SQP-Based Cable-Tension Allocation for Multi-Drone Load Transport

Multi-Agent Aerial Load Transport Systems (MAATS) offer greater payload capacity and fault tolerance than single-drone solutions. However, they have an underdetermined tension allocation problem that leads to uneven energy distribution, cable slack, or collisions between drones and cables. This paper presents a real-time optimization layer that improves a hierarchical load-position-attitude controller by incorporating a Sequential Quadratic Programming (SQP) algorithm. The SQP formulation minimizes the sum of squared cable tensions while imposing a cable-alignment penalty that discourages small inter-cable angles, thereby preventing tether convergence without altering the reference trajectory. We tested the method under nominal conditions by running numerical simulations of four quadrotors. Computational experiments based on numerical simulations demonstrate that the SQP routine runs in a few milliseconds on standard hardware, indicating feasibility for real-time use. A sensitivity analysis confirms that the gain of the cable-alignment penalty can be tuned online, enabling a controllable trade-off between safety margin and energy consumption with no measurable degradation of tracking performance in simulation. This framework provides a scalable path to safe and energy-balanced cooperative load transport in practical deployments.

💡 Research Summary

The paper addresses a fundamental challenge in Multi‑Agent Aerial Load Transport Systems (MAATS): the underdetermined allocation of cable tensions when several UAVs cooperate to lift a common payload. While prior works have focused either on minimizing a surrogate energy term or on enforcing geometric separation, they have not simultaneously tackled tension balancing, collision avoidance, and real‑time feasibility. To fill this gap, the authors embed a Sequential Quadratic Programming (SQP) based optimization layer into an existing four‑layer hierarchical controller (load‑level, tension allocation, position, and attitude).

Problem formulation
Given the virtual force u_L produced by the load‑level controller, the goal is to compute tension magnitudes T_i ≥ 0 and unit direction vectors α_i ∈ S² for each of the n cables such that

1. Force equilibrium: Σ T_i α_i = −u_L,
2. Unit‑norm constraints: ‖α_i‖ = 1,

while minimizing the cost

J = ½ Σ T_i² + μ Σ_{i<j}(α_i·α_j)².

The first term penalizes the sum of squared tensions, encouraging low total effort and a balanced distribution among UAVs. The second term, weighted by μ, penalizes small inter‑cable angles because (α_i·α_j) = cos θ_ij; when cables become parallel (θ_ij → 0) the penalty grows, thus actively discouraging configurations that could lead to cable convergence or UAV‑cable collisions.

SQP solution strategy
The nonlinear program is solved iteratively: at each iteration a quadratic approximation of the Lagrangian and a linearized set of constraints are built, yielding a small QP that can be solved analytically or with a fast QP solver. A warm‑start scheme uses the solution from the previous control cycle as the initial guess, guaranteeing continuity of cable configurations and dramatically reducing the number of SQP iterations needed for convergence. The gradient of the objective has a block‑diagonal structure (tensions and direction components are decoupled except through the alignment term), which the algorithm exploits to keep computational complexity linear in the number of agents.

Implementation details
For the four‑quadrotor case studied, the decision vector consists of 4 tension variables and 12 direction components (16 variables total). The authors implement the SQP layer on a standard desktop CPU; average computation time per control step is 1.8 ms, with a worst‑case of 2.3 ms, comfortably fitting within a 500 Hz control loop (2 ms sampling). The hierarchical controller then translates the optimal tensions into desired positions and attitudes for each UAV using the same equations as in the baseline controller.

Simulation setup

• Four quadrotors (m_i = 0.5 kg, inertia J_i = diag(2.1, 1.87, 3.97)·10⁻² kg·m²)
• Payload mass m_L = 0.225 kg, cable length L_i = 1 m, massless rigid cables
• Load trajectory: an ascending spiral (circular motion in the horizontal plane while gaining altitude) lasting 20 s
• Gains: k_pL = 8, k_dL = 2 for the load controller; k_pi = 40, k_di = 10, k_ii = 2 for the UAV position controllers

Results

1. Trajectory tracking – RMS position error of the payload is 2.97 cm, with a maximum deviation of 8 cm, matching or slightly improving upon the baseline controller that does not use optimization.
2. Tension distribution – The SQP allocator yields nearly equal tension profiles across all four UAVs, whereas the baseline geometric allocation shows one UAV bearing a significantly larger share of the load. This balanced distribution leads to more uniform battery discharge and reduces the risk of motor saturation.
3. Safety via cable angles – With μ = 0.15, the minimum pairwise cable angle stays above 44°, well over the 30° safety threshold. The worst‑case total tension peak reaches 3.33 N (1.24× the long‑term average), indicating that the safety margin does not come at the expense of excessive force.
4. Real‑time feasibility – The SQP routine consistently runs under 2 ms, confirming that the method can be embedded in high‑frequency flight controllers.
5. Sensitivity analysis – Varying μ provides an online tuning knob: larger μ improves angular safety but slightly increases the summed tension cost, allowing operators to trade energy efficiency against collision risk depending on mission requirements.

Conclusions and future work
The authors demonstrate that a lightweight SQP‑based tension allocation layer can be integrated into a hierarchical MAATS controller without degrading tracking performance, while simultaneously achieving balanced energy consumption and robust collision avoidance. The method scales linearly with the number of UAVs, preserving its real‑time capability for larger teams. Future research directions include hardware flight tests, robustness to communication delays and external disturbances, and distributed SQP formulations for very large swarms (10+ UAVs). The presented framework offers a practical pathway toward safe, energy‑balanced cooperative aerial transport in real‑world deployments.