Space-time area coverage control for robot motion synthesis

We propose a novel method for representing the interaction of a robot and an object. We create a virtual surface by taking a chain of linear segments attached to the robot links, we spatially extrude them in time, and we then compute the coverage of this surface around the object. Our approach uses a technique based on computation of electric flux, borrowed from electro dynamics. The advantage of using this method is that it is invariant to the relative transformations of the virtual surface, which makes it suitable as a complementary term in a cost function when constructing a multi-objective problem. We demonstrate the different types of interactions this method can represent, and how it can be integrated into trajectory optimisation based motion planners. We also demonstrate a practical application of such representation on a real robot.