PolyFly: Polytopic Optimal Planning for Collision-Free Cable-Suspended Aerial Payload Transportation

TL;DR

PolyFly addresses the problem of collision-free, time-efficient planning for a quadrotor with a suspended payload in tightly constrained environments by modeling the quadrotor, cable, payload, and obstacles as independent, orientation-aware polytopes and enforcing differentiable collision constraints via duality. It formulates a global optimization over states $\mathbf{x}$, inputs $\mathbf{u}$, and stage durations $\Delta t_k$, incorporating time minimization, input-smoothness, proximity to an initial A*-based guess, and consistency of time steps, while connecting to the dynamics $\mathbf{x}(k+1)=F(\mathbf{x}(k),\mathbf{u}(k),\Delta t_k)$. The key contributions include a non-conservative, polytope-based workspace representation with rotation-aware components, a dual-formulated collision constraint, and extensive validation showing faster trajectories than a state-of-the-art baseline in eight mazes, plus real-world hardware demonstrations with low tracking errors. The approach advances practical planning for aerial transportation by enabling aggressive maneuvers in maze-like environments and providing a pathway toward open-source benchmarking. The results suggest significant impact for disaster response and last-mile logistics where tight clearance and payload swing constraints are critical.

Abstract

Aerial transportation robots using suspended cables have emerged as versatile platforms for disaster response and rescue operations. To maximize the capabilities of these systems, robots need to aggressively fly through tightly constrained environments, such as dense forests and structurally unsafe buildings, while minimizing flight time and avoiding obstacles. Existing methods geometrically over-approximate the vehicle and obstacles, leading to conservative maneuvers and increased flight times. We eliminate these restrictions by proposing PolyFly, an optimal global planner which considers a non-conservative representation for aerial transportation by modeling each physical component of the environment, and the robot (quadrotor, cable and payload), as independent polytopes. We further increase the model accuracy by incorporating the attitude of the physical components by constructing orientation-aware polytopes. The resulting optimal control problem is efficiently solved by converting the polytope constraints into smooth differentiable constraints via duality theory. We compare our method against the existing state-of-the-art approach in eight maze-like environments and show that PolyFly produces faster trajectories in each scenario. We also experimentally validate our proposed approach on a real quadrotor with a suspended payload, demonstrating the practical reliability and accuracy of our method.

Figures (7)

• Figure 1: System diagram showing the four different polytopes used in PolyFly: Quadrotor$N_Q$, Payload$N_L$, Cable$N_C$, and Obstacles$M_i$. The quadrotor polytope enables accurate distance computations ${h}_{N_Q,M_i}$, whereas most methods use an ellipse around the quadrotor resulting in conservative and inaccurate distance computations $\tilde{h}_{N_Q,M_i}$.
• Figure 2: A* initialization of trajectories for Env. 6 (left) and Env. 8 (right)
• Figure 3: Visualization of optimized trajectories using PolyFly in 8 tightly cluttered environments. The quadrotor is in yellow, payload in green, cable in gray and obstacles in light blue
• Figure 4: Close up visualizations of the optimized trajectories through a narrow gap in Env. 7.
• Figure 5: Impact of incorporating quadrotor rotation in the polytopic model. Left: A rotation-agnostic planner produces a trajectory that collides with the ceiling. Right: By accounting for the robot's attitude, the optimized path descends to prevent collisions while accelerating.