The minimum constraint removal problem with three robotics applications

Abstract

This paper formulates a new Minimum Constraint Removal (MCR) motion planning problem in which the objective is to remove the fewest geometric constraints necessary to connect a start and goal state with a free path. It describes a probabilistic roadmap motion planner for MCR in continuous configuration spaces that operates by constructing increasingly refined roadmaps, and efficiently solves discrete MCR problems on these networks. A number of new theoretical results are given for discrete MCR, including a proof that it is NP-hard by reduction from SET-COVER. Two search algorithms are described that perform well in practice. The motion planner is proven to produce the optimal MCR with probability approaching 1 as more time is spent, and its convergence rate is improved with various efficient sampling strategies. It is demonstrated on three example applications: generating human-interpretable excuses for failure, motion planning under uncertainty, and rearranging movable obstacles.

Object Rearrangement with Nested Nonprehensile Manipulation Actions

“…Navigation and Manipulation among Movable Objects (NAMO): Rearrangement problems are related to NAMO [32], which is known to be NP-hard even for simple instances [33]. Thus, most efforts have focused on finding time-efficient algorithms that are near-optimal [19], [34], [35]. Minimum constraint removal is another problem related to NAMO, where the planner searches for a transfer path that collides with the minimum number of objects [36], [37].…”

“…Thus, most efforts have focused on finding time-efficient algorithms that are near-optimal [19], [34], [35]. Minimum constraint removal is another problem related to NAMO, where the planner searches for a transfer path that collides with the minimum number of objects [36], [37]. NAMO techniques were used to improve the computational efficiency of rearrangement planning [3], and can also be used for the approach proposed in the current work.…”

Implicit belief-space pre-images for hierarchical planning and execution

“…We might consider moving object a to a new pose, p 1 . This suggestion can be arrived at by finding a pose of a that does not overlap the swept volume of some robot path that allows obstacle collisions, but tries to minimize the number of collisions [29], [30]. We could then rewrite CRH(R ) to a conjunction P ose(a) ∈ (p 1 ± δ) & CRH(R , {Pose(a) ∈ (p 1 ± δ)}) The first term asserts that the pose of a is near p 1 , which is shown as the vertical pink stripe in the figure.…”

Integer Programming as a General Solution Methodology for Path-Based Optimization in Robotics: Principles, Best Practices, and Applications

“…INTRODUCTION The study of robot task and motion planning problems aims at finding a path (resp., paths) for the robot (resp., robots) to optimize certain cumulative cost or reward. While some settings admit efficient search-based algorithmic solutions, e.g., via dynamic programming, such problems are frequently computationally intractable [1], [2]. In such cases, two approaches are often employed: (i) designing polynomial-time algorithms that compute approximately optimal solutions, and (ii) applying greedy search, assisted with heuristics.…”

“…MCR, which requires finding a path while removing the least number of blocking obstacles, is relevant to constraint-based task and motion planning [27], [28], object rearrangement [12], [29], and control strategy design [30]. Two search-based solvers are provided in [1] that extend to weighted obstacles [31]. Methods exist that balance between optimality, path length and computation time [32].…”