Extending the Knowledge of Volumes approach to robot task planning with efficient geometric predicates

For robots to solve hard tasks in real-world manufacturing and service contexts, they need to reason about both symbolic and geometric preconditions, and the effects of complex actions. We use an existing Knowledge of Volumes approach to robot task planning (KVP), which facilitates hybrid planning with symbolic actions and continuous-valued robot and object motion, and make two important additions to this approach: (i) new geometric predicates are added for complex object manipulation planning, and (ii) all geometric queries-such as collision and inclusion of objects and swept volumes-are implemented with a single-sided, bounded approximation, which calculates efficient and safe robot motion paths. Our task planning framework is evaluated in multiple scenarios, using concise and generic scenario definitions.