Nonlinear Model Predictive Control for Cooperative Transportation and Manipulation of Cable Suspended Payloads with Multiple Quadrotors

TL;DR

This work addresses the challenge of coordinating multiple quadrotors to cooperatively transport and manipulate a rigid payload via suspended cables in all 6 DoF. It introduces a nonlinear model predictive control framework that optimizes cable tension distributions within the payload wrench space while exploiting a null-space structure to enable inter-robot separation and obstacle avoidance, all under actuator constraints. The NMPC uses a lightweight payload-centric state on the SE(3) manifold and solves a reduced-dimension optimization with RTI-SQP (ACADOS) and RK4 integration, achieving real-time performance. Experimental validation with three quadrotors demonstrates accurate payload tracking (RMSE ~0.1 m) and maintained inter-robot spacing, highlighting the method's potential for scalable, cable-based cooperative manipulation in applications like construction and delivery.

Abstract

Autonomous Micro Aerial Vehicles (MAVs) such as quadrotors equipped with manipulation mechanisms have the potential to assist humans in tasks such as construction and package delivery. Cables are a promising option for manipulation mechanisms due to their low weight, low cost, and simple design. However, designing control and planning strategies for cable mechanisms presents challenges due to indirect load actuation, nonlinear configuration space, and highly coupled system dynamics. In this paper, we propose a novel Nonlinear Model Predictive Control (NMPC) method that enables a team of quadrotors to manipulate a rigid-body payload in all 6 degrees of freedom via suspended cables. Our approach can concurrently exploit, as part of the receding horizon optimization, the available mechanical system redundancies to perform additional tasks such as inter-robot separation and obstacle avoidance while respecting payload dynamics and actuator constraints. To address real-time computational requirements and scalability, we employ a lightweight state vector parametrization that includes only payload states in all six degrees of freedom. This also enables the planning of trajectories on the $SE(3)$ manifold load configuration space, thereby also reducing planning complexity. We validate the proposed approach through simulation and real-world experiments.

Figures (7)

• Figure 1: Three quadrotors carrying a rigid-body payload via cables using the proposed NMPC.
• Figure 2: System convention definition: $\mathcal{I}$, $\mathcal{L}$, $\mathcal{B}_{k}$ denote the world frame, the payload body frame, and the $k^{th}$ robot body frames, respectively, for a generic quadrotor team that is cooperatively transporting and manipulating a cable-suspended payload.
• Figure 3: Visual illustration of the relationship among the payload wrench $\mathbf{W}^{\mathcal{L}}$, cable tension force $\bm{\mu}_{k}^{\mathcal{L}}$ and the tension vectors $\bm{\mu}_{\mathbf{N}k}^{\mathcal{L}}$ in the null space of the cable tension distribution matrix $\mathbf{P}$ in the payload frame $\mathcal{L}$.
• Figure 4: The control block diagram of the proposed approach.
• Figure 5: Tracking results of the payload following a circular trajectory in x-y plane.