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Stewart Platform

novio8
Posted 9 years ago

Hi, I downloaded Stewart Platform demo and I changed Long demonstration motion plan as follows:

demoMotionPlan =
  Block[{dx = 0.05, d\[Theta] = 10 \[Degree]},
   {
    {0, 0, 0, 0, 0, 0},
    {0, dx, 0, 0, 0, 0},
    {0, dx, 0, d\[Theta], 0, 0},
    {0, dx, 0, 0, 0, 0},
    {0, dx, 0, -d\[Theta], 0, 0},
    {0, dx, 0, 0, 0, 0},
    {0, dx, 0, 0, d\[Theta], 0},
    {0, dx, 0, 0, 0, 0},
    {0, dx, 0, 0, -d\[Theta], 0},
    {0, dx, 0, 0, 0, 0},
    {0, dx, 0, 0, 0, d\[Theta]},
    {0, dx, 0, 0, 0, 0},
    {0, dx, 0, 0, 0, -d\[Theta]},
    {0, dx, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0}
    }
   ];

Mathematica generates a file called PlatformPath. Only first and the third angle is calculaced correctly.

Attachments:
POSTED BY: novio8
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novio8
novio8
Posted 9 years ago
POSTED BY: novio8

Hi Mario,

Did you use something like:

ExportMotionPlan[motionPlan,legoffsets_: -{0.17035,0.17035,0.17035,0.17035,0.17035,0.17035}]?

The legoffsets_:{...} idiom is only used in the definition of the function. When you call the function, use:

ExportMotionPlan[ motionPlan, -{0.17035,0.17035,0.17035,0.17035,0.17035,0.17035} ]

Note that using an offset of 1.1313669977935081 is not realistic because the platform height is only 0.15 units. You will get leg lengths, but they won't be very meaningful. The purpose of subtracting the offsets is to get control values for the servo actuators.

Eric
POSTED BY: Eric Johnstone
novio8
novio8
Posted 9 years ago

Hi Eric, I copied your Code at the end of the Notebook. Replaced Zeroes with Offset Value and I'v received the following error: Syntax::sntxf: "legoffsets_:" cannot be followed by "{1.1313669977935081,1.1313669977935081,1.1313669977935081,1.1313669977935081,1.1313669977935081,1.1313669977935081}". Mario
POSTED BY: novio8

Hi Mario,

You can try this:

ExportMotionPlan[poses_List, legoffsets_: {0, 0, 0, 0, 0, 0}] :=
 Module[{framerate = 10, lengths, tabledata, time1, time2},
  lengths = {poses[[1, 2 ;; 7]]};
  time1 := poses[[1, 1]];

  Do[
   (
    time2 := wp[[1]];
    lengths = 
     Join[lengths, 
      Rest@PoseRange[{Last[lengths], wp[[2 ;; 7]]}, framerate, time1, 
        time2]];
    time1 = time2;
    ),
   {wp, Rest[poses]}];

  AppendTo[lengths, Last[lengths]];
  lengths = Map[PoseLegLengths, lengths];
  tabledata = 
   MapIndexed[Prepend[#, (First[#2] - 1)/framerate] &, lengths];
  {Export[
    FileNameJoin[{NotebookDirectory[], "DocumentationFiles", 
      "PlatformPath1.txt"}], {{"LegLengths", tabledata}}, 
    "ModelicaCombiTimeTable"], First[Last[tabledata]]};

  lengths = Map[# + legoffsets &, lengths];
  tabledata = 
   MapIndexed[Prepend[#, (First[#2] - 1)/framerate] &, lengths];
  {Export[
    FileNameJoin[{NotebookDirectory[], "DocumentationFiles", 
      "PlatformPath2.txt"}], {{"LegLengths", tabledata}}, 
    "ModelicaCombiTimeTable"], First[Last[tabledata]]}
  ]

I haven't tested this code, of course, because I don't have SystemModeler.

A good value to test the offsets would be -0.17035, the zero-position leg length.

Eric
POSTED BY: Eric Johnstone
Updating Name
Updating Name
Posted 9 years ago

Hi Eric, yes that is correct. I would like to Export two Motion Plans, one

as it is and the other one with Leg Offsets, but I was not successful

by copying ExportMotionPlan Cell and Entering Values in Offset Field.

Any suggestions?

Regards Mario
POSTED BY: Updating Name

Hi Mario,

Here is what the legoffsets are about:

Suppose you are using hydraulic actuators for the legs. The control signal tells the actuator to extend so many meters from the retracted position. The retracted position is the "legoffset". The distance that you want the actuator to extend is the calculated length minus the retracted length.

So, the legoffset could have been called "retracted length" and the code could have subtracted the legoffset instead of adding it. That would have been a little clearer.

On the other hand, the neutral position might be the reference length, depending on the way the software is arranged, so this could be the offset.

Eric
POSTED BY: Eric Johnstone
novio8
novio8
Posted 9 years ago
POSTED BY: novio8

Hi Mario,

I haven't been able to install SystemModeler on my old XP computer, so I don't have the elements needed to do the export. You'll have to stick to the notebook output for this discussion.

Can you re-phase your problem? Note that subtracting leg lengths will not give the motion that was originally calculated. Why do you want to do this? Or are you just verifying that the path will be different?

Generating a path from the leg lengths is called the forward kinematics. It was this problem that was difficult to solve in 1999 when I discovered that the path of the intended Stewart platform could hit the walls of the pit it was to be housed in.

Maybe you could import the path file back into Mathematica and we could work on it.

Eric
POSTED BY: Eric Johnstone
novio8
novio8
Posted 9 years ago

Hi Eric, I'm also confused about leg offsets purpose.

What I would like to do is to read PlatformPath.txt that was generated by ExportMotionPlan....

and substract initial leg length or any other arbitrary number from all of leg lengths written in file PlatformPath.txt and save it as PlatformPath 2.txt

Mario
POSTED BY: novio8
POSTED BY: Eric Johnstone
novio8
novio8
Posted 9 years ago
POSTED BY: novio8

Hi mario,

It's its own plan. The long and short plans are just longer or shorter. Their structure is the same.

But the motionPlan I implemented doesn't use the Block[]. That was necessary for the substitutions of dx and dtheta.

Inside the Blocks[] you will see the basic structure; a List[] of List[]s.

Eric
POSTED BY: Eric Johnstone
Updating Name
Updating Name
Posted 9 years ago

Hi Eric , thank you again.

I replaced original code with yours, what is confusing me is whether 

motionPlan = {
   {0, 0, 0.00, 0, 0, 0, 0},
   {1, 0, 0.01, 0, 0, 0, 0},
   {3, 0, -0.03, 0, 0, 0, 0},
   {4, 0, 0.04, 0, 0, 0, 0},
   {4.5, 0, -0.045, 0, 0, 0, 0}
   };

is Short test motion plan or Long demonstration motion plan?

Regards

Mario
POSTED BY: Updating Name
POSTED BY: Eric Johnstone
novio8
novio8
Posted 9 years ago
POSTED BY: novio8

Hi Mario,

I learned a lot from this discussion. Please keep asking.

Eric
POSTED BY: Eric Johnstone
novio8
novio8
Posted 9 years ago

Hi Eric, yes you are right, one has to follow certain rules like shift_enter.

You are a great help. I have many questions but I don't want to bother you

too much ...with all of them.

Thanks

Mario

POSTED BY: novio8

Hi Mario,

Coming to terms with the z,y and theta,phi interchanges requires some contemplation. It's like driving in England compared to the USA. You have to change the side of the road you call legal.

I tried the ExportMotionPlan[] with framerate=50 and it works OK. Don't forget that you have to re-compile it by hitting shift-enter after changing the framerate.

Eric
POSTED BY: Eric Johnstone
novio8
novio8
Posted 9 years ago

Hi Eric, I watched Wolfram Video ScreenCast at http://www.wolfram.com/broadcast/video.php?c=202&v=835

and I'm still confused about double flip y,z and Phi.

I also want to change the number of poses per second, originally 10 to 50.

I'v changed frame rate from 10 to 50, but I get the same amount of lines in file PlatformPath.txt.

ExportMotionPlan[poses_List, legoffsets_: {0, 0, 0, 0, 0, 0}] :=

 Module[{framerate = 50, lengths, tabledata},
  lengths = {First[poses]};
  Do[lengths = 
    Join[lengths, 
     Rest@PoseRange[{Last[lengths], wp}, framerate]], {wp, 
    Rest[poses]}]; AppendTo[lengths, Last[lengths]];
  lengths = Map[PoseLegLengths, lengths];
  lengths = Map[# + legoffsets &, lengths];
  tabledata = 
   MapIndexed[Prepend[#, (First[#2] - 1)/framerate] &, 
    lengths]; {Export[
    FileNameJoin[{NotebookDirectory[], "DocumentationFiles", 
      "PlatformPath.txt"}], {{"LegLengths", tabledata}}, 
    "ModelicaCombiTimeTable"], First[Last[tabledata]]}

Mario
POSTED BY: novio8
POSTED BY: Eric Johnstone
novio8
novio8
Posted 9 years ago

yes this is true for SphericalPlot3D. But original Inverse Kinematics Calculations are wrong. If you enter 5cm change in x,y z or correctly x,z,y direction you get the following results :

{PoseLegLengths[{0, 0, 0, 0, 0, 0}], PoseLegLengths[{0.05, 0, 0, 0, 0, 0}]}

{{0.17035, 0.17035, 0.17035, 0.17035, 0.17035, 0.17035}, {0.155246, 0.19491, 0.180185, 0.180185, 0.19491, 0.155246}}

{PoseLegLengths[{0, 0, 0, 0, 0, 0}], PoseLegLengths[{0, 0.05, 0, 0, 0, 0}]}

{{0.17035, 0.17035, 0.17035, 0.17035, 0.17035, 0.17035}, {0.215683, 0.215683, 0.215683, 0.215683, 0.215683, 0.215683}}

{PoseLegLengths[{0, 0, 0, 0, 0, 0}],  PoseLegLengths[{0, 0, 0.05, 0, 0, 0}]}

{0.17035, 0.17035, 0.17035, 0.17035, 0.17035, 0.17035}, {0.186301, 0.16337, 0.1533, 0.198841, 0.190654, 0.168317}} and changing [Theta], [Phi], [Tau]_} angels 10 degree

{PoseLegLengths[{0, 0, 0, 0, 0, 0}],  PoseLegLengths[{0, 0, 0, 10 \[Degree], 0, 0}]}

{{0.17035, 0.17035, 0.17035, 0.17035, 0.17035, 0.17035}, {0.160146, 0.166254, 0.185371, 0.185371, 0.166254, 0.160146}}

{PoseLegLengths[{0, 0, 0, 0, 0, 0}],   PoseLegLengths[{0, 0, 0, 0, 10 \[Degree], 0}]}

{{0.17035, 0.17035, 0.17035, 0.17035, 0.17035, 0.17035}, {0.17035, 0.17035, 0.17035, 0.17035, 0.17035, 0.17035}} CALCULATION ERROR 

{PoseLegLengths[{0, 0, 0, 0, 0, 0}],  PoseLegLengths[{0, 0, 0, 0, 0, 10 \[Degree]}]}

As one can immediately notice, only [Phi] calculation gives the result for Zero Degree.

Any Ideas Mario

POSTED BY: novio8
POSTED BY: Eric Johnstone
novio8
novio8
Posted 9 years ago

Hi Eric, I tested your workaround and it works. It is also unusual that z vertical is in second position,

so instead x,y,z it is x,z,y. You are right phi get's calculated only if theta is not 0.

Mario
POSTED BY: novio8

Hi Mario,

I've been playing around with the RotationTransform. Using it in the form that the author does, where he is transforming the vertical vector, {0, 1, 0}, by another vector {Sin[\[Theta]] Cos[\[Phi]], Cos[\[Theta]], Sin[\[Theta]] Sin[\[Phi]]} cannot be generated by successive theta and phi transformations.

So, although my workaround seems to work, it doesn't give the behaviour that the author intended.

RotationTransform[{{0,1,0},{Sin[\[Theta]]Cos[\[Phi]],Cos[\[Theta]],Sin[\[Theta]]Sin[\[Phi]]}}]

seems to work.

Hey, but, in looking at it, if theta is 0, {Sin[\[Theta]]Cos[\[Phi]],Cos[\[Theta]],Sin[\[Theta]]Sin[\[Phi]]} evaluates to {0,Cos[theta],0}, so the phi value doesn't get through.

Could this be the problem?

Eric
POSTED BY: Eric Johnstone
novio8
novio8
Posted 9 years ago

yes Leg Lengths are what I'm looking for, but they are not calculated correctly. If you change Long Demonstration Motion Plan, just one Angle at a time to something like this

demoMotionPlan =
  Block[{dx = 0.05, d\[Theta] = 0.5},
   {
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, d\[Theta], 0, 0},
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, -d\[Theta], 0, 0},
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, d\[Theta], 0},
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, -d\[Theta], 0},
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, d\[Theta]},
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, -d\[Theta]},
    {0, 0, 0, 0, 0, 0}
    }
   ];

Leg lengths are not calculated for [Phi]. Any Ideas Mario

POSTED BY: novio8
Updating Name
Updating Name
Posted 9 years ago

Hi Mario,

It took a while to go through the code, but I finally get the problem. I don't know what it is; you may have found a bug in Mathematica. But if you use separate RotationTrransforms like this:

PoseLegEndpoints[{x_, y_, z_, \[Theta]_, \[Phi]_, \[Tau]_}] := 
 Table[Composition[
    TranslationTransform[{x, y, z} + {0, platformHeight, 0}], 
    RotationTransform[\[Theta], {1, 0, 0}],
    RotationTransform[\[Phi], {0, 0, 1}],
    RotationTransform[\[Tau], {0, 1, 0}]][p], {p, 
   relativePlatformPoints}]

the second angle calculates.

For a motion path of 

testMotionPlan =
  Block[{dx = 0.05, d\[Theta] = 0.5},
   {
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, d\[Theta], 0},
    {0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, -d\[Theta], 0},
    {0, 0, 0, 0, 0, 0}
    }
   ];

the platform returns to its rest position at the {0, 0, 0, 0, 0, 0} points.

I used the ExportMotionPlan[] function with the last line commented out, as above.

Use MatrixPlot[] to see how the leg lengths change.

Eric
POSTED BY: Updating Name

Hi Mario,

If you comment out the last line:

ExportMotionPlan[poses_List,legoffsets_:{0,0,0,0,0,0}]:=
Module[{framerate=10,lengths,tabledata},
lengths={First[poses]};
Do[lengths=Join[lengths,Rest@PoseRange[{Last[lengths],wp},framerate]],{wp,Rest[poses]}];AppendTo[lengths,Last[lengths]];
lengths=Map[PoseLegLengths,lengths];
lengths=Map[#+legoffsets&,lengths];
tabledata=MapIndexed[Prepend[#,(First[#2]-1)/framerate]&,lengths](*{Export[FileNameJoin[{NotebookDirectory[],"DocumentationFiles","PlatformPath.txt"}],{{"LegLengths",tabledata}},"ModelicaCombiTimeTable"],First[Last[tabledata]]}*)
]

and run

ExportMotionPlan[demoMotionPlan]

without a semicolon, you get

{{0,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{1/10,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{1/5,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{3/10,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{2/5,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{1/2,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{3/5,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{7/10,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{4/5,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{9/10,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{1,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{11/10,0.177146,0.172484,0.179639,0.171251,0.18149,0.168899},{6/5,0.184186,0.175092,0.189321,0.173459,0.193351,0.168897},{13/10,0.191352,0.178177,0.199365,0.177031,0.205731,0.170305},{7/5,0.198544,0.181744,0.209743,0.181978,0.218455,0.173031},{3/2,0.20568,0.185795,0.220421,0.188265,0.231373,0.176951},{8/5,0.212696,0.190332,0.231367,0.195819,0.244357,0.18191},{17/10,0.219538,0.195353,0.242545,0.204538,0.257296,0.187744},{9/5,0.226167,0.200858,0.25392,0.214302,0.270095,0.194285},{19/10,0.232553,0.206839,0.265457,0.224982,0.282669,0.201373},{2,0.238676,0.213291,0.277118,0.236445,0.294946,0.208859},{21/10,0.230679,0.210296,0.269809,0.229228,0.282619,0.196616},{11/5,0.221762,0.207329,0.263004,0.223376,0.270155,0.184527},{23/10,0.211962,0.204354,0.256696,0.218952,0.257687,0.172825},{12/5,0.201327,0.201351,0.250866,0.215975,0.245361,0.16177},{5/2,0.189923,0.198317,0.245485,0.21441,0.23333,0.151648},{13/5,0.177829,0.195261,0.240512,0.21418,0.221758,0.142763},{27/10,0.165141,0.192212,0.235902,0.215159,0.21082,0.135414},{14/5,0.151974,0.189211,0.231602,0.217194,0.200694,0.129866},{29/10,0.138468,0.186313,0.22756,0.220108,0.191559,0.126306},{3,0.124796,0.183587,0.223719,0.223719,0.183587,0.124796},{31/10,0.124796,0.183587,0.223719,0.223719,0.183587,0.124796},{16/5,0.124796,0.183587,0.223719,0.223719,0.183587,0.124796},{33/10,0.124796,0.183587,0.223719,0.223719,0.183587,0.124796},{17/5,0.124796,0.183587,0.223719,0.223719,0.183587,0.124796},{7/2,0.124796,0.183587,0.223719,0.223719,0.183587,0.124796},{18/5,0.124796,0.183587,0.223719,0.223719,0.183587,0.124796},{37/10,0.124796,0.183587,0.223719,0.223719,0.183587,0.124796},{19/5,0.124796,0.183587,0.223719,0.223719,0.183587,0.124796},{39/10,0.124796,0.183587,0.223719,0.223719,0.183587,0.124796},{4,0.124796,0.183587,0.223719,0.223719,0.183587,0.124796},{41/10,0.137276,0.184049,0.21631,0.21631,0.184049,0.137276},{21/5,0.150357,0.185189,0.209514,0.209514,0.185189,0.150357},{43/10,0.163992,0.187016,0.203326,0.203326,0.187016,0.163992},{22/5,0.178131,0.189531,0.197736,0.197736,0.189531,0.178131},{9/2,0.192728,0.192728,0.192728,0.192728,0.192728,0.192728},{23/5,0.207734,0.196591,0.188284,0.188284,0.196591,0.207734},{47/10,0.223101,0.201095,0.184381,0.184381,0.201095,0.223101},{24/5,0.238779,0.206211,0.180997,0.180997,0.206211,0.238779},{49/10,0.254719,0.211904,0.178112,0.178112,0.211904,0.254719},{5,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{51/10,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{26/5,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{53/10,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{27/5,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{11/2,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{28/5,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{57/10,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{29/5,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{59/10,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{6,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{61/10,0.270072,0.223851,0.17247,0.179826,0.212818,0.271964},{31/5,0.269577,0.229882,0.170187,0.184719,0.207987,0.273337},{63/10,0.269394,0.236145,0.168924,0.190282,0.203724,0.274971},{32/5,0.269524,0.242563,0.168717,0.196405,0.200112,0.276846},{13/2,0.269966,0.249062,0.169572,0.202979,0.197221,0.278939},{33/5,0.270714,0.255573,0.171463,0.2099,0.195114,0.281224},{67/10,0.271758,0.262033,0.17434,0.217068,0.193838,0.283674},{34/5,0.273084,0.268384,0.178126,0.224392,0.193422,0.28626},{69/10,0.274675,0.27457,0.182729,0.231787,0.193875,0.288953},{7,0.27651,0.280545,0.188044,0.239176,0.195188,0.291724},{71/10,0.274675,0.27457,0.182729,0.231787,0.193875,0.288953},{36/5,0.273084,0.268384,0.178126,0.224392,0.193422,0.28626},{73/10,0.271758,0.262033,0.17434,0.217068,0.193838,0.283674},{37/5,0.270714,0.255573,0.171463,0.2099,0.195114,0.281224},{15/2,0.269966,0.249062,0.169572,0.202979,0.197221,0.278939},{38/5,0.269524,0.242563,0.168717,0.196405,0.200112,0.276846},{77/10,0.269394,0.236145,0.168924,0.190282,0.203724,0.274971},{39/5,0.269577,0.229882,0.170187,0.184719,0.207987,0.273337},{79/10,0.270072,0.223851,0.17247,0.179826,0.212818,0.271964},{8,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{81/10,0.271505,0.217083,0.173486,0.178048,0.219296,0.270328},{41/5,0.27223,0.216141,0.171378,0.180494,0.220565,0.269877},{83/10,0.273044,0.215312,0.169392,0.183043,0.221939,0.269517},{42/5,0.273947,0.214595,0.167532,0.185692,0.223416,0.26925},{17/2,0.274938,0.213993,0.165801,0.188437,0.224995,0.269076},{43/5,0.276015,0.213507,0.164205,0.191273,0.226673,0.268994},{87/10,0.277179,0.213137,0.162746,0.194196,0.228448,0.269006},{44/5,0.278428,0.212883,0.16143,0.197203,0.230319,0.26911},{89/10,0.279761,0.212747,0.160258,0.200289,0.232281,0.269307},{9,0.281176,0.212728,0.159235,0.203452,0.234334,0.269597},{91/10,0.276592,0.213504,0.15774,0.202283,0.235039,0.264813},{46/5,0.272299,0.214744,0.156869,0.201605,0.236165,0.260325},{93/10,0.268309,0.216438,0.156632,0.201421,0.237707,0.256149},{47/5,0.264638,0.218578,0.157034,0.201734,0.239657,0.252301},{19/2,0.261298,0.221149,0.158068,0.20254,0.242005,0.248795},{48/5,0.258302,0.224138,0.159723,0.203834,0.244739,0.245647},{97/10,0.255662,0.227527,0.16198,0.205607,0.247846,0.24287},{49/5,0.25339,0.231299,0.164814,0.207847,0.251313,0.240477},{99/10,0.251495,0.235436,0.168195,0.210538,0.255126,0.238479},{10,0.249986,0.239918,0.172091,0.213664,0.259268,0.236887},{101/10,0.246891,0.240055,0.174124,0.207722,0.255644,0.236333},{51/5,0.244167,0.240609,0.1767,0.202101,0.252365,0.236201},{103/10,0.241826,0.241575,0.179796,0.196828,0.249444,0.236493},{52/5,0.239879,0.242949,0.183385,0.191931,0.246893,0.237206},{21/2,0.238337,0.244725,0.18744,0.18744,0.244725,0.238337},{53/5,0.237206,0.246893,0.191931,0.183385,0.242949,0.239879},{107/10,0.236493,0.249444,0.196828,0.179796,0.241575,0.241826},{54/5,0.236201,0.252365,0.202101,0.1767,0.240609,0.244167},{109/10,0.236333,0.255644,0.207722,0.174124,0.240055,0.246891},{11,0.236887,0.259268,0.213664,0.172091,0.239918,0.249986},{111/10,0.238479,0.255126,0.210538,0.168195,0.235436,0.251495},{56/5,0.240477,0.251313,0.207847,0.164814,0.231299,0.25339},{113/10,0.24287,0.247846,0.205607,0.16198,0.227527,0.255662},{57/5,0.245647,0.244739,0.203834,0.159723,0.224138,0.258302},{23/2,0.248795,0.242005,0.20254,0.158068,0.221149,0.261298},{58/5,0.252301,0.239657,0.201734,0.157034,0.218578,0.264638},{117/10,0.256149,0.237707,0.201421,0.156632,0.216438,0.268309},{59/5,0.260325,0.236165,0.201605,0.156869,0.214744,0.272299},{119/10,0.264813,0.235039,0.202283,0.15774,0.213504,0.276592},{12,0.269597,0.234334,0.203452,0.159235,0.212728,0.281176},{121/10,0.26911,0.230319,0.197203,0.16143,0.212883,0.278428},{61/5,0.268994,0.226673,0.191273,0.164205,0.213507,0.276015},{123/10,0.26925,0.223416,0.185692,0.167532,0.214595,0.273947},{62/5,0.269877,0.220565,0.180494,0.171378,0.216141,0.27223},{25/2,0.270871,0.218135,0.175711,0.175711,0.218135,0.270871},{63/5,0.27223,0.216141,0.171378,0.180494,0.220565,0.269877},{127/10,0.273947,0.214595,0.167532,0.185692,0.223416,0.26925},{64/5,0.276015,0.213507,0.164205,0.191273,0.226673,0.268994},{129/10,0.278428,0.212883,0.16143,0.197203,0.230319,0.26911},{13,0.281176,0.212728,0.159235,0.203452,0.234334,0.269597},{131/10,0.26751,0.212055,0.158143,0.205212,0.221794,0.259272},{66/5,0.253696,0.211706,0.157477,0.207555,0.210425,0.25043},{133/10,0.239942,0.211794,0.157219,0.210316,0.20034,0.24316},{67/5,0.226483,0.212425,0.157368,0.213346,0.191629,0.237498},{27/2,0.213586,0.213693,0.157939,0.216518,0.184349,0.233413},{68/5,0.201547,0.215677,0.15896,0.219725,0.178515,0.230809},{137/10,0.190685,0.218431,0.160466,0.222882,0.174095,0.229532},{69/5,0.181329,0.221986,0.162503,0.225923,0.171012,0.229378},{139/10,0.173794,0.226345,0.165115,0.228801,0.169146,0.230112},{14,0.168346,0.231483,0.168346,0.231483,0.168346,0.231483},{141/10,0.164621,0.224944,0.164621,0.224944,0.164621,0.224944},{71/5,0.161675,0.21831,0.161675,0.21831,0.161675,0.21831},{143/10,0.159579,0.211641,0.159579,0.211641,0.159579,0.211641},{72/5,0.15839,0.205004,0.15839,0.205004,0.15839,0.205004},{29/2,0.15814,0.198472,0.15814,0.198472,0.15814,0.198472},{73/5,0.158836,0.192123,0.158836,0.192123,0.158836,0.192123},{147/10,0.160458,0.186044,0.160458,0.186044,0.160458,0.186044},{74/5,0.162963,0.180325,0.162963,0.180325,0.162963,0.180325},{149/10,0.166287,0.175062,0.166287,0.175062,0.166287,0.175062},{15,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{151/10,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{76/5,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{153/10,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{77/5,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{31/2,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{78/5,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{157/10,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{79/5,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{159/10,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{16,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035},{161/10,0.17035,0.17035,0.17035,0.17035,0.17035,0.17035}}

Is this the text you are looking for?

Eric
POSTED BY: Eric Johnstone
Updating Name
Updating Name
Posted 9 years ago

Hi Mario,

I downloaded SystemModeler onto my XP computer. Not compatible, it seems.

I see now that the problem I was having with the code you supplied is that the Y axis is the vertical. The PoseLegEndpoints[] function seems to work OK, but the range of values that it works for is hard to determine using Manipulate (especially when everything is turned 90 degrees).

Is the problem here:

ExportMotionPlan[demoMotionPlan];

*Export::nodir: Directory C:\Documents and Settings\Eric Johnstone\Local Settings\Temp\wz4602\StewartPlatform\DocumentationFiles\ does not exist. >>*

*OpenWrite::noopen: Cannot open C:\Documents and Settings\Eric Johnstone\Local Settings\Temp\wz4602\StewartPlatform\DocumentationFiles\PlatformPath.txt. >>*

?

Or is that because I don't have SystemModeler? Is this the problem you are referring to?

Eric
POSTED BY: Updating Name
novio8
novio8
Posted 9 years ago

Hi, yes it seems that Y is the vertical, which is weird and I can't figure it why. I'v run Evaluate Notebook in Mathematica only, without System Modeler running and it seems OK

It looks like PlatformPath.txt is saved in folder DocumentationFiles that has to be on the same root as Mathematica file StewartPlatform.nb

As I can see you'v saved Mathematica file in to Temp Folder

C:\Documents and Settings\Eric Johnstone\Local Settings\Temp\wz4602\StewartPlatform\DocumentationFiles\PlatformPath.txt. >>

ExportMotionPlan[poses_List, legoffsets_: {0, 0, 0, 0, 0, 0}] :=

 Module[{framerate = 10, lengths, tabledata},
  lengths = {First[poses]};
  Do[lengths = 
    Join[lengths, 
     Rest@PoseRange[{Last[lengths], wp}, framerate]], {wp, 
    Rest[poses]}]; AppendTo[lengths, Last[lengths]];
  lengths = Map[PoseLegLengths, lengths];
  lengths = Map[# + legoffsets &, lengths];
  tabledata = 
   MapIndexed[Prepend[#, (First[#2] - 1)/framerate] &, 
    lengths]; {Export[
    FileNameJoin[{NotebookDirectory[], "DocumentationFiles", 
      "PlatformPath.txt"}], {{"LegLengths", tabledata}}, 
    "ModelicaCombiTimeTable"], First[Last[tabledata]]}
  ]

Mario
POSTED BY: novio8
novio8
novio8
Posted 9 years ago
POSTED BY: novio8
POSTED BY: Eric Johnstone

Maybe I should leave this to the experts, but I've dug my hole now.

As above,

platformHeight=1;
relativePlatformPoints := 
 Table[{Cos[\[Theta]], Sin[\[Theta]], 0}, {\[Theta],  Range[0, 5]/6 2 Pi}]

But the RotationTransform seems to be much simpler:

PoseLegEndpoints[{x_,y_,z_,\[Theta]_,\[Phi]_,\[Tau]_}]:=
Table[
    Composition[
        TranslationTransform[{x,y,z}+{0,0,platformHeight}],
        RotationTransform[\[Theta],{1,0,0}],
        RotationTransform[\[Phi],{0,1,0}],
        RotationTransform[\[Tau],{0,0,1}]
    ]
    [p], {p,relativePlatformPoints}
]

    ListPlot3D[PoseLegEndpoints[{0,0,0,0,0,0}]//N,PlotRange->{{-1.5,1.5},{-1.5,1.5},{-1,2}}]

    Manipulate[
     ListPlot3D[
      PoseLegEndpoints[{x, y, z, \[Theta], \[Phi], \[Tau]}] // N, 
      PlotRange -> {{-1.5, 1.5}, {-1.5, 1.5}, {-1, 2}}], 
        {{x, 0}, -1, 1}, {{y, 0}, -1, 1}, {{z, 0}, -1, 1}, 
        {{\[Theta], 0}, -1, 1}, {{\[Phi], 0}, -1, 1}, {{\[Tau], 0}, -1, 1}]
POSTED BY: Eric Johnstone
novio8
novio8
Posted 9 years ago

Thank you Eric. I'm a newbie, just downloaded Mathematica. My goal is to generate correct Motion data from this Stewart Platform Demo. Hence stupid questions. I pasted your Code to Demo file in the place of the original Code and the result is platform collapse. Any Ideas Your help is much appreciated Mario
POSTED BY: novio8

If we give some values to platformHeight and relativePlatformPoints, and change the {0, platformHeight, 0} to {0, 0,platformHeight}

platformHeight=1;

relativePlatformPoints:=Table[{Cos[\[Theta]],Sin[\[Theta]],0},{\[Theta],Range[0,5]/6 2Pi}]

PoseLegEndpoints[{x_,y_,z_,\[Theta]_,\[Phi]_,\[Tau]_}]:=
    Table[
        Composition[
        TranslationTransform[{x,y,z}+{0,0,platformHeight}],
        RotationTransform[{{0,1,0},
        {Sin[\[Theta]] Cos[\[Phi]],
        Cos[\[Theta]],Sin[\[Theta]] Sin[\[Phi]]}}],
        RotationTransform[\[Tau],{0,1,0}]][p],
        {p,relativePlatformPoints}
    ]

ListPlot3D[PoseLegEndpoints[{0, 0, 0, 0, 0, 0}] // N, 
 PlotRange -> {{-1, 1}, {-1, 1}, {-1, 2}}]

This appears to work. But it needs thorough checking.

EDIT:

After playing around with this, later on, it seems to still need some work. Theta and phi were not working in the above, so I put them in separate RotationTransforms. The plot looks OK now. But it still needs checking. I'm not very experienced with these transformations, although I have had a lot of experience with Stewart platforms.

PoseLegEndpoints[{x_,y_,z_,\[Theta]_,\[Phi]_,\[Tau]_}]:=
   Table[
       Composition[
          TranslationTransform[{x,y,z}+{0,0,platformHeight}],
          RotationTransform[\[Theta],{Sin[\[Theta]] Cos[\[Phi]],Cos[\[Theta]],Sin[\[Theta]] Sin[\[Phi]]}],
          RotationTransform[\[Phi],{Sin[\[Theta]] Cos[\[Phi]],Cos[\[Theta]],Sin[\[Theta]] Sin[\[Phi]]}],
          RotationTransform[\[Tau],{0,0,1}]][p],
    {p,relativePlatformPoints}
]

ListPlot3D[PoseLegEndpoints[{0,0,0,0,0,0}]//N,PlotRange->{{-1,1},{-1,1},{-1,2}}]
POSTED BY: Eric Johnstone
novio8
novio8
Posted 9 years ago

maybe inverse kinematics formula is not correct:

The "pose" of the moveable platform is defined by 6 coordinates {x,y,z,[Theta],[Phi],[Tau]}. The position of the center of the platform is {x,y,z}. The normal vector pointing upwards out of the platform points in the direction {[Theta],[Phi]} in spherical coordinates. The rotation of the platform about the normal vector is the angle [Tau].

PoseLegEndpoints[{x_, y_, z_, \[Theta]_, \[Phi]_, \[Tau]_}] := 
 Table[Composition[
    TranslationTransform[{x, y, z} + {0, platformHeight, 0}], 
    RotationTransform[{{0, 1, 0}, {Sin[\[Theta]] Cos[\[Phi]], 
       Cos[\[Theta]], Sin[\[Theta]] Sin[\[Phi]]}}], 
    RotationTransform[\[Tau], {0, 1, 0}]][p], {p, 
   relativePlatformPoints}]

please help
POSTED BY: novio8
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