Automated Layout and Control Co-Design of Robust Multi-UAV Transportation Systems

TL;DR

This paper tackles robust co-design of the physical layout and control for cooperative aerial payload transportation using multiple quadcopters connected to a payload by rigid attachments. It introduces an $H_2$-inspired cost and a Mahalanobis-margin objective to jointly optimize the attachment layout and the LQR controller, solving the algebraic Riccati equations to obtain $K^*(\boldsymbol{\theta})$, $S_1$, and $S_2$, and employing a Nelder–Mead search with inner QPs to maximize the probability of feasible thrusts. The authors demonstrate the method on 3–4 quadcopters with various panel payloads, showing that the optimal layouts improve disturbance rejection and tracking, sometimes yielding counterintuitive asymmetric layouts for symmetric shapes. The results validate the approach and suggest extensions to nonlinear controllers or online payload parameter estimation for deployment.

Abstract

The joint optimization of physical parameters and controllers in robotic systems is challenging. This is due to the difficulties of predicting the effect that changes in physical parameters have on final performances. At the same time, physical and morphological modifications can improve robot capabilities, perhaps completely unlocking new skills and tasks. We present a novel approach to co-optimize the physical layout and the control of a cooperative aerial transportation system. The goal is to achieve the most precise and robust flight when carrying a payload. We assume the agents are connected to the payload through rigid attachments, essentially transforming the whole system into a larger flying object with ``thrust modules" at the attachment locations of the quadcopters. We investigate the optimal arrangement of the thrust modules around the payload, so that the resulting system achieves the best disturbance rejection capabilities. We propose a novel metric of robustness inspired by H2 control, and propose an algorithm to optimize the layout of the vehicles around the object and their controller altogether. We experimentally validate the effectiveness of our approach using fleets of three and four quadcopters and payloads of diverse shapes.

Figures (9)

• Figure 1: Four quadcopters cooperatively carrying a single panel payload.
• Figure 2: a) Extrusion payload geometry and representation of the mid-plane. Its intersection with the side faces is the curve $\Gamma$. b) Schematics of four quadcopters attached around the payload along $\Gamma$. Representation of the local body reference frame centered at the centroid of $\Gamma$, placement variables defined by the angles $\boldsymbol{\theta_i}$ ($i=1, ..., 4$), and disturbance force $\mathbf{f}_d$ and torque $\mathbf{t}_d$.
• Figure 3: Two dimensional example of minimum Mahalanobis distance to input saturations. In this case, the random variables are $u_1, u_2 \in [u_l, u_h]$. The ellipses depicted, centered at the mean $\Bar{\mathbf{u}}$, represent the level curves of the Mahalanobis distance and are obtained as $(\mathbf{u} - \Bar{\mathbf{u}})^T\Sigma_\mathbf{u}^{-1}(\mathbf{u} - \Bar{\mathbf{u}}) = q$ ($q$ being a positive scalar parameter). The "point of minimum distance" sought is given by the tangency between the largest ellipsoid contained in the bounding box and the corresponding saturation hyperplane.
• Figure 4: Diagram of the control infrastructure. The specific loop rates are relative to the available experimental testbed.
• Figure 5: Optimal layouts for various object shapes and masses using different number of quadcopters. Our approach can handle both convex and non-convex polygons. It is interesting to note that, in contrast to common intuition, the optimal drone placement around a symmetric shape might not be symmetric.