Discrete Planning Research Articles

Design of smooth hybrid controllers for a class of non‐linear systems

Symbolic planning techniques rely on abstract information about a continuous system to design a discrete planner to satisfy desired high-level objectives. However, applying the generated discrete commands of the discrete planner to the original system may face several challenges, including real-time implementation, preserving the properties of high-level objectives in the continuous domain, and issues such as discontinuity in control signals that may physically harm the system. To address these issues and challenges, the authors proposed a novel hybrid control structure for systems with non-linear multi-affine dynamics over rectangular partitions. In the proposed framework, a discrete planner can be separately designed to achieve high-level specifications. Then, the proposed hybrid controller generates jumpless continuous control signals to drive the system over the partitioned space executing the discrete commands of the planner. The hybrid controller generates continuous signals in real-time while respecting the dynamics of the system and preserving the desired objectives of the high-level plan. The design process is described in detail and the existence and uniqueness of the proposed solution are investigated. Finally, several case studies are provided to verify the effectiveness of the developed technique.

Learning Feasibility for Task and Motion Planning in Tabletop Environments.

Task and motion planning (TMP) combines discrete search and continuous motion planning. Earlier work has shown that to efficiently find a task-motion plan, the discrete search can leverage information about the continuous geometry. However, incorporating continuous elements into discrete planners presents challenges. We improve the scalability of TMP algorithms in tabletop scenarios with a fixed robot by introducing geometric knowledge into a constraint-based task planner in a robust way. The key idea is to learn a classifier for feasible motions and to use this classifier as a heuristic to order the search for a task-motion plan. The learned heuristic guides the search towards feasible motions and thus reduces the total number of motion planning attempts. A critical property of our approach is allowing robust planning in diverse scenes. We train the classifier on minimal exemplar scenes and then use principled approximations to apply the classifier to complex scenarios in a way that minimizes the effect of errors. By combining learning with planning, our heuristic yields order-of-magnitude run time improvements in diverse tabletop scenarios. Even when classification errors are present, properly biasing our heuristic ensures we will have little computational penalty.