursuing relevant courses. However, there are experts dealing in marketing assignment help by going through different formats of writing. Our aims are to provide exceptional features of on-time assignment delivery, plagiarism check, partial payment, etc. In case you like numbers and interested in knowing our customer ratings, it is available on our website at Online Assignment Expert and meet our hard-working online assignment help experts. Feel free to take our contact us anytime.

    ReplyDelete
  60. This blog is so informative. After reading this blog, I have actually come to know why students come up with queries such as “do my assignment for me” and more. It is all because they not only have shortage of time in their lives, but also because they lack some or other writing skills that are needed in solving such assignments.

    So, whenever I decide to pay someone to do assignment, I always rely upon My Assignment Services. This is because when you pay to do assignment, this firm always lives up to your expectations. They not only offer an extensive range of academic consultation services, but also offer you with a wide range of value-added services such as the live one-on-one session with the experts, free copy of the Turnitin report, free editing and proofreading services and many more.

    So, I always take my “do my assignment for me” queries to this firm

    ReplyDelete
  61. I really enjoyed your blog Thanks for sharing such an informative post.
    https://www.login4ites.com/

    ReplyDelete
  62. As you order for nursing papers made easy you must find out if your essay writing company offers extra facilities like making corrections and amendments if there are mistakes made by writers. You can also purchase custom research paper.

    ReplyDelete
  63. 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
  64. This comment has been removed by the author.

    ReplyDelete
  65. It’s good to share information with others. I am also sharing something very important for students seeking MATLAB Assignment Help. Visit
    matlabsolutions.com and get best assistance in your MATLAB, simulink assignments and projects. You can also visit MatlabHelpers for Matlab Assignment Help from Mathworks certified experts that provide online help services to students

    ReplyDelete
  66. CANON Printer Customer Care Phone Number1-800-382-3046 doesn't have any affiliation with canon company as we are third party vendor and provide very cheap and valuable service for solving canon printer related issues via our helpline number. For any assistance regarding your canon printer then just dial for fast and reliable helpline number of The service we provide for Independent items can also be available from the person brand proprietors on their specific websites, and can also be provided by them totally free.
    Canon Printer Customer Care Phone Number

    ReplyDelete
  67. Thanks for sharing this information. I have shared this link with other keep posting such information to offering 200, 300 and 500-hours Yoga Teacher Training in Rishikesh, Yoga Course Rishikesh, as well as Yoga for Beginners and Yoga Retreats.
    Yoga Teacher Training in Rishikesh
    Yoga Teacher Training in India
    200 hours yoga teacher training in Rishikesh
    300 hours yoga teacher training in Rishikesh
    500 hours yoga teacher training in Rishikesh
    yoga retreats in India
    yoga classes for beginners in Rishikesh

    ReplyDelete
  68. 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



  69. 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