Why does the control of wheeled mobile robots (WMR) differ from the control of cars and trucks? Does the lateral velocity have something to do with that?
The steering method is the reason why ... If you mean by WMR, the differentially driven robot, then the steering is based on the speeds of the left and right wheels of the robot; however, steering in cars and trucks depends on the steering angle of the front two wheel of cars and trucks (this mechanism is known as Ackerman steering mechanism)...
The main issue is limited turning radius of cars and trucks due to mechanical design limitations. Where as the conventional 3 wheel differential drive robot can have any turning radius. It can turn about its own center (any point on line joining the rear wheels).
The difference is the mathematical model, you can see the difference as degree of system, or as number of inputs and outputs and the class of the system. If the model is the same, there will be no difference. Control engineers build there control based on the mathematical model of each robot.
I think that the difference stems from different dynamic features of these systems. Mobile robots have lower mass and work in lower velocities with different tire dynamics. When we design a controller for a mobile robot, we don't think about the stability of the robot. if the robot cannot track a trajectory, only the tracking problem is failed. Or it is not so important if the robot looses its stability since it is not dealt with people's health.
However, when we design a controller for a passenger car, we know that if the vehicle cannot track the trajectory, it may loos stability. Usually, when we design a controller for a passenger car, we assume that the vehicle is equipped with ESP (electronic stability program). Therefore, if the vehicle is going to loose stability, ESP prevents it. In trucks, the stability is more susceptible, and further attentions must be considered.
about the lateral velocity, I have to say that when a vehicle is loosing stability, its lateral velocity is increasing. In other word, lateral velocity can be a measure of stability.
The key here is that the inertias of a mobile robot will be easy to manage due to its lower mass (in fact, many controllers do not consider them explicitly). On the contrary, for trucks and cars the inertias have to be taken into account to guarantee the stability of the system.
Also, when designing a controller for a mobile robot we tend to prioritize precision (avoid deviations from the desired path), but for a truck/car other things should be put in the first place, like stability and/or passenger comfort, and of course the safety.
Finally, the control has to be different due to the different dynamics. A robot will use the velocities of the wheels to maneuver during the turnings, but a car/truck can only be controlled with the speed and the steering wheel. This impacts the maximum curvature that the car/truck can take, and has to be explicitly modeled for each vehicle.