Null space optimization for effective coverage of 3D surfaces using redundant manipulators

In this paper we consider the problem of null space minimization in coverage path planning of 3D surfaces for redundant manipulators. Existing coverage solutions only focus on Euclidean cost functions and often return suboptimal paths with respect to the joint space. In the approach described here, we explicitly consider the null space by treating different inverse kinematics solutions as individual nodes in a graph and model the problem as a generalized traveling salesman problem (GTSP). The GTSP is a generalization of the TSP where the nodes of the graph are subdivided into clusters and at least one node in each cluster needs to be visited. We evaluate our approach using a PR2 robot and complex objects. Our results demonstrate that our method outperforms Euclidean coverage algorithms in terms of manipulation effort and completion time.