Affine trajectory correction for nonholonomic mobile robots

TL;DR

This paper introduces an affine transformation-based method for quickly deforming planned trajectories of nonholonomic robots, enabling efficient corrections and adaptations without re-planning or re-integration.

Contribution

The paper presents a novel, algebraic affine transformation approach for trajectory correction in nonholonomic robots, offering a fast and exact alternative to re-planning.

Findings

Method is algebraically exact and computationally fast.

Applicable to planar wheeled robots and underwater vehicles.

Enables advanced applications like obstacle avoidance and kinodynamic planning.

Abstract

Planning trajectories for nonholonomic systems is difficult and computationally expensive. When facing unexpected events, it may therefore be preferable to deform in some way the initially planned trajectory rather than to re-plan entirely a new one. We suggest here a method based on affine transformations to make such deformations. This method is exact and fast: the deformations and the resulting trajectories can be computed algebraically, in one step, and without any trajectory re-integration. To demonstrate the possibilities offered by this new method, we use it to derive position and orientation correction algorithms for the general class of planar wheeled robots and for a tridimensional underwater vehicle. These algorithms allow in turn achieving more complex applications, including obstacle avoidance, feedback control or gap filling for sampling-based kinodynamic planners.