  Motion planning is a difficult problem in robot control. The complexity of
the problem is directly related to the dimension of the robot's configuration
space. While in many theoretical calculations and practical applications the
configuration space is modeled as a continuous space, we present a discrete
robot model based on the fundamental hardware specifications of a robot. Using
lattice path methods, we provide estimates for the complexity of motion
planning by counting the number of possible trajectories in a discrete robot
configuration space.
