Robot chassis 20% mc, Ic Left track module 20% mm,l, Im,l Left track with 20% mt,l, It,l adhering members Right track module 20% mm,r, Im,r Right track with 20% mt,r, It,r adhering members Notes: Mass percentage based on typical construction of MRWS system I* = Ic +( Im.l + It.l + Im.r + It,r) + (mm,l + mt,l + mm,r + mt,r)b2 What about I about the track axes?. Fig. 5: CAD Model with components labeled. From table I, parameters represent the coordinates of the center of mass (cm) in dl, dtl, dr, dtr x the robot frame for the left track module, left track, right track module and right track respectively while parameter represents the coordinate of the cm for each of the MRWS b y components. This assumes that the center of mass for the left and right tracks and track modules lie on the track centerline and are symmetric about the robot axis. x The dynamic equations are derived using Lagrange techniques and written in the general form, () with () the mass matrix, () the vector of coriolis and centripetal accelerations, () the gravity vector, () the input torque vector, () the constraint matrix, () The vector of lagrange multipliers and () the vector non-conservative forces in the system (other than gravity forces and the inputs). In this model, there are five generalized accelerations (), two input torques () and three lagrange multipliers (). In the usual solution method for a wheeled mobile robot, the kinematic model is fully known according to the no slip, pure roll constraints consisting of two holonomic and one non-holonomic constraint (CITATION HERE!). The holonomic constraints can be used to reduce the generalized coordinate set (SEE FOR EXAMPLE A CITATION THAT DOES THIS) or included in the lagrange multipliers (SEE FOR EXAMPLE A CITATION THAT DOES THIS). Thus, two inputs would be defined, yielding four (or eight if holonomic constraints are retained in equations of motion) unknowns to be solved from the three (five) equations of motion
Robot chassis mc, Ic 20% Left track module mm,l, Im,l 20% Left track with adhering members mt,l, It,l 20% Right track module mm,r, Im,r 20% Right track with adhering members mt,r, It,r 20% Notes: Mass percentage based on typical construction of MRWS system I* = Ic +( Im.l + It.l + Im.r + It,r) + (mm,l + mt,l + mm,r + mt,r)b2 What about I about the track axes?. Fig. 5: CAD Model with components labeled. From table I, parameters dl, dtl, dr, dtr represent the x coordinates of the center of mass (cm) in the robot frame for the left track module, left track, right track module and right track respectively while parameter b represents the y coordinate of the cm for each of the MRWS components. This assumes that the center of mass for the left and right tracks and track modules lie on the track centerline and are symmetric about the robot x axis. The dynamic equations are derived using Lagrange techniques and written in the general form, () with () the mass matrix, () the vector of coriolis and centripetal accelerations, () the gravity vector, () the input torque vector, () the constraint matrix, () The vector of lagrange multipliers and () the vector non-conservative forces in the system (other than gravity forces and the inputs). In this model, there are five generalized accelerations (), two input torques () and three lagrange multipliers (). In the usual solution method for a wheeled mobile robot, the kinematic model is fully known according to the no slip, pure roll constraints consisting of two holonomic and one non-holonomic constraint (CITATION HERE!). The holonomic constraints can be used to reduce the generalized coordinate set (SEE FOR EXAMPLE A CITATION THAT DOES THIS) or included in the lagrange multipliers (SEE FOR EXAMPLE A CITATION THAT DOES THIS). Thus, two inputs would be defined, yielding four (or eight if holonomic constraints are retained in equations of motion) unknowns to be solved from the three (five) equations of motion