【正文】 Mobile Robot Vehicles This chapter discusses how a robot platform moves, that is, how its pose changes with time as a function of its control inputs. There are many different types of robot platform as shown on pages 61–63 but in this chapter we will consider only two which are important exemplars. The first is a wheeled vehicle like a car which operates in a 2dimensional world. It can be propelled forwards or backwards and its heading direction controlled by changing the angle of its steered wheels. The second platform is a quadcopter, a flying vehicle, which is an example of a robot that moves in 3dimensional space. Quadcopters are being increasing popular as a robot platform since they can be quite easily modelled and controlled. However before we start to discuss these two robot platforms it will be helpful to consider some general, but important, concepts regarding mobility. lMobility We have already touched on the diversity of mobile robots and their modes of this section we will discuss mobility which is concerned with how a vehicle moves in space. We first consider the simple example of a train. The train moves along rails and its positionis described by its distance along the rail from some datum. The configuration of the train can be pletely described by a scalar parameter q which is called its generalized coordinate. The set of all possible configurations is the configuration space, or Cspace, denoted by C and q∈C. In this case C?R. We also say that the train has one degree of freedom since q is a scalar. The train also has one actuator (motor) that propels it forwards or backwards along the rail. With one motor and one degree of freedom the train is fully actuated and can achieve any desired configuration, that is, any position along the rail. Another important concept is task space which is the set of all possible poses ξ of the vehicle and ξ ∈ T. The task space depends on the application or task. If our task was motion along the rail then T ?R. If we cared only about the position of the train in a plane then T ?R2. If we considered a 3dimensional world then T ? SE(3), and its height changes as it moves up and down hills and its orientation changes as it moves around curves. Clearly for these last two cases the dimensions of the task space exceed the dimensions of the configuration space and the train cannot attain an arbitrarypose since it is constrained to move along fixed rails. In these cases we say that the train moves along a manifold in the task space and there is a mapping from q
ξ. Interestingly many vehicles share certain characteristics with trains – they are good at moving forward but not so good at moving sideways. Cars, hovercrafts, ships and aircraft all exhibit this characteristic and require plex manoeuvring in order to move sideways. Nevertheless this is a very sensible design approach since it caters to the motion we most monly require of the vehicle. The less mon motions such as parking a car, docking a ship or landing an aircraft are more plex, but not impossible,and humans can learn this skill. The benefit of this type of design es from simplification and in particular reducing the number of actuators required. Next consider a hovercraft which has two propellors whose axes are parallel but not collinear. The sum of their thrusts provide a forward force and the difference in thrusts generates a yawing torque for steering. The hovercraft moves over a planar surface and its configuration is entirely described by three generalized coordinates q =(x, y, θ) ∈ C and in this case C ? R2 S. The configuration space has 3 dimensions and the vehicle therefore has three degrees of freedom. The hovercraft has only two actuators, one fewer than it has degrees of freedom,and it is therefore an underactuated system. This imposes limitations on the way in which it can move. At any point in time we can control the forward (parallel to the thrust vectors) acceleration and the rotational acceleration of the the hovercraft but there is zero sideways (or lateral) acceleration since it does not generate any lateral thrust. Nevertheless with some clever manoeuvring, like with a car, the hovercraft can follow a path that will take it to a place to one side of where it started. The advantage of underactuation is the reduced number of actuators, in this case two instead of penalty is that the vehicle cannot move directly to an any point in its configuration space, it must follow some path. If we added a third propellor to the hovercraft with its axis normal to the first two then it would be possible to mand an arbitraryforward, sideways and rotational acceleration. The task space of the hovercraft is T ? SE(2) which is equivalent, in this case, to the configuration space. A helicopter has four actuators. The main rotor generates a thrust vector whose magnitude i