13.1.2 Kinematics for Wheeled Systems

The most common family of examples in robotics arises from wheels that are required to roll in the direction they are pointing. Most wheels are not designed to slide sideways. This imposes velocity constraints on rolling vehicles. As a result, there are usually less action variables than degrees of freedom. Such systems are therefore called underactuated. It is interesting that, in many cases, vehicles can execute motions that overcome the constraint. For example, a car can parallel park itself anywhere that it could reach if all four wheels could turn to any orientation. This leads to formal concepts such as nonholonomic constraints and small-time local controllability, which are covered in Section 15.4.