Efficient variable-length hanging tether parameterization for marsupial robot planning in 3D environments

TL;DR

This paper introduces an efficient analytical model for parameterizing and estimating the state of a hanging tether in 3D environments, improving planning speed for marsupial robots without overly restricting movement.

Contribution

It proposes a novel analytical approach that approximates the catenary curve using parabola similarities, enabling faster and collision-free tether state estimation during planning.

Findings

The model accelerates tether state computation significantly.

It maintains accurate tether shape estimation compared to traditional methods.

The approach reduces planning time in complex 3D environments.

Abstract

This paper presents a novel approach to efficiently parameterize and estimate the state of a hanging tether for path and trajectory planning of a UGV tied to a UAV in a marsupial configuration. Most implementations in the state of the art assume a taut tether or make use of the catenary curve to model the shape of the hanging tether. The catenary model is complex to compute and must be instantiated thousands of times during the planning process, becoming a time-consuming task, while the taut tether assumption simplifies the problem, but might overly restrict the movement of the platforms. In order to accelerate the planning process, this paper proposes defining an analytical model to efficiently compute the hanging tether state, and a method to get a tether state parameterization free of collisions. We exploit the existing similarity between the catenary and parabola curves to derive analytical expressions of the tether state.