Combinatorics of a Discrete Trajectory Space for Robot Motion Planning

TL;DR

This paper introduces a discrete model for robot motion planning based on hardware specifications, using lattice path methods to estimate the complexity by counting possible trajectories in the configuration space.

Contribution

It presents a novel discrete approach to robot motion planning, providing combinatorial estimates for trajectory complexity based on hardware specifications.

Findings

Discrete model enables combinatorial analysis of trajectories

Estimates of motion planning complexity derived from lattice path counting

Provides a new perspective on configuration space analysis

Abstract

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.