hypr: An R package for hypothesis-driven contrast coding

The hypr package in R provides the researcher with a straightforward interface to generate contrast matrices from research hypotheses and the reverse. It can be used to derive contrast matrices for custom research hypotheses and as an instructional tool to understand what research hypotheses a given contrast matrix tests. We previously reviewed the statistical methodolgy in a tutorial on contrast coding based on the generalized matrix inverse (Schad et al. 2020).

Applying a Unit-Consistent Generalized Matrix Inverse for Stable Control of Robotic Systems

It is well understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs well in one particular Euclidean coordinate frame then it should be expected to perform identically if that coordinate frame is arbitrarily rotated or scaled. Similarly, the performance of the system should not be affected if its key parameters are all consistently defined in metric units or in imperial units. In this paper we show that a recently introduced generalized matrix inverse permits performance consistency to be rigorously guaranteed in control systems that require solutions to underdetermined and/or overdetermined systems of equations. We analyze and empirically demonstrate how these theoretical guarantees can be directly obtained in a practical robotic arm system.