Abstract— There are many examples of minimally invasive surgery in which tethered robots are incapable of accurately reaching target locations deep inside the body either because they are too large and result in tissue damage or because the tortuosity of the path leads to loss of tip control. In these situations, small untethered magnetically-powered robots may hold the potential to act as delivery vehicles for therapeutic agents. While MRI scanners provide a means to power, control and image such robots as they move throughout the body, a substantial challenge arises if the clinical application requires more than one such robot. The resulting system is underactuated and thus its controllability is in question. This paper presents a simple motion planning algorithm for two magnetic capsules and demonstrates through simulation and experiment that nonlinear fluid damping can be exploited to independently control the positions of the capsules. I. INTRODUCTION LUID filled pathways within the body provide natural highways for groups of small robots to reach tissue targets with minimal damage. The ventricles, for example, provide access throughout the brain and can be reached via the spinal canal. Robots injected into the spine could be directed to any desired targets within the ventricles. If properly equipped, they could provide highly targeted delivery of drugs within the brain. Alternately, they could distribute a network of sensors that could be used to monitor for abnormal pressure distributions. Depending on the application, the robots could be designed to be biodegradable, e.g., for drug delivery, or could simply be controlled to swim back down the spine for retrieval. In contrast to the circulatory system, the relative uniformity of cerebrospinal fluid spaces and the low flow rate of cerebrospinal fluid make the brain a hospitable environment for such robots. We are not the first to propose such magnetically controlled robots. Excellent work has been performed by a number of groups on this topic. For example, micrometer scale swimming robots have been demonstrated in [1-5] and proposed for use in a variety of medical applications including drug delivery within the eye [6] and targeted This work was supported by the Wyss Institute for Biologically Inspired Engineering and by the National Institutes of Health under grant R01HL073647. P. Vartholomeos and P. Dupont are with Cardiovascular Surgery, Children’s Hospital Boston, Harvard Medical School, Boston MA, 02115, USA. {panagiotis.vartholomeos, pierre.dupont}@childrens.harvard.edu. M.Reza Akhavan-Sharif is with the Beth Israel Deaconess Medical Center, Boston MA, 02215, USA. rakhavan@bidmc.harvard.edu. chemotherapeutic delivery through the vasculature [7]. Besides swimming, researchers have also considered magnetically powered robots moving on a planar surface [8], [9]. Most of the research to date has been focused on optimizing the design and motion control of individual robots. Also, much of the work has been conducted using custom magnetic coils while only a few investigators have employed clinical MRI scanners [1,4,5]. This choice has a substantial effect on the control methods available. Furthermore, past work has focused on micron-scale robots that operate at low Reynolds numbers and so experience Stokes flow. In contrast, only a few researchers have considered motion control at the millimeter scale. In particular, MRI control of a 2.5 mm ball bearing in the carotid artery of a pig was demonstrated in [10]. Millimeter-scale magnetic robots offer advantages for some clinical applications since they can produce larger magnetic forces and carry larger payloads. They operate at higher Reynolds numbers (1-1000), however, and so must be modeled using quadratic damping at high speeds. The topic that has received the least attention in the literature is that of controlling groups of magnetic robots. Group control is an important problem in medical applications since the size of an individual robot limits its payload in drug delivery applications. Furthermore, it may be necessary to deliver drugs over a sustained period of time to multiple locations – which could be easily accomplished if multiple robots could be directed to the individual sites. Group robot control is difficult because the same magnetic field is applied to all of the robots. For such underactuated systems, independent control can be achieved by exploiting nonlinearities in the system dynamics. This approach has been recently demonstrated for magnetic microrobots on a planar surface in a fluid using custom coils [8]. By designing the robots to maximize the difference in their stick-slip properties on the planar surface, it is possible to design a motion planner to achieve independent control their position on the plane [8]. The contribution of this paper is to provide a motion planner for millimeter-scale robots swimming freely in a fluid and powered by an MRI scanner. We show that, unlike the case of very low Reynolds numbers, the combination of inertial dynamics and drag forces provided by quadratic fluid damping at this size scale enables independent control of robots that possess differences in either drag cross section or magnetic material. The paper is arranged as follows. The next section describes the capsule robots and provides their dynamic Motion planning for Multiple Millimeter-scale Magnetic Capsules in a Fluid Environment Panagiotis Vartholomeos, Member, IEEE, M.Reza Akhavan-Sharif and Pierre E. Dupont, Fellow, IEEE F 2012 IEEE International Conference on Robotics and Automation RiverCentre, Saint Paul, Minnesota, USA May 14-18, 2012 978-1-4673-1404-6/12/$31.00 ©2012 IEEE 1927