View Planning Problem with Combined View and Traveling Cost

In this paper, we introduce the problem of view planning with combined view and traveling cost, denoted by traveling VPP. It refers to planning a sequence of sensing actions with minimum total cost by a robot-sensor system to completely inspect the surfaces of objects in a known workspace. The cost to minimize is a combination of the view cost, proportional to the number of viewpoints planned, and the traveling cost for the robot to realize them. First, we formulate traveling VPP as an integer linear program (ILP). The focus of this paper is to design an approximation algorithm that guarantees worst-case performance (w.r.t. the optimal solution cost). We propose a linear program based rounding algorithm that achieves an approximation ratio of the order of view frequency, defined to be the maximum number of viewpoints that see a single surface patch of the object. Together with the result we showed (2006), the best approximation ratio for Traveling VPP is either the order of view frequency or a poly-log function of the input size, whichever is smaller. Motivated from the robot motion planning techniques, where the graph built for robot traveling is a tree, we then consider the corresponding special case of traveling VPP, and give a polynomial sized LP formulation. We conclude with a discussion of realistic issues and constraints towards implementing our algorithm on real robot-sensor systems.