Energy-Aware Trajectory Generation via Conic Programming for a Multirotor-Slung Load System with a Varying-Length Cable

This paper studies energy-aware trajectory generation for the gate-passage maneuver of a multirotor-slung load system with a varying-length cable. The mission requires load and drone gate clearance while enforcing positive cable tension and recovered thrust, body torque, and winch torque limits, resulting in a highly constrained nonconvex problem. Using conic programming, a conservative convex optimization formulation is developed whose surrogate objective provides an upper bound on the original objective over a restricted feasible set. The conic construction enables fast solution and global optimality with primal–dual certificates for the solved restriction. In the two numerical scenarios, it reduces solution time by approximately 74% and 90% relative to the locally optimal nonconvex solutions, while increasing the actuator effort proxy and relative electrical energy estimate by only approximately 4%–5%. Post-optimization checks verify positive actuator margins, while closed-loop simulations demonstrate trackability and retain positive gate and cable tension margins. The proposed conic formulation provides a significant computational improvement at the cost of only a modest increase in relative energy demand.