Integrable Whole-body Orientation Coordinates for Legged Robots

Complex multibody legged robots can have complex rotational control challenges. In this paper, we propose a concise way to understand and formulate a \emph{whole-body orientation} that (i) depends on system configuration only and not a history of motion, (ii) can be representative of the orientation of the entire system while not being attached to any specific link, and (iii) has a rate of change that approximates total system angular momentum. We relate this orientation coordinate to past work, and discuss and demonstrate, including on hardware, several different uses for it.