Spatial planning with constraints on translational distances between geometric objects

TL;DR

This paper introduces a Minkowski-based technique for generating translational C-space maps that accommodate complex constraints on the relative positions of geometric objects, enhancing spatial planning in robotics, CAD, and packaging.

Contribution

It presents a novel method for handling complex and directional distance constraints in spatial planning using Minkowski operations, extending beyond simple non-overlap conditions.

Findings

Enables planning with various distance constraints

Supports directional and rotational distance constraints

Applicable to dynamic geometric scenarios

Abstract

The main constraint on relative position of geometric objects, used in spatial planning for computing the C-space maps (for example, in robotics, CAD, and packaging), is the relative non-overlapping of objects. This is the simplest constraint in which the minimum translational distance between objects is greater than zero, or more generally, than some positive value. We present a technique, based on the Minkowski operations, for generating the translational C-space maps for spatial planning with more general and more complex constraints on the relative position of geometric objects, such as constraints on various types (not only on the minimum) of the translational distances between objects. The developed technique can also be used, respectively, for spatial planning with constraints on translational distances in a given direction, and rotational distances between geometric objects, as well as for spatial planning with given dynamic geometric situation of moving objects.