Reachability Map / Inverse Reachability Map

A precomputed record of which end-effector poses an arm can reach; the inverse version looks up where to place the base to reach a target.

A reachability map is an offline precomputation of a manipulator's workspace: the space around the end effector is divided into 3D voxels, several orientations are sampled within each voxel, and inverse kinematics checks whether each one is reachable; the results (often expressed as the fraction of reachable orientations) are stored in a lookup table, so the arm doesn't have to re-solve inverse kinematics repeatedly at run time. Zacharias and colleagues introduced this kind of capability map in 2007. The inverse reachability map inverts every reachable pose to instead give a distribution of where the base can be placed relative to a target end-effector pose — Vahrenkamp and colleagues used it in 2013 to solve base placement for mobile manipulation. Both are commonly used to filter out unreachable grasps during grasp planning, to choose a standing position for mobile manipulation, and to evaluate a robot's design and mounting location; a 2024 method called RM4D compresses both into a single 4D data structure.

ExampleA mobile robot approaching a table to pick up a cup: it queries the inverse reachability map centered on the candidate grasp pose, getting a region on the floor from which that grasp is reachable, filters out spots that would collide with the table or are unreachable, and picks the point with the highest reachability score as its navigation target.

Also called

RM / IRM, Capability Map, Inverse Capability Map

Related

Workspace · Inverse Kinematics (IK) · Mobile Manipulation · Mobile Manipulator · Grasp Planning · Manipulability

Sources

RM4D: A Combined Reachability and Inverse Reachability Map for Common 6-/7-axis Robot Arms (arXiv 2410.06968)