Autonomous suspended load operations via trajectory optimization and variational integrators

This paper presents a real-time implementable trajectory optimization framework for autonomous suspended load operations in outdoor environments. The framework solves the posed optimal control problem with the iterationbased differential dynamic programming algorithm. The algorithm uses a variational integrator to propagate the modeled system's state configuration and linearize the resulting discrete dynamics. The variational integrator is an excellent candidate for real-time implementation because it remains accurate despite relatively large discretization time steps. Therefore, the computational effort of the differential dynamic programming algorithm can be mitigated through the reduction of discrete time points. The state of the slung load is estimated via an augmentation to the existing navigation system that only uses vision-based measurements of the load. Simulation studies and a flight test are presented to demonstrate the effectiveness of the proposed framework.