Differential Flatness-Based Real-Time Trajectory Planning for Multihelicopter Cooperative Transportation in Crowded Environments

Abstract

Trajectory planning for a multihelicopter transportation system requires optimizing numerous variables while considering obstacle avoidance, formation shape change, multibody dynamics and other feasibility constraints, making it challenging to achieve real-time effectiveness and convergence. To overcome this issue, a real-time trajectory planning method based on differential flatness and a minimum control effort (MINCO) trajectory expression is proposed. This method enables the implicit consideration of dynamic constraints and formation shape change requirements, and it handles obstacle avoidance and feasibility constraints linearly, reducing the complexity of planning. Specifically, the flatness characteristics and related assumptions of the system are given in detail by considering two cases where the load is modeled as a mass point or a rigid body. The obstacle avoidance trajectory planning problem is transformed into an unconstrained optimization problem based on MINCO and its spatial–temporal deformation. This optimization aims to minimize the trajectory energy and total time consumption while considering cost functions related to load obstacle avoidance, load state feasibility, helicopter obstacle avoidance, swarm avoidance between helicopters, cable obstacle avoidance, and cable force feasibility constraints. Finally, simulations are conducted in both cases where the load is modeled as a mass point and a rigid body to verify the feasibility of the proposed method. Overall, the proposed method has the potential to solve the problem of trajectory planning with obstacle avoidance in a multihelicopter transportation system in real time with improved efficiency and effectiveness.