Exploiting Information Content in Relative Motion Dhananjay Raghunathan and John Baillieul Abstract—We present a formal protocol for communication based on modulating the relative motion between mobile agents. This type of communication is typically dependent on context in that a particular motion or gesture will indicate something related to the current activity. The focus of this article is on enabling such motion-based signaling between non-holonomic mobile agents moving in R 2 . A Control law that enables such signaling is presented and analyzed. Properties of signals that are amenable to such signaling are presented, as are error bounds to the sensing of such motion by the agent receiving the signal. We conclude with a presentation of potential applications and current technological challenges towards enabling these applications. I. I NTRODUCTION Gesturing is a common means for signaling for animals and humans alike. Ranging from explicit hand gestures in an effort to communicate with another individual across a noisy hall, to the more subtle yet effective facial expressions, gesturing is indeed an art form that most of us have learned to use effectively. There are three important aspects to any gesture: the ability to effect motion, the ability to perceive motion and, the ability to comprehend an observed motion. Mobile robots of today have the ability to move, and to sense motion. Further, most have on-board computers and hence, the ability to process sensed information. Thus, with appropriate control laws, mobile robots should be capable of motion-based communication. This article presents control laws that enable motion-based information exchange between mobile robots. There is considerable advantage to motion-based signaling. One can avoid using wireless modes of signaling such as 802.11, and benefit from the stealth. This mode of signaling can also be used by formations of agents to signal between each other. Finally, by formalizing the information theory of such signaling, we may gain useful insight into the limits of our cognitive ability to communicate through gestures. The actuation bandwidth of the electro-mechanical systems that propel and control the motion of autonomous vehicles tend to be in the range of tens of hertz, and this bandwidth limits the data rate. Thus there are limitations on the types of messages that can be transmitted by means of motions. The expectation is that the proposed mode of communication has applications in niche areas such as signaling through formations and augmenting communications through existing wireless networking technologies. There is considerable interest today in the creating and maintaining rigid formations of unmanned ground and aerial This work was supported in the U.S. by ODDR&E MURI07 Program Grant Number FA9550-07-1-0528 and by the National Science Foundation ITR Program Grant Number DMI-0330171. The authors are with the Mechanical Engineering Department at Boston University, Boston MA, USA.({rdjay,johnb}@bu.edu) vehicles (see for instance [?][?][?][?].) A stable control law for tracking a reference frame is presented in [?] based on global positioning information. [?] tackles a similar problem with a local coordinate frame. Trajectory tracking for non- holonomic vehicles has been studied as well (for instance [?][?][?][?].) Algorithms that enable wireless connectivity between mobile autonomous agents by exploiting their mo- bility have been studied as well (see for instance [?][?].) The wireless connectivity of the agents enables information to be exchanged between agents over the wireless medium, but the motion of the agents in itself is not used to communicate information. The distinguishing feature of our work is that we use motion itself to communicate information between agents. We extend the notion of static formations of robots, to formations where the agents follow a signaling pattern such that the relative motion they observe between each other contains useful information. The participating agents can be considered to be moving in dynamic formation. We present control laws by which signaling patterns can be achieved and observed by participating agents. The sequel is organized as follows. We start out by describing the notion of signaling using relative motion and formulate the problem for non-holonomic robots moving in R 2 . We then discuss properties of signals that can be exchanged given the constraints of the robotic motion. A control law is presented and analyzed to achieve this signaling, and bounds on the errors are computed. We present properties of viable codebooks for signaling using relative motion. Simulations and one detailed protocol are presented. We conclude by presenting open challenges to bringing this idea into a full- fledged technology that can be exploited by mobile robots. II. SIGNALING USING RELATIVE MOTION IN R 2 Figure ?? shows two robot agents moving in the plane, with R 2 executing a motion that conveys information to R 1 . The information is encoded in a simple function, r(s), and the information is exchanged by having R 1 measure the position (ideally (s, r(s))) of R 2 relative to its own position (s, 0). Because R 1 and R 2 control their motions independently, each will have its own local coordinate s 1 and s 2 recording its location in the x-axis direction of the coordinate frame. In general it will not be possible to exactly maintain s 1 ≡ s 2 throughout the signaling maneuver, and part of the challenge in implementing this simple motion-based signaling protocol is to ensure that |s 1 − s 2 | remains small. We can suppose that the parameter s 1 is just the arclength along agent R1’s path along the x-axis. Assume R 1 moves with unit velocity, and hence s 1 (t)= t. The agent R 2 traces the path (s 2 ,r(s 2 )), with the goal of keeping |s 2 (t) − t| small. To the extent that 2009 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA June 10-12, 2009 ThA06.4 978-1-4244-4524-0/09/$25.00 ©2009 AACC 2166