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Cooperative dual-crane lifting is an important but challenging process involved in heavy and critical lifting tasks. This paper considers the path planning for the cooperative dual-crane lifting. It aims to automatically generate optimal dual-crane lifting paths under multiple constraints, i.e., collision avoidance, coordination between the two cranes, and balance of the lifting target. Previous works often used oversimplified models for the dual-crane lifting system, the lifting environment, and the motion of the lifting target. They were thus limited to simple lifting cases and might even lead to unsafe paths in some cases. We develop a novel path planner for dual-crane lifting that can quickly produce optimized paths in complex 3-D environments. The planner has fully considered the kinematic structure of the lifting system. Therefore, it is able to robustly handle the nonlinear movement of the suspended target during lifting. The effectiveness and efficiency of the planner are enabled by three novel aspects: 1) a comprehensive and computationally efficient mathematical modeling of the lifting system; 2) a new multiobjective parallel genetic algorithm designed to solve the path planning problem; and 3) a new efficient approach to perform continuous collision detection for the dual-crane lifting target. The planner has been tested in complex industrial environments. The results show that the planner can generate dual-crane lifting paths that are easy for conductions and optimized in terms of costs for complex environments. Comparisons with two previous methods demonstrate the advantages of the planner, including safer paths, higher success rates, and the ability to handle general lifting cases.

We present a general computational framework to locally characterize any shape space of meshes implicitly prescribed by a collection of non-linear constraints. We computationally access such manifolds, typically of high dimension and co-dimension, through first and second order approximants, namely tangent spaces and quadratically parameterized osculant surfaces. Exploration and navigation of desirable subspaces of the shape space with regard to application specific quality measures are enabled using approximants that are intrinsic to the underlying manifold and directly computable in the parameter space of the osculant surface. We demonstrate our framework on shape spaces of planar quad (PQ) meshes, where each mesh face is constrained to be (nearly) planar, and circular meshes, where each face has a circumcircle. We evaluate our framework for navigation and design exploration on a variety of inputs, while keeping context specific properties such as fairness, proximity to a reference surface, etc.