For assembly planning, robots necessitate certain cognitive skills: high-level planning of actuation actions is needed to decide for their order, while geometric reasoning is needed to check their feasibility. For collaborative assembly tasks with humans, robots require further cognitive capabilities, such as commonsense reasoning, sensing, and communication skills, not only to cope with the uncertainty caused by incomplete knowledge about the humans behaviors, but also to ensure safer collaborations. We introduce a novel formal framework for collaborative assembly planning under uncertainty that utilizes hybrid conditional planning extended with commonsense reasoning and a rich set of communication actions for collaborative tasks. We show the applicability of our approach over a furniture assembly domain, where a bi-manual Baxter robot collaborates with a human to assemble a table, with dynamic simulations and physical implementations. We also evaluate our approach experimentally in this domain with respect to quantitative and qualitative performance measures
