Caging Micromanipulation for Automated Microassembly David J. Cappelleri, Michael Fatovic, and Utsav Shah Abstract— This paper introduces the concept of caging micromanipulation for use in automated open loop microassembly tasks. Utilizing a caging transport motion primitive along with rotational and translation primitives, we demonstrate full control of the state of the part. Additionally, a framework for planar microassembly task planning is provided based on the A* algorithm. It is used to determine the optimal assembly sequences and part starting locations in the workspace. We also describe a test-bed suitable for planar micro, meso-scale, and nano-scale manipulation and assembly tasks and present simulation and experimental results of this work. I. INTRODUCTION Gripping and manipulation techniques for micro-assembly applications is an active area of research [1]. Specifically, there is a body of work pertaining to pick-and-place micro- assembly tasks using micro-gripping techniques and strate- gies [2], [3], [4], [5], [6], [7], [8]. For micro-scale manipula- tion, sticking effects due to Van der Walls forces and static electricity make the manipulator motions and part release complicated [9], [10]. Micro-manipulators also have limited degrees of freedom when compared to manipulators at the macro-scale. Some of these problems are addressed in [11]. However, the focus here is rather on using micro-scale pushing operations, which are better suited for open loop or quasi-open loop manipulations, for solving a representative microassembly problem as shown in Fig. 1. The derivation of the fundamental mechanics of pushing operations and sliding objects have been extensively studied by [12], [13], [14]. There is also extensive work addressing the analysis and simulation of mechanical systems with frictional contacts [15], [16]. In particular, the problem of finding motion primitives that rely on pushing and are robust to errors has received significant attention [17], [18], [19]. Much work has been done on investigating techniques and strategies for micromanipulation (see review in [20]). However, literature addressing micromanipulation with real- time sensor feedback is limited. The primary reason for this is that obtaining accurate sensor data is a difficult problem at this scale. Sensors cannot easily be affixed to tiny precision instruments without compromising their functionality [10]. The use of high resolution optical systems with controllable parameters for micro-assembly tasks are examined by [21]. Even with this sensor data, calibration and vision-based control at this scale can present technical difficulties. Without accurate sensor data, it is hard to develop models, and therefore controllers, for micromanipulation. Previous work on cooperative manipulation has utilized the concepts of form and force closure to manipulate large objects [22], [23], [24]. The force closure condition assumes that the grasp on the object can withstand any external force applied to the object. Form closure can be defined as the D. Cappelleri, M. Fatovic, and U. Shah are with the Multi-Scale Robotics and Automation Lab, Department of Mechanical Engineering, Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ USA 07030 [dcappell, mfatovic, ushah1] @stevens.edu Fig. 1. Representative microassembly problem condition to guarantee force closure without requiring fric- tional contacts to do so [25]. It is possible to use conditional force closure to transport an object by pushing on it from an initial position to a goal position [26], [19]. Conditional force closure makes use of both the manipulation forces generated by contacts from the robots as well as the external forces acting on the object, such as friction and gravity. Object clo- sure or caging is variation of this. It simply requires that the objected be caged by the robots and confined to a compact set in the configuration space [27]. In [28], decentralized control policies for a group of mobile robots to move toward a goal position while maintaining the object closure condition are presented. Multirobot manipulation of non-circular objects and cooperative manipulation in environments with obstacles has recently been demonstrated [29], [27] with macro-scale mobile robots. We look to use similar principles here for mi- cromanipulation and assembly tasks. While a multi-fingered micromechanism for coordinated micro/nano manipulation has been presented in [30], it has a very limited range of motion and is not well-suited for high throughput assembly of micro-scale components and devices. We build on our prior work [31], [32] and [33] to construct rotational and 1D translation motion primitives and develop a new micro-scale caging transport primitive here. We also present a planning and search algorithm to identify an optimal part starting location for a particular micro-assembly sequence as well as for determining the optimal assembly sequence for a give part starting location along with simulation and experimental results. II. PROBLEM FORMULATION We consider a group of N micromanipulators with single point probes (robots) operating in the XY plane with kine- matics given by ˙ q mi = u mi (1) where q mi =(x mi ,y mi ) T and u mi denote the i th tip po- sition of the manipulator’s probe and corresponding control input. We assume each manipulator is localized in a global coordinate frame. Our objective is to design a set of control inputs to enable a team of N micromanipulators to surround and transport an object to a desired location and orientation while avoiding obstacles in the environment in order to solve the representative microassembly problem depicted in Fig.1. 2011 IEEE International Conference on Robotics and Automation Shanghai International Conference Center May 9-13, 2011, Shanghai, China 978-1-61284-380-3/11/$26.00 ©2011 IEEE 3145