Motion Planning in Irreducible Path Spaces

TL;DR

This paper introduces the concept of irreducible paths to reduce the complexity of motion planning in high-dimensional configuration spaces, demonstrating its applicability to various robotic systems while preserving planning completeness.

Contribution

It defines irreducible path space, proves planning in this space maintains completeness, and applies the concept to complex robotic motion scenarios.

Findings

Irreducible paths reduce configuration space complexity.

Planning in irreducible space preserves completeness.

Successful application to snake, octopus, and humanoid robot motions.

Abstract

The motion of a mechanical system can be defined as a path through its configuration space. Computing such a path has a computational complexity scaling exponentially with the dimensionality of the configuration space. We propose to reduce the dimensionality of the configuration space by introducing the irreducible path --- a path having a minimal swept volume. The paper consists of three parts: In part I, we define the space of all irreducible paths and show that planning a path in the irreducible path space preserves completeness of any motion planning algorithm. In part II, we construct an approximation to the irreducible path space of a serial kinematic chain under certain assumptions. In part III, we conduct motion planning using the irreducible path space for a mechanical snake in a turbine environment, for a mechanical octopus with eight arms in a pipe system and for the sideways motion of a humanoid robot moving through a room with doors and through a hole in a wall. We demonstrate that the concept of an irreducible path can be applied to any motion planning algorithm taking curvature constraints into account.