I. Introduction
Efficient and scalable manipulation planning is of paramount importance in robotics and automation to solve real-world tasks. However, in most cases, manipulation of objects imposes hard kinematic constraints on the robot that limit its allowable range of motion. Examples of such instances include moving an object from one place to another that might also contain orientation constraints [1], maintaining contact with the environment such as in robot surgery [2], and performing bi-manual manipulation [3]. In all of these cases, kinematic constraints form one or more low-dimensional manifolds of a set of robot configurations embedded in a high-dimensional ambient space, and are often known as manifold constraints [4].