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Stewart Platform

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, d0, 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
35 Replies
Posted 9 years ago

Hi Eric, I'v found the solution to the problem: So your Code:

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]]}
  ]

is correct and the error I was getting: Syntax::sntxf: "legoffsets_:" cannot be followed by "{1.1313669977935081,1.1313669977935081,1.1313669977935081,1.1313669977935081,1.1313669977935081,1.131366997793508 can be avoided just by deleting the colon in egoffsets_: and retyping it again.

I don't know why, but it works.

I wonder if you have any suggestion for my next question:

In Motion plan one can enter platform positions at certain time, then the positions (frames) are calculated in linear way. I wold like to change that by using for instance logaritmic or any other curve.

Any Ideas how.

Regards

Mario

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

Hi Eric, yes that's what I had in mind to import path file back at the end of this Notebook or even a new one.

Mario

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

Hi Eric, yeah me too. I would like to modify the code so that I can enter pose data in Long demonstration motion plan but every second as it is now, but instead only at certain time positions: like the following example:

pose 1 at 1sec,

pose 2 at 4sec,

pose 3 at 4,5sec,

etc. Any suggestions ? Mario

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

Edwards & Penny p840

This is the way spherical coordinates are usually presented, but Mathematica interchanges theta and phi. When theta is zero in PoseLegEndpoints[], (phi in the diagram), the vector is pointing straight up, right at the north pole.

This vector is the normal to the platform surface; that is, the platform surface has to move so that its surface is normal to the vector OP in the diagram.

This is what the line of code

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

does. It takes the vector {0,1,0} (the vertical) and transforms it to {Sin[\[Theta]]Cos[\[Phi]],Cos[\[Theta]],Sin[\[Theta]]Sin[\[Phi]]}.

The {0,1,0} vector is the z axis in the diagram and the OP vector is {Sin[\[Theta]]Cos[\[Phi]],Cos[\[Theta]],Sin[\[Theta]]Sin[\[Phi]]}.

But the author has thrown a double whammy by making the y axis the vertical and interchanging theta and phi.

Now look at the z axis in the diagram. If the OP vector is on the z axis, any value of theta (in the diagram) will not change the vertical position of the vector OP.

So the PoseLegEndpoints[] is correct in not changing the leg lengths if theta is zero and phi is any other value.

Does that make sense?

Eric

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

Hi Mario,

Mathematica seems to flip the meanings of theta and phi. According to the documentation for SphericalPlot3D:

(Pi/2 - theta) corresponds to "latitude"; theta is 0 at the "north pole", and Pi at the "south pole".

Phi corresponds to "longitude", varying from 0 to 2 Pi counterclockwise looking from the north pole.

My text books reverse the definitions of theta and phi.

So, with this in mind, there is nothing wrong with the PoseLegEndpoints[] function. If theta is zero, the vector is pointing towards the north pole, so the value of phi is immaterial.

Eric

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