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

2.2 Generalized Modeling 24⎡1 0¯M = S T MS = m ⎢⎣0 x⎤⎥⎦ 2ICR + I , 0 ˙θ¯C = S T MṠ = mx ICR⎡⎢⎣−˙θ ẋ⎤⎥⎦ ,ICR⎡⎤⎡ ⎤F rx ( ˙q)¯R = ¯R = ⎢⎣x ICR F ry ( ˙q) + M r ( ˙q)⎥⎦ , ¯B = ¯B = 1 1 1r⎢⎣−c c⎥⎦ .2.2 Generalized ModelingThe simplified kinematic and dynamic models presented in the previous section hold ifand only if the robot is strictly moving on a two dimensional plane, that is only two linearvelocities parallel to the plane and the angular velocity around an axis perpendicular to theplane are considered. This assumption is generally a good approximation of the real robotmotion when the roll and pitch motion, i.e. the rotation around the x and y axis, are negligible,which is generally true, as long as the robot stability is guaranteed, for trajectorytracking control and robot localization applications. The robot stability can be guaranteed byhaving, for instance, the height of CoM much smaller than the distance between the wheel/-ground contact points, or the moment of inertia along the x, y much lower than along the zaxis, or a very stiff robot structure and wheel/ground interaction. However, the conditionson the robot motion stability do not depend only on the geometric and dynamic properties ofthe robot structure, but they also depend on the kinematic and dynamic constraints of robotmotion, which might come from limits on robot velocities and interactions with the environment.Although such constraints play an important role in vehicle dynamics because of highvelocities and slipping conditions [17], they are usually negligible for steered mobile robots(SMRs) [3], [18], [19]. In fact, for steered mobile robots non-slipping and pure rolling conditionsare mostly satisfied, therefore, for relatively low velocities, reactive friction forcesare usually much lower than forces resulting from inertia. Conversely, for SSMRs, when therobot is changing its orientation, reactive friction forces are usually much higher than forcesresulting from inertia. As a consequence, even for relatively low velocities, dynamic propertiesof SSMRs can cause jerky motion and large amplitude vibrations, which influence robotmotion and stability much more than for SMRs.In [10], [4], [5], [11], [11], [15], the SSMR modeling is provided for trajectory trackingcontrol and localization applications, therefore the dynamic properties due to the complexwheel/ground interaction are handled only by introducing the wheel slip, while no conse-