Design and Simulation of Time-energy Optimal Anti-swing Trajectory Planner for Autonomous Tower Cranes

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.

Multi-objective Anti-swing Trajectory Planning of Double-pendulum Tower Crane Operations using Opposition-based Evolutionary Algorithm

Underactuated tower crane lifting requires time-energy optimal trajectories for the trolley/slew operations and reduction of the unactuated swings resulting from the trolley/jib motion. In scenarios involving non-negligible hook mass or long rig-cable, the hook-payload unit exhibits double-pendulum behaviour, making the problem highly challenging. This article introduces an offline multi-objective anti-swing trajectory planning module for a Computer-Aided Lift Planning (CALP) system of autonomous double-pendulum tower cranes, addressing all the transient state constraints. A set of auxiliary outputs are selected by methodically analyzing the payload swing dynamics and are used to prove the differential flatness property of the crane operations. The flat outputs are parameterized via suitable B\'{e}zier curves to formulate the multi-objective trajectory optimization problems in the flat output space. A novel multi-objective evolutionary algorithm called Collective Oppositional Generalized Differential Evolution 3 (CO-GDE3) is employed as the optimizer. To obtain faster convergence and better consistency in getting a wide range of good solutions, a new population initialization strategy is integrated into the conventional GDE3. The computationally efficient initialization method incorporates various concepts of computational opposition. Statistical comparisons based on trolley and slew operations verify the superiority of convergence and reliability of CO-GDE3 over the standard GDE3. Trolley and slew operations of a collision-free lifting path computed via the path planner of the CALP system are selected for a simulation study. The simulated trajectories demonstrate that the proposed planner can produce time-energy optimal solutions, keeping all the state variables within their respective limits and restricting the hook and payload swings.