Constrained reachability problems for a planar manipulator

TL;DR

This paper develops a method for solving constrained reachability problems for planar manipulators, incorporating obstacle geometry through an analytical distance approximation, with applications to hyper-redundant and soft robots.

Contribution

It introduces an analytical approximation of the distance function from ellipses and applies it to optimize reachability in constrained environments for specific manipulator models.

Findings

Effective distance approximation for elliptical obstacles.

Successful application to hyper-redundant and soft manipulators.

Numerical experiments demonstrating method viability.

Abstract

We address an optimal reachability problem for a planar manipulator in a constrained environment. After introducing the optmization problem in full generality, we practically embed the geometry of the workspace in the problem, by considering some classes of obstacles. To this end, we present an analytical approximation of the distance function from the ellipse. We then apply our method to particular models of hyper-redundant and soft manipulators, by also presenting some numerical experiments.