Page 92 - Introduction to Autonomous Mobile Robots

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Mobile Robot Kinematics
An alternative way to describe a holonomic robot is based on the relationship between
the differential degrees of freedom of a robot and the degrees of freedom of its workspace:
a robot is holonomic if and only if DDOF = DOF . Intuitively, this is because it is only
through nonholonomic constraints (imposed by steerable or fixed standard wheels) that a
robot can achieve a workspace with degrees of freedom exceeding its differential degrees
of freedom, DOF > DDOF . Examples include differential drive and bicycle/tricycle con-
figurations.
In mobile robotics, useful chassis generally must achieve poses in a workspace with
dimensionality 3, so in general we require DOF = 3 for the chassis. But the “holonomic”
abilities to maneuver around obstacles without affecting orientation and to track at a target
while following an arbitrary path are important additional considerations. For these rea-
sons, the particular form of holonomy most relevant to mobile robotics is that of
DDOF = DOF = 3 . We define this class of robot configurations as omnidirectional: an
omnidirectional robot is a holonomic robot with DDOF = . 3

3.4.3 Path and trajectory considerations
In mobile robotics, we care not only about the robot’s ability to reach the required final con-
figurations but also about how it gets there. Consider the issue of a robot’s ability to follow
paths: in the best case, a robot should be able to trace any path through its workspace of
poses. Clearly, any omnidirectional robot can do this because it is holonomic in a three-
dimensional workspace. Unfortunately, omnidirectional robots must use unconstrained
wheels, limiting the choice of wheels to Swedish wheels, castor wheels, and spherical
wheels. These wheels have not yet been incorporated into designs allowing far larger
amounts of ground clearance and suspensions. Although powerful from a path space point
of view, they are thus much less common than fixed and steerable standard wheels, mainly
because their design and fabrication are somewhat complex and expensive.
Additionally, nonholonomic constraints might drastically improve stability of move-
ments. Consider an omnidirectional vehicle driving at high speed on a curve with constant
diameter. During such a movement the vehicle will be exposed to a non-negligible centrip-
etal force. This lateral force pushing the vehicle out of the curve has to be counteracted by
the motor torque of the omnidirectional wheels. In case of motor or control failure, the vehi-
cle will be thrown out of the curve. However, for a car-like robot with kinematic con-
straints, the lateral forces are passively counteracted through the sliding constraints,
mitigating the demands on motor torque.
But recall an earlier example of high maneuverability using standard wheels: the bicycle
on which both wheels are steerable, often called the two-steer. This vehicle achieves a
degree of steerability of 2, resulting in a high degree of maneuverability:
δ = δ + δ = 1 + 2 = 3 . Interestingly, this configuration is not holonomic, yet has a
M m s
high degree of maneuverability in a workspace with DOF = 3 .