GROW$^2$: Grounding Which and Where for Robot Tool Use

Can the robot use a plate to cut a cake if no knife is available? Tool use greatly expands robot capabilities, but to use tools creatively beyond their intended functions, the robot faces the challenge of $\textit{open-world affordance grounding}$: select an open-category object to act as a tool and localize its specific region of action. To this end, we introduce GROW$^2$ (GROunding Which and Where), which leverages object parts as a natural abstraction to split the grounding process hierarchically into semantic and geometric levels, thus bypassing the need for data-heavy, end-to-end training