Modelica - Internal error for overconstrained stewart platform model

Question

OpenModelica v1.17.0 (64-bit)

OMSimulator v2.0.0.post284-gc8ec782-mingw

Modelica Standard Library 3.2.3

Hello, I'm currently working on the implementation of a dynamic model of a Stewart Platform in OpenModelica similar to the one in https://www.xarg.org/paper/inverse-kine … -platform/ (6RSS parallel robot) and apparently, I'm not able to connect multiple legs to the same platform due to the following error:

[1] 13:08:36 Translation Error
Internal error It is not possible to select continuous time states because Number of Equations 18 greater than number of States 17 to select from.

[2] 13:08:36 Translation Error
Internal error - IndexReduction.dynamicStateSelectionWork failed!

From what I have seen in the documentation of Modelica, this might be caused by some loop in the spanning tree generated during the translation phase of the model where some non-flow equations became dependent on each other resulting in an overconstrained (even if still solvable) system. It follows the source code of the package that I have created in which there are present a base, a platform, and only two RSS legs which create the issue.

package sixRSS_parallelRobot
model platform
  import Modelica.SIunits;
  import Modelica.Math;
  constant SIunits.Length l = 0.7;
  constant StateSelect stateSelect = StateSelect.prefer annotation(
    Dialog(tab = "Advanced"));
  final constant Real pi = 2 * Modelica.Math.asin(1.0);
  parameter Boolean useQuat = false;
  Modelica.Mechanics.MultiBody.Parts.Body body(enforceStates = stateSelect == StateSelect.always,m = 1, r_0(each fixed = true, start = {0, 0.5, 0}), r_CM = {0, 0, 0}, useQuaternions = useQuat, v_0(each fixed = true, start = {0, 0, 0}), w_a(each fixed = true)) annotation(
    Placement(visible = true, transformation(origin = {70, 2}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation1(r = {l * cos(0 * (pi / 180) + (-5) * (pi / 180)), 0, l * sin(0 * (pi / 180) + (-5) * (pi / 180))}) annotation(
    Placement(visible = true, transformation(origin = {-18, 68}, extent = {{-10, -10}, {10, 10}}, rotation = 180)));
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation2(r = {l * cos(0 * (pi / 180) + 5 * (pi / 180)), 0, l * sin(0 * (pi / 180) + 5 * (pi / 180))}) annotation(
    Placement(visible = true, transformation(origin = {-14, 50}, extent = {{-10, -10}, {10, 10}}, rotation = 180)));
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation3(r = {l * cos(120 * (pi / 180) + (-5) * (pi / 180)), 0, l * sin(120 * (pi / 180) + (-5) * (pi / 180))}) annotation(
    Placement(visible = true, transformation(origin = {-18, 24}, extent = {{-10, -10}, {10, 10}}, rotation = 180)));
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation4(r = {l * cos(120 * (pi / 180) + 5 * (pi / 180)), 0, l * sin(120 * (pi / 180) + 5 * (pi / 180))}) annotation(
    Placement(visible = true, transformation(origin = {-12, 2}, extent = {{-10, -10}, {10, 10}}, rotation = 180)));
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation5(r = {l * cos(240 * (pi / 180) + (-5) * (pi / 180)), 0, l * sin(240 * (pi / 180) + (-5) * (pi / 180))}) annotation(
    Placement(visible = true, transformation(origin = {-14, -24}, extent = {{-10, -10}, {10, 10}}, rotation = 180)));
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation6(r = {l * cos(240 * (pi / 180) + 5 * (pi / 180)), 0, l * sin(240 * (pi / 180) + 5 * (pi / 180))}) annotation(
    Placement(visible = true, transformation(origin = {-16, -46}, extent = {{-10, -10}, {10, 10}}, rotation = 180)));
  //outer Modelica.Mechanics.MultiBody.World world;
  Modelica.Mechanics.MultiBody.Interfaces.Frame_b frame_b[6] annotation(
    Placement(visible = true, transformation(origin = {-76, 10}, extent = {{-16, -16}, {16, 16}}, rotation = 0), iconTransformation(origin = {-100, 6}, extent = {{-16, -16}, {16, 16}}, rotation = 0)));

equation
  connect(fixedTranslation1.frame_a, body.frame_a) annotation(
    Line(points = {{-8, 68}, {30, 68}, {30, 2}, {60, 2}}, color = {95, 95, 95}));
  connect(fixedTranslation2.frame_a, body.frame_a) annotation(
    Line(points = {{-4, 50}, {30, 50}, {30, 2}, {60, 2}}, color = {95, 95, 95}));
  connect(fixedTranslation3.frame_a, body.frame_a) annotation(
    Line(points = {{-8, 24}, {30, 24}, {30, 2}, {60, 2}}));
  connect(fixedTranslation4.frame_a, body.frame_a) annotation(
    Line(points = {{-2, 2}, {60, 2}}));
  connect(fixedTranslation5.frame_a, body.frame_a) annotation(
    Line(points = {{-4, -24}, {30, -24}, {30, 2}, {60, 2}}, color = {95, 95, 95}));
  connect(fixedTranslation6.frame_a, body.frame_a) annotation(
    Line(points = {{-6, -46}, {30, -46}, {30, 2}, {60, 2}}, color = {95, 95, 95}));
  connect(fixedTranslation2.frame_b, frame_b[2]) annotation(
    Line(points = {{-24, 50}, {-56, 50}, {-56, 10}, {-76, 10}}, color = {95, 95, 95}));
  connect(fixedTranslation3.frame_b, frame_b[3]) annotation(
    Line(points = {{-28, 24}, {-56, 24}, {-56, 10}, {-76, 10}}, color = {95, 95, 95}));
  connect(fixedTranslation4.frame_b, frame_b[4]) annotation(
    Line(points = {{-22, 2}, {-56, 2}, {-56, 10}, {-76, 10}}, color = {95, 95, 95}));
  connect(fixedTranslation5.frame_b, frame_b[5]) annotation(
    Line(points = {{-24, -24}, {-56, -24}, {-56, 10}, {-76, 10}}, color = {95, 95, 95}));
  connect(fixedTranslation6.frame_b, frame_b[6]) annotation(
    Line(points = {{-26, -46}, {-56, -46}, {-56, 10}, {-76, 10}}, color = {95, 95, 95}));
  connect(fixedTranslation1.frame_b, frame_b[1]) annotation(
    Line(points = {{-28, 68}, {-56, 68}, {-56, 10}, {-76, 10}}, color = {95, 95, 95}));
  annotation(
    uses(Modelica(version = "3.2.3")));

end platform;

model base
  import Modelica.SIunits;
  import Modelica.Math;
  constant SIunits.Length l = 0.7;
  constant StateSelect stateSelect = StateSelect.prefer annotation(
    Dialog(tab = "Advanced"));
  final constant Real pi = 2 * Modelica.Math.asin(1.0);
  parameter Boolean useQuat = false;
  Modelica.Mechanics.MultiBody.Parts.Fixed fixed annotation(
    Placement(visible = true, transformation(origin = {-16, 12}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.Fixed fixed1(r = {l * cos(0 * (pi / 180) + (-5) * (pi / 180)), 0, l * sin(0 * (pi / 180) + (-5) * (pi / 180))}) annotation(
    Placement(visible = true, transformation(origin = {54, -2}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.Fixed fixed2(r = {l * cos(0 * (pi / 180) + 5 * (pi / 180)), 0, l * sin(0 * (pi / 180) + 5 * (pi / 180))}) annotation(
    Placement(visible = true, transformation(origin = {52, 30}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.Fixed fixed3(r = {l * cos(120 * (pi / 180) + (-5) * (pi / 180)), 0, l * sin(120 * (pi / 180) + (-5) * (pi / 180))}) annotation(
    Placement(visible = true, transformation(origin = {-46, 76}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.Fixed fixed4(r = {l * cos(120 * (pi / 180) + 5 * (pi / 180)), 0, l * sin(120 * (pi / 180) + 5 * (pi / 180))}) annotation(
    Placement(visible = true, transformation(origin = {-74, 50}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.Fixed fixed5(r = {l * cos(240 * (pi / 180) + (-5) * (pi / 180)), 0, l * sin(240 * (pi / 180) + (-5) * (pi / 180))}) annotation(
    Placement(visible = true, transformation(origin = {-68, -26}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.Fixed fixed6(r = {l * cos(240 * (pi / 180) + 5 * (pi / 180)), 0, l * sin(240 * (pi / 180) + 5 * (pi / 180))}) annotation(
    Placement(visible = true, transformation(origin = {-44, -68}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.Body body(enforceStates = stateSelect == StateSelect.always,m = 5, r_CM = {0, 0, 0}, useQuaternions = useQuat)  annotation(
    Placement(visible = true, transformation(origin = {12, 12}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  outer Modelica.Mechanics.MultiBody.World world;
Modelica.Mechanics.MultiBody.Interfaces.Frame_a frame_a[6] annotation(
    Placement(visible = true, transformation(origin = {104, 16}, extent = {{-16, -16}, {16, 16}}, rotation = 0), iconTransformation(origin = {108, 0}, extent = {{-16, -16}, {16, 16}}, rotation = 0)));
equation
  connect(fixed.frame_b, body.frame_a) annotation(
    Line(points = {{-6, 12}, {2, 12}}, color = {95, 95, 95}));
connect(fixed1.frame_b, frame_a[1]) annotation(
    Line(points = {{64, -2}, {86, -2}, {86, 16}, {104, 16}}));
connect(fixed2.frame_b, frame_a[2]) annotation(
    Line(points = {{62, 30}, {86, 30}, {86, 16}, {104, 16}}, color = {95, 95, 95}));
connect(fixed3.frame_b, frame_a[3]) annotation(
    Line(points = {{-36, 76}, {86, 76}, {86, 16}, {104, 16}}));
connect(fixed4.frame_b, frame_a[4]) annotation(
    Line(points = {{-64, 50}, {86, 50}, {86, 16}, {104, 16}}));
connect(fixed5.frame_b, frame_a[5]) annotation(
    Line(points = {{-58, -26}, {86, -26}, {86, 16}, {104, 16}}));
connect(fixed6.frame_b, frame_a[6]) annotation(
    Line(points = {{-34, -68}, {86, -68}, {86, 16}, {104, 16}}));
  annotation(
    uses(Modelica(version = "3.2.3")));

end base;

  model fullmodel
    inner Modelica.Mechanics.MultiBody.World world annotation(
      Placement(visible = true, transformation(origin = {-68, 14}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
    sixRSS_parallelRobot.platform platform(useQuat = true)  annotation(
      Placement(visible = true, transformation(origin = {106, 12}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
    sixRSS_parallelRobot.base base(useQuat = true)  annotation(
      Placement(visible = true, transformation(origin = {-26, 14}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Joints.Revolute revolute(n = {1, 0, 0}, phi(displayUnit = "rad"))  annotation(
      Placement(visible = true, transformation(origin = {-1, 29}, extent = {{-7, -7}, {7, 7}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.BodyShape bodyShape(m = 0.01, r = {0, 0, -0.2}, r_CM = {0, 0, -0.1})  annotation(
      Placement(visible = true, transformation(origin = {19, 29}, extent = {{-7, -7}, {7, 7}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Joints.Spherical spherical annotation(
      Placement(visible = true, transformation(origin = {35, 29}, extent = {{-7, -7}, {7, 7}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.BodyShape bodyShape1(m = 0.002, r = {0, 0.5, 0.2}, r_CM = {0, 0.25, 0.1})  annotation(
      Placement(visible = true, transformation(origin = {51, 29}, extent = {{-7, -7}, {7, 7}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Joints.Spherical spherical1 annotation(
      Placement(visible = true, transformation(origin = {71, 29}, extent = {{-7, -7}, {7, 7}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Joints.Revolute revolute1(n = {1, 0, 0}, phi(displayUnit = "rad")) annotation(
      Placement(visible = true, transformation(origin = {1, -1}, extent = {{-7, -7}, {7, 7}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.BodyShape bodyShape2(m = 0.01, r = {0, 0, 0.2}, r_CM = {0, 0, 0.1}) annotation(
      Placement(visible = true, transformation(origin = {21, -1}, extent = {{-7, -7}, {7, 7}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Joints.Spherical spherical2 annotation(
      Placement(visible = true, transformation(origin = {37, -1}, extent = {{-7, -7}, {7, 7}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.BodyShape bodyShape3(m = 0.002, r = {0, 0.5, -0.2}, r_CM = {0, 0.25, -0.1}) annotation(
      Placement(visible = true, transformation(origin = {53, -1}, extent = {{-7, -7}, {7, 7}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Joints.Spherical spherical3 annotation(
      Placement(visible = true, transformation(origin = {73, -1}, extent = {{-7, -7}, {7, 7}}, rotation = 0)));
  equation
  connect(revolute.frame_b, bodyShape.frame_a) annotation(
      Line(points = {{6, 29}, {12, 29}}));
  connect(bodyShape.frame_b, spherical.frame_a) annotation(
      Line(points = {{26, 29}, {28, 29}}, color = {95, 95, 95}));
  connect(spherical.frame_b, bodyShape1.frame_a) annotation(
      Line(points = {{42, 29}, {44, 29}}, color = {95, 95, 95}));
  connect(bodyShape1.frame_b, spherical1.frame_a) annotation(
      Line(points = {{58, 30}, {64, 30}}));
  connect(revolute.frame_a, base.frame_a[1]) annotation(
      Line(points = {{-8, 30}, {-10, 30}, {-10, 14}, {-16, 14}}));
  connect(spherical1.frame_b, platform.frame_b[1]) annotation(
      Line(points = {{78, 30}, {88, 30}, {88, 12}, {96, 12}}, color = {95, 95, 95}));
  connect(base.frame_a[2], revolute1.frame_a) annotation(
      Line(points = {{-16, 14}, {-10, 14}, {-10, 0}, {-6, 0}}, color = {95, 95, 95}));
  connect(revolute1.frame_b, bodyShape2.frame_a) annotation(
      Line(points = {{8, 0}, {14, 0}}, color = {95, 95, 95}));
  connect(bodyShape2.frame_b, spherical2.frame_a) annotation(
      Line(points = {{28, 0}, {30, 0}}, color = {95, 95, 95}));
  connect(spherical2.frame_b, bodyShape3.frame_a) annotation(
      Line(points = {{44, 0}, {46, 0}}, color = {95, 95, 95}));
  connect(bodyShape3.frame_b, spherical3.frame_a) annotation(
      Line(points = {{60, 0}, {66, 0}}));
  connect(spherical3.frame_b, platform.frame_b[2]) annotation(
      Line(points = {{80, 0}, {88, 0}, {88, 12}, {96, 12}}));
  end fullmodel;
  annotation(
    uses(Modelica(version = "3.2.3")));
end sixRSS_parallelRobot;

Since I'm new to Modelica, I think I'm missing some basic concepts of modelling multibody mechanics especially when kinematics loops take place. I've already made some tests on the planar loop fourbar example in the Modelica library but I think this is something different. Is there a way to solve this error and finally obtain a working model of the 6RSS parallel robot?

Thank you in advance for your help!

score 1 · Answer 1 · answered Nov 09 '21 at 11:32

1

Not actually an answer, I know, but with a comment only, adding the gif below wouldn't be possible.

The model works in Dymola 2022 (after converting to MSL 4.0.0) and Dymola 2020x (with MSL 3.2.3) without any important warning. So, given the result below is what you would expect, then there is no fundamental error within the model. The resulting animation looks like this:

Dymola does dynamic state selection for the model - I'm not sure whether OpenModelica is able to do that as well. Generally I can't really help with OpenModelica unfortunately. But Probably this is already of help for you...

answered Nov 09 '21 at 11:32

Markus A.

6,300
10
26

Thank you for your quick reply! From what I have seen, OpenModelica can implement both dynamicStateSelection and dummyDerivatives as Index reduction method, but actually none of the seems to work. I tried to change the configuration of all the rigid bodies and the spherical joints in order not to use quaternions during simulation (Parameters windows -> Advanced tab -> useQuaternions = false) and now the simulation starts with some "matrix singular" error during the translation phase. Does this rings a bell? I've also tried using MSL 4.0.0 with useQuternions =true but I get the same error. – Roberto A. Nov 09 '21 at 14:03
1

When setting useQuaternions=false three angles are used to describe the orientation of bodies. This can result in singular computations in case the body is in a certain orientation. Did you try to change the "squence_angleStates" parameters (in the Advanced tab)? If I remember correctly, this could help, not sure though... This could be an interesting read: https://modelica.org/events/Conference2003/papers/h37_Otter_multibody.pdf, especially the paragraph starting with "Via a parameter in the “Advanced” menu" in section 6.5. – Markus A. Nov 09 '21 at 14:19
The paper you cited was the reason I tried to set useQuaternions=false in every component of the model. I'm not really sure on the effects of changing "sequence_angleStates" (should I do it with useQuaternions set to true or false, may you elaborate?). – Roberto A. Nov 09 '21 at 14:54
As far as I understood it you can either use quaternions OR angles to define the orientation of the body. Therefore useQuaternions has to be false. The system of equations gets singular if one of the necessary angles causes the overall system to get singular. Changing the sequence can solve the issue for this special application. The same could be true for changing the values of the angle (e.g. by changing the initialization) and keeping the sequence of angles... – Markus A. Nov 09 '21 at 15:51

Modelica - Internal error for overconstrained stewart platform model

1 Answers1