With the increasing demand for inspecting part surfaces, automated and efficient visual inspection is becoming a trend in industrial production. Due to the complexity of inspection planning problems where both viewpoint planning and path planning belong to the non-determinism of polynomial complexity problem, most of the current research studies the above two problems separately and seeks the minimum viewpoints to satisfy the viewpoint coverage by viewpoint planning, then obtaining efficient inspection paths via path planning for the set of viewpoints. However, viewpoint planning and path planning are coupled problems, and the distribution of viewpoints and paths can easily make the inspection efficiency fall into the local optimum. Therefore, some researchers propose to combine the viewpoint and path planning problems and simplify them into a single objective problem for global optimization, which improves inspection efficiency to a certain extent. However, during the optimization, viewpoints should be continuously added to the viewpoint set to meet the viewpoint coverage, which causes low planning efficiency. To this end, we propose a multi-objective holistic planning method of viewpoints and paths to quickly seek the viewpoint set and its path that satisfy viewpoint coverage and optimal inspection time cost.

In response to the need for efficient inspection of batch parts, we study the inspection planning method of automated visual inspection to reduce the inspection time cost of single parts. Inspection planning includes two subproblems of viewpoint planning and path planning. To seek the optimal solution of inspection time cost in inspection planning, we propose a multi-objective holistic planning method for viewpoints and paths, which models the viewpoint planning problem and path planning problem as a combinatorial optimization problem for multi-objective optimization. The proposed method performs adaptive redundant sampling of viewpoints based on surface curvature to cope with difficult coverage of complex curved surfaces and constructs a set of sampled viewpoints with both quality and diversity for subsequent inspection planning considered. A constraint-based non-dominated sorting genetic algorithm Ⅱ (C-NSGA-Ⅱ) is put forward for simultaneous optimization of the two objectives of viewpoint coverage and inspection time cost. During the optimization, the viewpoint coverage is constrained to be around the minimum coverage, and the globally optimal solution for the inspection time cost is quickly sought to achieve the holistic planning of viewpoints and paths and minimize the inspection time cost.

We propose a multi-objective holistic planning method for viewpoints and paths. Firstly, a redundant viewpoint sampling method based on surface curvature is proposed in the viewpoint sampling stage. Meanwhile, it is experimentally verified that compared with the commonly adopted random viewpoint sampling method, the viewpoint set sampled by the proposed method has better performance in subsequent inspection planning, which proves that the proposed viewpoint sampling method can construct a higher-quality and diversified sampled viewpoint set (Table 2). Then, C-NSGA-Ⅱ is put forward to carry out holistic planning for the problem of two successive coupling of viewpoint planning and path planning. Compared with the holistic planning method that is simplified into a single-objective optimization problem, the computational efficiency of C-NSGA-Ⅱ is improved by about 90% (Fig. 13). Compared with the traditional individual planning method of viewpoint first and then path, the inspection time cost planned by the proposed method is reduced by more than 10.52% (Table 3). Finally, the effectiveness and superiority of the proposed inspection planning method are verified in robot automated vision inspection applications (Table 4).

To reduce the inspection time cost of automated visual inspection, we propose a multi-objective holistic planning method for viewpoints and paths. The proposed method does not take reducing the number of planned viewpoints as the only goal, but directly takes the viewpoint coverage and inspection time cost as the optimization goals. The above two objectives are globally optimized by C-NSGA-Ⅱ, and the viewpoint set and its path with the optimal inspection time cost are finally planned. Compared with the holistic planning method that is simplified into a single-objective optimization problem, the proposed method does not need to be forced to meet the viewpoint coverage requirements during the optimization, which greatly improves computing efficiency. The experiments prove that the proposed method can quickly solve the global optimal solution compared with individual planning methods and other holistic planning methods, which helps improve the efficiency of automated visual inspection and provides a method for efficient inspection planning in real production. In the subsequent research, on the one hand, the accuracy evaluation index can be added to judge the viewpoints, and on the other hand, the influence of the field environment can be considered to provide feedback on the imaging quality of the viewpoints and make adjustments accordingly.