Distributed manipulation by shaping magnetic field (MagMan platform)
We study the problem of noncontact planar manipulation by shaping a magnetic (force) field. The field is generated by a regular array of coils and we shape it by controlling the electric currents through the coils. The field is shaped so that one or several steel balls placed on top of a flat surface above the coils are (simultaneously yet independently) steered along specified paths and/or to specified target destinations. Feedback from measured position(s) is used. Measurements are made either using a resistive touch foil (as used in some handheld devices) or using a computer vision system.
From the viewpoint of control engineering, the distinguished feature of such control challenge is that when viewed as a MIMO control system design, the contribution from an individual actuator (coil) to the global force field usually affects the situation in the neighbouring zones too. Although the set of command (or cotrol) signals is finite (however large), the derived force field is spatially continuous. An object or a number of objects located in the force field are fully described by a finite state vector (position and velocity for each object). Hence we obtain a dynamic system with a finite number of states and a huge and a very specially structured input matrix in the state-space model, which is furthermore dependent on the state vector. The topic of research is to find control strategies for this type of dynamical systems, exploiting their structure.
Our ultimate motivation is to contribute to development of efficient distributed feedback manipulation schemes. Although the presented experimental setup lives at a centimeter scale, it can also be used to demonstrate the essence of some issues at a micrometer scale (of course with some modifications such as less pronounced inertia effects), which may find some use in the fields such as biotechnology and analytical chemistry. See the description of our research in the domain of planar manipulation by shaping electric field (dielectrophoresis).
The particular experimental platform that we have developed (we call it MagMan) was designed and implemented in a modular way. Each module (sized 50x50x75mm) carries four coils with iron cores, driving circuitry, a powerful processor (ARM Cortex M3, 72 MHz) and connectors for interfacing with other modules via RS-485 bus. Hence the platform offers both centralized and distributed control strategies.
The presented experimental setup was awarded the first place in 2013 Matlab and Simulink Student Design Challenge and was presented during 2013 IEEE Conference on Decision and Control (within the a joint demonstration with The Mathworks).