Exploiting Nonslip Wall Contacts to Position Two Particles Using the Same Control Input

Steered particles offer a method for targeted therapy, interventions, and drug delivery in regions inaccessible by large robots. For example, magnetic actuation of particles has the benefits of requiring no tethers, being able to operate from a distance, and in some cases allows imaging for feedback (e.g., MRI). This paper investigates position control of particles using uniform forces (the same force is applied everywhere in the workspace). Given a controllable field that can generate bidirectional forces in three orthogonal directions, steering one particle in three-dimensional (3-D) is trivial. Adding additional particles to steer makes the system underactuated because there are more states than control inputs. However, the walls of in vivo and artificial environments often have surface roughness such that the particles do not move unless actuation pulls them away from the wall. In the previous work, we showed that the individual two-dimensional (2-D) position of two particles is controllable using global inputs in a square workspace with nonslip wall contact [1]. Because in vivo environments are usually not square, this paper extends the previous work to all convex workspaces, and shows how this could be extended to 3-D positioning of neutrally buoyant particles. We investigate analytically an idealized variant of this problem with nonslip boundaries and control inputs that are applied uniformly to all particles in the workspace. This paper also implements the algorithms in 2-D using a hardware setup inspired by the gastrointestinal tract.