Vector Field Control Methods for Discretely Variable Passive Robotic Devices

Abstract

Passive transmission-based robotic devices are capable of providing motion guidance while ensuring user safety and engagement. To circumvent some of the drawbacks associated with steering continuously variable transmissions based on rolling contacts, we are exploring a class of discretely variable devices, based on brakes and hydrostatic transmissions. Previously available control methods for discretely variable devices were built on velocity fields and only developed to stabilize a one-dimensional (1-D) target manifold. For n-DOF devices, methods to stabilize target manifolds of dimensions 1 to n-1 are of interest. In this article, we contribute constraint field methods that stabilize n$-$1 dimensional target manifolds while leaving the orthogonal subspace free to the control of the operator. We also contribute force-modulated single degree of freedom (DOF) velocity fields, which add between 1 and n-2 virtual DOFs to the motion of devices whose physical constraints leave one DOF. Control performance is demonstrated in simulation for 3-DOF devices capable of imposing 1-D or 2-D constraints and in experiment for 2-DOF devices imposing 1-D constraints. Our experimental apparatus features digital hydraulic transmissions that are easily configured for an n-dimensional space and capable of imposing constraints of any dimension, thus motivating the contributed methods.