Page 89 - Introduction to Autonomous Mobile Robots

Chapter 3
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system further constrains the kinematics such that in reality δ = 1 . Finally, we can com-
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pute maneuverability based on these values: δ M = 2 for a synchro drive robot.
This result implies that a synchro drive robot can only manipulate, in total, two degrees
of freedom. In fact, if the reader reflects on the wheel configuration of a synchro drive robot
it will become apparent that there is no way for the chassis orientation to change. Only the
x – y position of the chassis can be manipulated and so, indeed, a synchro drive robot has
only two degrees of freedom, in agreement with our mathematical conclusion.

3.4 Mobile Robot Workspace

For a robot, maneuverability is equivalent to its control degrees of freedom. But the robot
is situated in some environment, and the next question is to situate our analysis in the envi-
ronment. We care about the ways in which the robot can use its control degrees of freedom
to position itself in the environment. For instance, consider the Ackerman vehicle, or auto-
mobile. The total number of control degrees of freedom for such a vehicle is δ = 2 , one
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for steering and the second for actuation of the drive wheels. But what is the total degrees
of freedom of the vehicle in its environment? In fact it is three: the car can position itself
on the plane at any xy, point and with any angle . θ
Thus identifying a robot’s space of possible configurations is important because surpris-
ingly it can exceed δ . In addition to workspace, we care about how the robot is able to
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move between various configurations: what are the types of paths that it can follow and,
furthermore, what are its possible trajectories through this configuration space? In the
remainder of this discussion, we move away from inner kinematic details such as wheels
and focus instead on the robot chassis pose and the chassis degrees of freedom. With this
in mind, let us place the robot in the context of its workspace now.

3.4.1 Degrees of freedom
In defining the workspace of a robot, it is useful to first examine its admissible velocity
space. Given the kinematic constraints of the robot, its velocity space describes the inde-
pendent components of robot motion that the robot can control. For example, the velocity
space of a unicycle can be represented with two axes, one representing the instantaneous
forward speed of the unicycle and the second representing the instantaneous change in ori-
·
θ
entation, , of the unicycle.
The number of dimensions in the velocity space of a robot is the number of indepen-
dently achievable velocities. This is also called the differentiable degrees of freedom
(DDOF ). A robot’s DDOF is always equal to its degree of mobility δ . For example,
m
a bicycle has the following degree of maneuverability: δ = δ + δ = 1 + 1 = 2 . The
s
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DDOF of a bicycle is indeed 1.