Advance Modeling of a Skid-Steering Mobile Robot for Remote ...
Advance Modeling of a Skid-Steering Mobile Robot for Remote ...
Advance Modeling of a Skid-Steering Mobile Robot for Remote ...
- No tags were found...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
5.1 Identification <strong>of</strong> the Geometric and Inertial Parameters 66with respect to their CoM <strong>for</strong> a frame parallel to the robot frame, by using standard <strong>for</strong>mulas<strong>for</strong> regular geometric shapes. Then, the tensor <strong>of</strong> inertia <strong>of</strong> the robot can be computed byusing the Huygens-Steiner Theorem and Superimposition Principle <strong>of</strong> moment <strong>of</strong> inertia <strong>for</strong>a rigid body, stating respectively:I O = I O ′ + mOO ˆ ′∑I =iI iˆOO ′Twhere m, I are the mass and tensor <strong>of</strong> inertia <strong>of</strong> the body, I O , I O ′ are the tensors <strong>of</strong> inertiacalculated in two generic points O, O ′ ,ˆ OO ′ is the skew-symmetric matrix <strong>of</strong> the vector OO ′and I i is the tensor <strong>of</strong> inertia <strong>of</strong> the i − th component <strong>of</strong> the body calculated with respect tothe same frame.By using the <strong>for</strong>mulas above and the tensor <strong>of</strong> inertia <strong>of</strong> the robot’s components, the tensor<strong>of</strong> inertia <strong>of</strong> the whole robot obtained is:⎡⎤1.13 0.001 −0.04I = 0.001 1.52 −0.002⎢⎣−0.04 −0.002 0.91⎥⎦To check the correctness <strong>of</strong> the above estimation and to have even a better estimation, theideal robot tensor <strong>of</strong> inertia is calculated by using a Solidworks model <strong>of</strong> the robot, whichwas already made by Pr<strong>of</strong>essor M. Stein <strong>for</strong> a previous project (Figure 5.2). Thereby, thetensor <strong>of</strong> inertia, automatically calculated by Solidworks, which will be considered in thefollowing is:⎡⎤1.21 0.000355 −0.0655I = 0.000355 1.41 −0.00125⎢⎣−0.0655 −0.00125 0.922⎥⎦(5.1)The data provided by the Solidworks model confirm also the approximated location <strong>of</strong>the robot CoM. In particular, the position <strong>of</strong> the CoM, with respect to an output coordinatesystem placed at one corner <strong>of</strong> the rear-right square tube with its axes parallel to the robotprincipal axes (Figure 5.2) (defined by default), is:o p CoM = [0.087 0.139 − 0.041] T