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

TL;DR

This paper tackles the challenging problem of time-energy optimal anti-swing trajectory planning for underactuated double-pendulum tower cranes within a CALP framework. It develops a differential-flatness-based approach that identifies flat outputs and parameterizes them with Bézier curves, reformulating the problem as constrained multi-objective optimization. A novel CO-GDE3 optimizer with collective oppositional initialization and an average fuzzy membership-based selector is proposed to efficiently generate a diverse set of high-quality Pareto solutions for trolley and slew motions. Simulation results demonstrate that the planner produces collision-free, swing-suppressed trajectories that satisfy all state constraints, with CO-GDE3 offering faster convergence and greater solution reliability than standard GDE3. The work lays the groundwork for offline, multi-objective reference trajectory generation in autonomous crane operations, with future directions including robust tracking control and hardware validation.

Abstract

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 Bézier 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.

Figures (14)

• Figure 1: Structure of double-pendulum tower crane with actuated and unactuated DOFs.
• Figure 2: Trolley motion of double-pendulum tower crane with its auxiliary output.
• Figure 3: Slew motion of double-pendulum tower crane with its auxiliary outputs.
• Figure 4: Positions and ranges of various opposites (opposite solution $\breve{x}$, quasi-opposite solution $\breve{x}^{qo}$, quasi-reflected solution $\breve{x}^{qr}$, extended opposite solution $\breve{x}^{eo}$, reflected extended opposite solution $\breve{x}^{reo}$) of a random solution $x$ within the interval $[\underline{x},\overline{x}]$. $U(l,u)$ indicates a randomly sampled number following a uniform probability distribution within $[l,u]$. Two possible cases are shown with the position of $x$ lying before and after the center of its domain.
• Figure 5: Algorithmic flowchart of (a) GDE3 and (b) CO-GDE3.

Theorems & Definitions (5)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5