Combinatorics of a Discrete Trajectory Space for Robot Motion Planning
This work addresses motion planning complexity for robotics, offering a discrete modeling approach that is incremental in nature.
The paper tackles the complexity of robot motion planning by modeling the configuration space as discrete based on hardware specifications, and uses lattice path methods to estimate the number of possible trajectories, providing concrete counts for complexity analysis.
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.