Optimal Trajectory Planning for Cooperative Manipulation with Multiple Quadrotors Using Control Barrier Functions

TL;DR

This work tackles the problem of planning collision-free trajectories for a team of quadrotors that cooperatively manipulate a cable-suspended payload in cluttered environments. It introduces a nonlinear optimization framework that represents the payload, cables, and quadrotors as convex polytopes and enforces obstacle avoidance with discrete-time Control Barrier Functions (CBFs), augmented by a Duality-based reformulation to reduce computational burden. The planner integrates both payload-level and full-system constraints, with an optional simple global reference (e.g., $A^*$) to mitigate local minima, and is validated in simulation and real-world experiments, including tight-gap navigation. The results demonstrate effective, collision-free trajectory generation for cooperative transportation tasks, highlighting practical viability for aerial manipulation in constrained spaces.

Abstract

In this paper, we present a novel trajectory planning algorithm for cooperative manipulation with multiple quadrotors using control barrier functions (CBFs). Our approach addresses the complex dynamics of a system in which a team of quadrotors transports and manipulates a cable-suspended rigid-body payload in environments cluttered with obstacles. The proposed algorithm ensures obstacle avoidance for the entire system, including the quadrotors, cables, and the payload in all six degrees of freedom (DoF). We introduce the use of CBFs to enable safe and smooth maneuvers, effectively navigating through cluttered environments while accommodating the system's nonlinear dynamics. To simplify complex constraints, the system components are modeled as convex polytopes, and the Duality theorem is employed to reduce the computational complexity of the optimization problem. We validate the performance of our planning approach both in simulation and real-world environments using multiple quadrotors. The results demonstrate the effectiveness of the proposed approach in achieving obstacle avoidance and safe trajectory generation for cooperative transportation tasks.

Figures (6)

• Figure 1: Multiple quadrotors manipulating a payload to move through narrow opening.
• 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: Polytopic approximation of the payload, cables, and quadrotors.
• Figure 4: Sample trajectory generation in sim environments. Every 80th point is shown with axis for clarity .
• Figure 5: System block diagram in the real-world experiments.