  Recent advances in robot skill learning have unlocked the potential to
construct task-agnostic skill libraries, facilitating the seamless sequencing
of multiple simple manipulation primitives (aka. skills) to tackle
significantly more complex tasks. Nevertheless, determining the optimal
sequence for independently learned skills remains an open problem, particularly
when the objective is given solely in terms of the final geometric
configuration rather than a symbolic goal. To address this challenge, we
propose Logic-Skill Programming (LSP), an optimization-based approach that
sequences independently learned skills to solve long-horizon tasks. We
formulate a first-order extension of a mathematical program to optimize the
overall cumulative reward of all skills within a plan, abstracted by the sum of
value functions. To solve such programs, we leverage the use of tensor train
factorization to construct the value function space, and rely on alternations
between symbolic search and skill value optimization to find the appropriate
skill skeleton and optimal subgoal sequence. Experimental results indicate that
the obtained value functions provide a superior approximation of cumulative
rewards compared to state-of-the-art reinforcement learning methods.
Furthermore, we validate LSP in three manipulation domains, encompassing both
prehensile and non-prehensile primitives. The results demonstrate its
capability to identify the optimal solution over the full logic and geometric
path. The real-robot experiments showcase the effectiveness of our approach to
cope with contact uncertainty and external disturbances in the real world.
