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

6.1 Simulink Model 80On the right hand side, there appear also two blocks, namely ¨Cable Force¨ and ¨Accelerometers¨which provide respectively the external force by the testing machine when pulling the robotsidewards or backwards and the data from the three 1-axis accelerometers. The ¨Accelerometers¨block simply implements (3.4), without considering any noise and band-pass filtering due tothe accelerometers properties. The ¨Cable Force¨ block implements the non-linear springdampedforce produced by the steel cable when pulling it with the testing machine (seeFigure 6.2(b)). The non-linearity is due to the double characteristic of a cable to provide aspring-damped force when it is pulled and a zero force when it is pushed, and it is implementedby using a saturation block. The displacement providing the cable spring force isgiven by the difference between the testing machine position, represented by the ramp block,and the robot position. The spring term of the force is, therefore, obtained by multiplying thecable displacement by the cable elasticity coefficient K cable , and the damping term is obtainedby multiplying the robot velocity by the cable damping coefficient D cable . The overall forceis then multiplied by J cable , which transforms the cable force vector from the fixed frame tothe body frame and is defined by means of the Plücker transformation of spatial force vectorsgiven in (2.52), where the matrix ˆX is substituted by ˆp cable , being p cable the position of theapplication point of the cable force with respect to the robot CoM. As the steel cable is muchmore stiff then the tire and does not perceive relatively high frequency vibrations (see figuresin Section 3.3), we set K cable ≫ K tire and D cable = 4 √ mK cable .The tire reaction forces and torques expressed in the body frame are provided by thefour ¨Wheel¨ blocks, giving the desired wheel angular velocity and the robot acceleration˙V as inputs. As the four ¨Wheel¨ blocks are identical with each other, except for the skewsymmetricmatrix of the contact point position ˆp i employed in the computation of the wheelcenter velocities and the toques exerted at the CoM. Thereby, the block is first masked,setting as dialog parameter the value for ˆp i , and then put in a Simulink library model, so thatevery change made on the block is automatically updated for every wheel. The block schemeinside the ¨Wheel¨ block is depicted in Figure 6.3.The block in yellow represents the wheel motor and the motor velocity servo-controller.We assume that the motor can always provide the angular velocity required by the motorvelocity servo-controller and that it takes a certain time t eq = 3K wto reach the desired velocity.In such conditions, the motor dynamics can be described by a first order system defined asfollows: