Page 63 - Introduction to Autonomous Mobile Robots

Chapter 3
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mobile robot is a self-contained automaton that can wholly move with respect to its envi-
ronment. There is no direct way to measure a mobile robot’s position instantaneously.
Instead, one must integrate the motion of the robot over time. Add to this the inaccuracies
of motion estimation due to slippage and it is clear that measuring a mobile robot’s position
precisely is an extremely challenging task.
The process of understanding the motions of a robot begins with the process of describ-
ing the contribution each wheel provides for motion. Each wheel has a role in enabling the
whole robot to move. By the same token, each wheel also imposes constraints on the
robot’s motion; for example, refusing to skid laterally. In the following section, we intro-
duce notation that allows expression of robot motion in a global reference frame as well as
the robot’s local reference frame. Then, using this notation, we demonstrate the construc-
tion of simple forward kinematic models of motion, describing how the robot as a whole
moves as a function of its geometry and individual wheel behavior. Next, we formally
describe the kinematic constraints of individual wheels, and then combine these kinematic
constraints to express the whole robot’s kinematic constraints. With these tools, one can
evaluate the paths and trajectories that define the robot’s maneuverability.

3.2 Kinematic Models and Constraints

Deriving a model for the whole robot’s motion is a bottom-up process. Each individual
wheel contributes to the robot’s motion and, at the same time, imposes constraints on robot
motion. Wheels are tied together based on robot chassis geometry, and therefore their con-
straints combine to form constraints on the overall motion of the robot chassis. But the
forces and constraints of each wheel must be expressed with respect to a clear and consis-
tent reference frame. This is particularly important in mobile robotics because of its self-
contained and mobile nature; a clear mapping between global and local frames of reference
is required. We begin by defining these reference frames formally, then using the resulting
formalism to annotate the kinematics of individual wheels and whole robots. Throughout
this process we draw extensively on the notation and terminology presented in [52].

3.2.1 Representing robot position
Throughout this analysis we model the robot as a rigid body on wheels, operating on a hor-
izontal plane. The total dimensionality of this robot chassis on the plane is three, two for
position in the plane and one for orientation along the vertical axis, which is orthogonal to
the plane. Of course, there are additional degrees of freedom and flexibility due to the
wheel axles, wheel steering joints, and wheel castor joints. However by robot chassis we
refer only to the rigid body of the robot, ignoring the joints and degrees of freedom internal
to the robot and its wheels.