Basic robotics with LEGO NXT
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1. Mount light sensor, facing downwards on front of NXT and plugged into Port 3.
2. Mount a switch sensor on the NXT, plugged into Port 2.
3. Use a piece of dark tape (i.e. electrical tape) to mark a track on a flat, light
coloured surface. Make sure the tape and the surface are coloured differently
enough that the light sensor returns reasonably different values between the two
surfaces.
4. Write a program so that the tribot follows the line.
4.4 Classical control theory
4.4.1 Inverse plant dynamics and feedback control
In this section we discuss control systems that are at the brains of robots. Control
systems are necessary to guide actions in an uncertain environment. The principle idea
of a control system is to use sensory and motivational information to produce goal
directed behavior.
A control system is characterized by a control plant and contoller. A control plant
is the dynamical object that should be controlled, such as a robot arm. The state of this
object is described by a state vector
zT(t)=(1,x(t),x(1)(t),x(2) (t), ....),(4.1)
where x(t)are basic coordinates such as the positions on a plane for a land-based
robot and its heading direction at a particular time. We also included a constant part in
the description of the plant, as well as higher derivatives by writing the i-th derivative
as x(i)(t).
The state of the plant is influenced by a control command u(t). A control command
can be, for example, sending a specific current to motors, or the initiation of some
sequences of inputs to the robot. The effect of a control command u(t)when the plant
is in state z(t)is given by the plant equation
z(t+ 1) = f(z(t),u(t)),(4.2)
Learning the plant function fwill be an important point in adaptive control discussed
later, and we will discuss some examples below.
The control problem is to find the appropriate commands to reach desired states
z∗(t). We assume for now that this desired state is a specific point in the state space,
also called setpoint. Such a control problem with a single desired state is called . The
control problem is called tracking if the desired state is changing. In an ideal situation
we might be able to calculate the appropriate control commands. For example, if the
plant is linear in the control commands, that is, if fhas the form
z(t+1)=g(z(t)u(t),(4.3)
and ghas an inverse, then it is possible to calculate the command to reach the desired
state as
u∗=g−1(z)z∗.(4.4)
For example let u=tbe the motor command for the Tribot to move forward for t
seconds with a certain motor power. If the tribot moves a distance of d1in one second,
