DR UMAR!! On generating the motion of industrial robot manipulators | In this study, ... to the desired position and orientation of an industrial robot's manipulator end effector. ... It can reduce the motor jitter to ensure the smooth operation of the robot. ... Although the problem of discontinuous surfaces between the adjacent 

Article On generating the motion of industrial robot manipulators

Article Variable structure position control of an industrial robotic...

Regards-

Dear Abubakar Umar,

I suggest you to see links and attached files on topic.

https://sites.ualberta.ca/~mlipsett/MGLipsettPhDdissertation.pdf

https://www.scielo.br/scielo.php?pid=S0100-73862002000300004&script=sci_arttext&tlng=en.

https://www.elsevier.com/books/advances-in-applied-mechanics/bordas/978-0-12-802128-6

Best regards

Aha, really very interesting question of discontinuities. See, wrists are inherently nonlinear. So it is hard to track your question and boil the answer down.

All you are saying makes a lot of sense to me, but not the way you are explaining your question. It could be that at joint 1 you are solving an inverse dynamics algorithm and it poses the wrist making a complete turn or something. Why you do not try to animate the steps around the undesired discontinuity and see what happens. It strikes my curiosity even more when I think of how your 3-dof wrist is made ? They are incredibly tricky to design. I have never see a yaw-pitch-roll wrist fully functional in detail. Always the RPR old one.

I could not answer but if you streamline a bit what you are saying it would be very cool. Best of luck then, very interesting question.

not sure how you produce this but few observations:

-your output is restricted between [-pi,pi]

-this what causes your output to jump from pi at x=2.1 to -pi

-look in your code and see if there is anything restrict that

-use atan2 instead of atan

-fastest sol: you can hard code it by taking the abs value and if the output is negative you add +pi

Good luck!

Dear Proffessor Ijaz Durrani , Thank you very much for the reply, I would go through the papers and update my findings. Thank you.

Dear Prof. Mohamed-Mourad Lafifi , thank you for the suggestions, I would read the recommendations and hopefully find a solution. Thank you

Dear Prof. Alcy Rodolfo dos Santos Carrara , I have not tried animation yet, but I guess it would give same funny results because converting the joint angles from radians to degrees also results in the sudden jump observed. Nevertheless I would try animating and also try streamlining the question for more clarity. thank you.

Dear Dr Turki Haj Mohamad , my output is actually restricted between 0 and 2*pi, that's why I am even more alarmed at the results. Also, I am using the "atan2" function. I would try going over the codes again and probably try using the "atan" function and see what the results would be. thank you.

Dear Dr. Abubakar Umar I would not do that. SInce the start of new computer languages such as ANSI C, C Parallel (nowadays) and others we have to build the ATAN2 algorithm ourselves. That is what is causing us all a surprise when we get funny results. Go over Robotics books such as Schilling, Craig (very used is France as a text book for undergrads), Koivo or even the spanish book by Barrientos that incorporated the new Robotics era of ultra-precision. Consult book in programming which cover your problem in detail such as Numerical Recipes (C, Pascal and Fortran, old stuff). There you find your solution. Best of luck. I wll go together with you people in the links that Dr. Mohamed-Mourad Lafifi has mentioned and try to be careful about the "looks" of your code. Also the book by Niku is pristine in detailed code work. Just be more specific in your search. Hope I have given you some help. Also the things that Dr. Turki Haj Mohamad has pointed out.

Dear Prof Umar, very interesting topic.

Can you try to plot the yaw-pitch-roll results?

I finally figure out that it was a singularity problem. I never knew that the first link of the scorbot/puma type of robot could experience singularity, I always assumed it was a 360 degrees Joint. confining the trajectory within two quadrants solved the problem, instead of allowing the robot rotate 360 degrees about its first joint axis (covering all four quadrants).

Dr. Turki Haj Mohamad your were right, when using "atan2(x,y)", taking absolute values and adding pi where the values should be negative resolves the problem of sudden shifts from pi to -pi. During my investigations I discovered that when the "y" component is negative, the result is negative so I just added 2*pi to the results when the "y" components were negative which gives pretty much same results. Obviously "atan" function didn't work here (lol). Thank you very much.

Prof. Alcy Rodolfo dos Santos Carrara your suggestions were very helpful, I particularly found the books by J. Craig, L.W. Tsai and S.K. Saha (for undergrads) particularly helpful. I would definitely look into basic programming books like fortran and pascal to improve my ability to generate my own codes which should be more reliable and specific to solving my problems. Thanks once again.

Dear Prof. Luigi Bibbo , sorry I have deleted the results so I am unable to show the roll-pitch-yaw plots (End-effector trajectory in cartesian space). The joint displacement plots shown above were prepared previously. Thank you for the response.

MY TAKE AWAYS:

I was trying to develop an optimized circular trajectory for dynamic parameter estimation for robot manipulators using an improved Fourier series which is implemented at the End-effector of the manipulator (as opposed to implementing at the joints) in MATLAB environment.

A swarm-based algorithm was used to generate random trajectories, some of which were out-of-bound or ran into singularity. These faulty trajectories sometimes ran into errors forcing the algorithm to be prematurely terminated, so error traps were implemented to avoid such premature termination of the algorithm. For example during inverse-kinematic analysis, when using "atan2(x,y)" to solve for joint positions, "x" and "y" components must always be less than one (except in the first joint), values greater than one signify that the position is out of the robots reach causing the algorithm to be prematurely terminated. An error trap can be implemented using the "if" command together with a simple formula like "x=x-(ceil(x-1))" to flag trajectories that go out of reach and bring the trajectories back into range so as not to prematurely terminate the algorithm. The formula above maintains the value of "x" if its less than one, and is also capable of returning values greater than one back to acceptable range (i.e. 0