【正文】 cribing a motion. This sequence could e from a column in a gait control table, but in our implementation the joint angles are calculated using a cyclic function with period T . Every time a module has pleted a specified fraction d of the period a message is sent through the child connectors. If the signal is received the child module resets its action sequence making it delayed d pared to the parent. This way the actions of the individual module are decoupled from the synchronization mechanism resulting in a faster and more reliable system. Furthermore, there is no need to make changes to the algorithm if the number of modules changes. 3. Rolebased control We assume that the modules are connected to form a tree structure, that a parent connector is specified, and that this connector is the only one that can connect to child connectors of other modules. Furthermore, we assume that the modules can municate with the modules to which they are connected. The algorithm is instantiated by specifying three ponents. The first ponent is a cyclic action sequence A(t), where t ∈ [0 : T ]. T is the second ponent that needs to be specified and is the period of the action sequence. A(t) describes the actions that each module repeats cycle after cycle. In our implementation A(t) returns joint angles to control the two degrees of freedom of the CONRO module, but the action sequence could also be used to trigger different behaviors at different times during a cycle. The third ponent is a delay d. This delay specifies the fraction of a period the children’s action sequences are delayed pared to their parents. The skeleton algorithm looks like this: t=0 while(true) { if(t=d)then signal child modules if parent signals then t=0 perform action A(t) t=(t+1) modulus T } Ignoring the first two lines of the loop, the module repeatedly goes through a sequence of actions parameterized by the cyclic counter t. This part of the algorithm alone can make a single module repeatedly perform the specified sequence of actions. In order to coordinate the actions of the individual modules to produce the desired global behavior the modules need to be synchronized. Therefore, at step t = d a signal is sent through all child connectors. If a child receives a signal it knows that the parent is at t = d and therefore sets its own step counter to t = 0. This enforces that the child is delayed d pared to its parent. From the time the modules are connected it takes time proportional to d times the height of the configuration tree for all the modules to synchronize. To avoid problems with uncoordinated modules initially we make sure the modules do not start moving until they receive the first synchronization signal. After the startup phase the modules stay synchronized using only constant time. 4. Experimental setup To evaluate our algorithm we conducted several experiments using the CONRO (CONfigurable RObot) modules of which one is shown in Fig. 1. The CONRO modules have been developed at USC/ISI [5,9]. The modules are roughly shaped as rectangular boxes measuring 10 cm cm cm and weigh 100 g. The modules have a female connector at one end and three male connectors located at the other. Each connectorhas a infrared transmitter and receiver used for local munication and sensing. The modules have two controllable degrees of freedom: pitch (up and down) and yaw (side to side). Processing is taken care of by an onboard Basic Stamp 2 processor. The modules have onboard batteries, but these do not supply enough power for the experiments reported here and therefore the modules are powered through cables. Refer to for more details and videos of the experiments reported later. 5. Experiments In this section we describe three different lootion gaits implemented using rolebased control. For each gait we have chosen to report the length of our programs as a measure of the plexity of the control algorithm. These results are used to support our claim that the implemented control systems are minimal. We also report the speed of the lootion patterns, but this should only be considered an example, the reason being that in our system the limiting factors are how robust the modules physically are, how powerful the motors are, and how much power we can pull from the power source. To report a top speed is not meaningful before we run the robot autonomously on batteries. . Caterpillar lootion We connect eight of our modules in a chain and designate the male opposite the female connector to be the parent connector. We then implement the algorithm described above with the following parameters. T = 180, _ pitch(t) = 50? sin 2π t , T yaw(t) = 0, d = 51 T. (1) Pitch and yaw is measured in a coordinate system where a yaw and a pitch of zero mean that the joints are straight. The motor control of our modules makes the joint go to the desired angle as fast as possible. This means that waypoints have to be specified to avoid jerky motion. The period T can be used to control the number of waypoints and therefore the smoothness and speed of the motion. The action sequence is an oscillation around 0? with an amplitude of 50? for the pitch angle and the yaw joint is kept straight. Each module is delayed onefifth of a period pared to its parent. The modules are connected and after they synchronize a sine wave is traveling along the length of the robot. Refer to Fig. 2. This produces caterpillarlike lootion at a speed of 4 cm/s. Note that it is easy to adjust the parameters of this motion. For instance, the length of the wave can be controlled using the delay. The program is simple. The main loop contains 13 lines of code excluding ments and labels (shown in Fig. 2). The initialization including variable and constant