Automating motion trajectory Of crane-lifted loads

• The issue of piece-wise linear trajectories for crane lifting paths is discussed.
• Algorithms to express lifting path planning as sequence of rotations and translations
• Lifting path planning along edges of circular sectional envelopes around obstacles
• Mapping a circular grid onto a 2D matrix adapted to A* algorithm
• Application of the proposed algorithms to an industrial case study

Crane Lifting Path Planning (CLPP) is an important task, especially in congested construction sites. This activity becomes extremely complex since, as the project advances, new (and sometimes unpredicted) constraints may occur. These constraints force lift engineers to explore the possibility of alternative paths for the objects still to be moved. Under severe time constraints, manual analysis of such paths is practically impossible, which makes it necessary to rely on computer implementations in order to avoid project delays. From a mathematical standpoint, if the crane payload trajectory is to be defined analytically, the polar coordinate system,(r, θ), is naturally the most suitable. As a result, this paper proposes an algorithm for CLPP in which the path is represented as a piece-wise continuous function where each portion is defined either by constant radius (rotation of the load) or a constant angle (translation of the load). In other words, rather than forcing a crane to adapt to un-natural rectilinear trajectories as obtained by traditional path searching procedures, it is the trajectory that is adapted to the crane motion. In fact, even though (mathematically) a precise balance between the rates of rotation and translation of the jib (or boom) will make the payload follow any continuous path (regardless of its complexity), the coupling between the rotations and translations increases the difficulty of the lifting activity. However, a crane lifting path in which these motions are uncoupled will lead to less stringent requirements in terms of controlling the balance between rotations and translations.