The inertia matrix (aka inertia tensor) of a sphere should be diagonal with The center of mass is given as the origin (0,0,0). Which is close to the computed value of 12.425. The surface area should be 4*PI (12.566), It is not exact since it is a triangular approximation. Which is close to the computed value of 4.095. VolumeĪ sphere of radius 1.0 should have a volume of 4/3*PI (4.189), Which implies that the sphere has a radius of 1.0. The bounding box of the sphere is a cube with side length 2.0, The sphere gives the following output: Mesh Bounding Box Size 2.000000 2.000000 2.000000 The lower part of the Layers dialog should now show some info about the inertial measures. Next, command MeshLab to compute the inertial parameters.Ĭhoose Filters->Quality Measure and Computations->Compute Geometric Measures from the menu. To compute the inertial parameters, you first need to display the Layers dialog - View->Show Layer Dialog.Ī panel opens in the right part of the window which is split in half - we're interested in the lower part containing text output. Computing the inertial parameters Computing inertia of sphere Once installed, you can view your meshes in MeshLab (both DAE and STL formats are supported, which are those ones supported by Gazebo/ROS). The installation should be straightforward. Preparation Installing MeshLabĭownload MeshLab from the official website and install it on your computer. This wikipedia entry is a great resource. If you're curious about the math behind the inertia matrix, or just want an easy way to calculate the tensor for simple shapes, This difficulty motivates the use of software tools for computing That typically make it much more difficult to estimate moments of inertia The moments of inertia are proportional to massīut vary in a non-linear manner with respect to size.Īdditionally, there are constraints on the relative values Yields its principal moments of inertia (the eigenvalues)Īnd the orientation of its principal axes (the eigenvectors). With 3 diagonal elements, and 3 unique off-diagonal elements.Įach inertia matrix is defined relative to a coordinate frame Of a symmetric positive-definite 3x3 matrix, The moments of inertia can be expressed as the components It depends on the mass, size, and shape of a body Represent the spatial distribution of mass in a rigid body. This parameter is a Vector3 with units of position. The center of mass is the point where the sum of weighted mass moments is zero.įor a uniform body, this is equivalent to the geometric centroid. It is a scalar with default units in Gazebo of kilograms (kg).įor a 3D uniform mesh, mass is computed byĬalculating the geometric volume Īnd multiplying by density. The mass is most easily measured by weighing an object. You can also use the commercial product SolidWorks to compute these information.įor a guide on using SolidWorks, please refer to Or inertia properties of your model, or quickly clean the model,Ī tool which runs MeshLab internally for this purpose. If you wish to skip the setup and only compute the volume, center of mass, It is shown how to obtain inertial data using the free software MeshLab. These parameters if you have 3D models of the links.Īssuming homogeneous bodies (uniform mass density), This tutorial will guide you through the process of obtaining and setting An accurate simulation requires physically plausible inertial parameters:Īnd the moment of inertia matrix of all links.
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