Efficiency and abstraction in task and motion planning

Abstract

Modern robots are capable of complex and highly dynamic behaviors, yet the decisionmaking algorithms that drive them struggle to solve problems involving complex behaviors like manipulation. The combination of continuous and discrete dynamics induced by contact creates severe computational challenges, and most known practical approaches rely on hand-designed discrete representations to mitigate computational issues. However, the relationship between the discrete representation and the physical robot is poorly understood and cannot easily be empirically verified, and so many planning systems are brittle and prone to failure when the robot encounters situations not anticipated by the model designer. This thesis addresses the limitations of conventional representations for task and motion planning by introducing a constraint-based representation that explicitly places continuous and discrete dynamics on equal footing.

We argue that the challenges in modelling problems with both discrete and continuous dynamics can be reduced to a trade-off between model complexity and empirical accuracy. We propose the use of abstraction to combine models that balance those two constraints differently, and we claim that by using abstraction we can build systems that reliably generate high-quality plans, even in complex domains with many objects. Using our representation, we construct and analyze several new algorithms, providing new insight into long-standing open problems about the decidability and complexity of motion planning. We describe algorithms for sampling-based planning in hybrid domains, and show that these algorithms are complete and asymptotically optimal for systems that can defined by analytic constraints. We also show that the reachability problem can be decided using polynomial space for systems described by polynomial constraints satisfying a certain technical conditions.

This class of systems includes many important robotic planning problems, and our results show that the decision problem for several benchmark task and motion planning languages is PSPACE-complete.