MASPA: An efficient strategy for path planning with a tethered marsupial robotics system

TL;DR

The paper tackles 3D path planning for tethered marsupial systems (UGV-UAV linked by a tether) in cluttered environments modeled with cuboids, with the objective of minimizing the total ground and aerial travel, subject to tether length constraints. It introduces MASPA, a sequential planning framework that decouples ground and aerial planning via a discrete set of take-off points derived from Polygonal Visibility Problems (PVP) solved by Polygonal Visibility Algorithms (PVA-2D and PVA-3D), and a ground visibility graph solved by shortest-path methods; for loose tethers, it extends to Catenary Visibility (CVP) and Minimum Length Tether Problems (MLTP). The main technical contributions are the novel PVP/PVA formulations with $O(n^2)$ preprocessing, the 3D extension for near-optimal search, and the CVP framework enabling efficient planning under tether flexure; empirically, MASPA outperforms the baseline $RRT^*$ in both total path length and execution time, including dramatic speedups when the PVA visibility module is used. The work demonstrates practical impact for emergency exploration and search-and-rescue tasks, and provides an open-source implementation to facilitate adoption and further research.

Abstract

A tethered marsupial robotics system comprises three components: an Unmanned Ground Vehicle (UGV), an Unmanned Aerial Vehicle (UAV), and a tether connecting both robots. Marsupial systems are highly beneficial in industry as they extend the UAV's battery life during flight. This paper introduces a novel strategy for a specific path planning problem in marsupial systems, where each of the three components must avoid collisions with ground and aerial obstacles modeled as 3D cuboids. Given an initial configuration in which the UAV is positioned atop the UGV, the goal is to reach an aerial target with the UAV. We assume that the UGV first moves to a position from which the UAV can take off and fly through a vertical plane to reach an aerial target. We propose an approach that discretizes the space to approximate an optimal solution, minimizing the sum of the lengths of the ground and air paths. First, we assume a taut tether and use a novel algorithm that leverages the convexity of the tether and the geometry of obstacles to efficiently determine the locus of feasible take-off points for the UAV. We then apply this result to scenarios that involve loose tethers. The simulation test results show that our approach can solve complex situations in seconds, outperforming a baseline planning algorithm based on RRT* (Rapidly exploring Random Trees).

Figures (9)

• Figure 1: Model of the marsupial system with the UGV and the UAV positioned at $X$ and $T$, respectively. The UAV path with minimum length between $Y=top(X)$ and $T$ is denoted as $\mathcal{P}^*(Y)$ and has the same shape as the tether. An enlarged obstacle is also depicted.
• Figure 2: An scenario of the marsupial path planning problem. Two paths are required, a ground path (red) for the UGV carrying the UAV from the starting point $S$ to a ground point $X$ from which the UAV can reach the target $T$ using a collision-free aerial path (blue). In the scenario, two possible solutions are showed; the general problem is to find the one that minimizes the sum of the lengths.
• Figure 3: An intance of PVP-2D. Aerial obstacles are in gray and ground obstacles in blue. $\mathcal{P}(Y)$ is a CICP from $top(X)$ to $T$.
• Figure 4: The red and blue points in $r_{top}$ indicate the vertices of the maximal non $p_L$-visible intervals. Notice that the red point $l_2$ belongs both to the paths $\mathcal{P}^*(B_2)$ and $\mathcal{P}^*(A_4)$. The take-off point $Q$ is the leftmost point that can reach $T$ with a tether of maximum length $L$.
• Figure 5: Proof of Lemma \ref{['lemma:alg-opening']}. Segment $\overline{u_il_j}$ is the one with greatest slope if $Y$ is the first $p_L$-visible point to the left of $B$.

Theorems & Definitions (17)

• Definition 1
• Definition 2
• Definition 3
• Lemma 1
• Lemma 2
• Remark 1
• Remark 2
• Lemma 3
• proof
• Lemma 4