Fabien Lagriffoul

Constraint propagation on interval bounds for dealing with geometric backtracking

The combination of task and motion planning presents us with a new problem that we call geometric backtracking. This problem arises from the fact that a single symbolic state or action may be geometrically instantiated in infinitely many ways. When a symbolic action cannot be geometrically validated, we may need to backtrack in the space of geometric configurations, which greatly increases the complexity of the whole planning process. In this paper, we address this problem using intervals to represent geometric configurations, and constraint propagation techniques to shrink these intervals according to the geometric constraints of the problem. After propagation, either (i) the intervals are shrunk, thus reducing the search space in which geometric backtracking may occur, or (ii) the constraints are inconsistent, indicating the non-feasibility of the sequence of actions without further effort. We illustrate our approach on scenarios in which a two-arm robot manipulates a set of objects, and report experiments that show how the search space is reduced.

Efficiently combining task and motion planning using geometric constraints

We propose a constraint-based approach to address a class of problems encountered in combined task and motion planning (CTAMP), which we call kinematically constrained problems. CTAMP is a hybrid planning process in which task planning and geometric reasoning are interleaved. During this process, symbolic action sequences generated by a task planner are geometrically evaluated. This geometric evaluation is a search problem per se, which we refer to as geometric backtrack search. In kinematically constrained problems, a significant computational effort is spent on geometric backtrack search, which impairs search at the task level. At the basis of our approach to address this problem, is the introduction of an intermediate layer between task planning and geometric reasoning. A set of constraints is automatically generated from the symbolic action sequences to evaluate, and combined with a set of constraints derived from the kinematic model of the robot. The resulting constraint network is then used to prune the search space during geometric backtrack search. We present experimental evidence that our approach significantly reduces the complexity of geometric backtrack search on various types of problem.

Geometric backtracking for combined task and motion planning in robotic systems

Planners for real robotic systems should not only reason about abstract actions, but also about aspects related to physical execution such as kinematics and geometry. We present an approach to hybrid task and motion planning, in which state-based forward-chaining task planning is tightly coupled with motion planning and other forms of geometric reasoning. Our approach is centered around the problem of geometric backtracking that arises in hybrid task and motion planning: in order to satisfy the geometric preconditions of the current action, a planner may need to reconsider geometric choices, such as grasps and poses, that were made for previous actions. Geometric backtracking is a necessary condition for completeness, but it may lead to a dramatic computational explosion due to the large size of the space of geometric states. We explore two avenues to deal with this issue: the use of heuristics based on different geometric conditions to guide the search, and the use of geometric constraints to prune the search space. We empirically evaluate these different approaches, and demonstrate that they improve the performance of hybrid task and motion planning. We demonstrate our hybrid planning approach in two domains: a real, humanoid robotic platform, the DLR Justin robot, performing object manipulation tasks; and a simulated autonomous forklift operating in a warehouse.

Combining task and motion planning

Solving problems combining task and motion planning requires searching across a symbolic search space and a geometric search space. Because of the semantic gap between symbolic and geometric representations, symbolic sequences of actions are not guaranteed to be geometrically feasible. This compels us to search in the combined search space, in which frequent backtracks between symbolic and geometric levels make the search inefficient. We address this problem by guiding symbolic search with rich information extracted from the geometric level through culprit detection mechanisms.