  For autonomous crane lifting, optimal trajectories of the crane are required
as reference inputs to the crane controller to facilitate feedforward control.
Reducing the unactuated payload motion is a crucial issue for under-actuated
tower cranes with spherical pendulum dynamics. The planned trajectory should be
optimal in terms of both operating time and energy consumption, to facilitate
optimum output spending optimum effort. This article proposes an anti-swing
tower crane trajectory planner that can provide time-energy optimal solutions
for the Computer-Aided Lift Planning (CALP) system developed at Nanyang
Technological University, which facilitates collision-free lifting path
planning of robotized tower cranes in autonomous construction sites. The
current work introduces a trajectory planning module to the system that
utilizes the geometric outputs from the path planning module and optimally
scales them with time information. Firstly, analyzing the non-linear dynamics
of the crane operations, the tower crane is established as differentially flat.
Subsequently, the multi-objective trajectory optimization problems for all the
crane operations are formulated in the flat output space through consideration
of the mechanical and safety constraints. Two multi-objective evolutionary
algorithms, namely Non-dominated Sorting Genetic Algorithm (NSGA-II) and
Generalized Differential Evolution 3 (GDE3), are extensively compared via
statistical measures based on the closeness of solutions to the Pareto front,
distribution of solutions in the solution space and the runtime, to select the
optimization engine of the planner. Finally, the crane operation trajectories
are obtained via the corresponding planned flat output trajectories. Studies
simulating real-world lifting scenarios are conducted to verify the
effectiveness and reliability of the proposed module of the lift planning
system.
