Best estimates for the construction of robots in environments with obstacles

The authors consider the design of robots that work in environments with obstacles. The environment and the obstacles are fixed and the robot consists of telescoping links with two degrees of freedom each, one revolute and one prismatic. The objective is to estimate the lowest number of telescoping links that the robot should have so that it can reach all the points in the workspace that are not inside the obstacles. Several estimates are derived for the planar case using different polygonal shapes for the obstacles and the outside boundary of the environment. An algorithm for finding a suboptimal estimate for the number of links in the plane is outlined. Some results for the three-dimensional case with polyhedral obstacles are obtained