Mobile robots
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This Chapter treats mobile robots, i.e., devices such as unicycles, bicycles, cars, and, especially, the mobile devices that have two independently driven wheels on one axle and one or more passive support wheels on a second axle. This text calls them differentially-driven robots. Caster robot is another name, referring to the caster wheel (or “castor” wheel) which helps to keep the robot's balance. A caster wheel is a wheel mounted in a swivel frame, and in daily live also used for supporting furniture, trucks, portable machines, etc. The caster wheel is not actuated. This text only considers mobile robots that move over a plane (or a reasonably good approximation of it). Hence, their configuration space has two translational and one rotational degree of freedom; the rotation axis is perpendicular to the translations. The joint space for a car-like robot is one-dimensional (turning the steering wheel does not move the robot!), but it is two-dimensional for a differentially-driven robot.
Mobile robots, at first sight, are rather different in nature from the serial and parallel robots discussed in other Chapters. However, this Chapter will highlight many similarities, such that no new concepts are needed for a comprehensive treatment of mobile robot kinematics.
Nonholonomic constraint. The common characteristic of mobile robots is that they cannot autonomously produce a velocity which is transversal to the axle of their wheels. A differentially-driven robot has one such constraint (the caster wheels are mounted on a swivel and hence give no constraint, except for friction); bicycles and cars have two constraints: one on the front wheel axle and one on the rear wheel axle. These constraits are nonholonomic constraints on the velocity of the robots, i.e., they cannot be integrated to give a constraint on the robots' Cartesian pose. (The word “holonomic” is built from the Greek words holos (“integral”) and nomos (“law”); the terminology was introduced by Hertz in 1894.) In other words, the vehicle cannot move transversally instantaneously, but it can reach any position and orientation by moving backward and forward while turning appropriately. Parking your car is a typical example of this maneuver phenomenon. The nonholonomic constraints reduce the mobile robot's instantaneous velocity degrees of freedom.