Advance Modeling of a Skid-Steering Mobile Robot for Remote ...

5.1 Identification of the Geometric and Inertial Parameters 66with respect to their CoM for a frame parallel to the robot frame, by using standard formulasfor regular geometric shapes. Then, the tensor of inertia of the robot can be computed byusing the Huygens-Steiner Theorem and Superimposition Principle of moment of inertia fora rigid body, stating respectively:I O = I O ′ + mOO ˆ ′∑I =iI iˆOO ′Twhere m, I are the mass and tensor of inertia of the body, I O , I O ′ are the tensors of inertiacalculated in two generic points O, O ′ ,ˆ OO ′ is the skew-symmetric matrix of the vector OO ′and I i is the tensor of inertia of the i − th component of the body calculated with respect tothe same frame.By using the formulas above and the tensor of inertia of the robot’s components, the tensorof inertia of 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 of the above estimation and to have even a better estimation, theideal robot tensor of inertia is calculated by using a Solidworks model of the robot, whichwas already made by Professor M. Stein for a previous project (Figure 5.2). Thereby, thetensor of 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 ofthe robot CoM. In particular, the position of the CoM, with respect to an output coordinatesystem placed at one corner of 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