Motion Planning for Multiple Heterogeneous Magnetic Robots Under Global Input

Abstract

Magnetism provides an untethered actuation mechanism and an alternative way to actuate robots. Using a magnetic field we can control the motion of robots embedded with magnets. This scales down the size of the robots dramatically such that they can be used in applications like drug delivery, sample collection, micromanipulation, and noninvasive procedures. Despite all advantages and potentials, magnetic actuation has one major drawback. Due to the similar interaction between the magnetic field and the embedded magnets in multirobot systems, controlling the robots independently is challenging. Using heterogeneous magnetic robots is one way to overcome the independent control challenge. Here, motion planning for multiple magnetic robots that move in parallel directions at different speeds in response to a global input is addressed in the absence of obstacles in a polygonal workspace. Through controllability analysis, it will be shown that having <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> linearly independent heterogeneous responses to the global input, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Modes of Motion</i> here, enables independent position control of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> robots in the system. Further, a procedure to have a potentially feasible sequence of motion is presented and intrarobot collision free directions of movement are formulated mathematically. These procedures are then used in the proposed optimization-based motion planning algorithm. Also, an innovative millimeter scale multimode magnetic pivot walker design is introduced and used for benchmarking in the experiments. Finally, the motion planning algorithm is used in multiple experiments, using our innovative pivot walkers, and its efficacy is illustrated.