Constrained Manipulation Planning

Every planning problem in robotics involves constraints. Whether the robot must avoid collision or joint limits, there are always states that are not permissible. Some constraints are straightforward to satisfy while others can be so stringent that feasible states are very difficult to find. What makes planning with constraints challenging is that, for many constraints, it is impossible or impractical to provide the planning algorithm with the allowed states explicitly; it must discover these states as it plans. The goal of this thesis is to develop a framework for representing and exploring feasible states in the context of manipulation planning. Planning for manipulation gives rise to a rich variety of tasks that include constraints on collision-avoidance, torque, balance, closed-chain kinematics, and end-effector pose. While many researchers have developed representations and strategies to plan with a specific constraint, the goal of this thesis is to develop a broad representation of constraints on a robot's configuration and identify general strategies to manage these constraints during the planning process. Some of the most important constraints in manipulation planning are functions of the pose of the manipulator's end-effector, so we devote a large part of this thesis to end-effector placement for grasping and transport tasks. We present an efficient approach to generating paths that uses Task Space Regions (TSRs) to specify manipulation tasks which involve end-effector pose goals and/or path constraints. We show how to use TSRs for path planning using the Constrained BiDirectional RRT (CBiRRT2) algorithm and describe several extensions of the TSR representation. Among them are methods to plan with object pose uncertainty, find optimal base placements, and handle more complex pose constraints by chaining TSRs together. We also explore the problem of automatically generating end-effector pose constraints for grasping tasks and present two grasp synthesis algorithms that can generate lists of grasps in extremely cluttered environments. We then describe how to convert these lists of grasps to TSRs so they can be used with CBiRRT2. We have applied our framework to a wide range of problems for several robots, both in simulation and in the real world. These problems include grasping in cluttered environments, lifting heavy objects, two-armed manipulation, and opening doors, to name a few. These example problems demonstrate our framework's practicality, and our proof of probabilistic completeness gives our approach a theoretical foundation. In addition to the above framework, we have also developed the Constellation algorithm for finding configurations that satisfy multiple stringent constraints where other constraint-satisfaction strategies fail. We also present the GradienT-RRT algorithm for planning with soft constraints, which outperforms the state-of-the-art approach to high-dimensional path planning with costs.