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Consider many particles actuated by a uniform global external field (e.g. gravitational or magnetic fields). This paper presents analytical results using workspace obstacles and global inputs to reshape such a group of particles. Shape control of many particles is necessary for conveying information, construction, and navigation. First we show how the particles’ characteristic angle of repose can be used to reshape the particles by controlling angle of attack and the magnitude of the driving force. These can then be used to control the force and torque applied to a rectangular rigid body. Next, we examine the full set of stable, achievable mean and variance configurations for the shape of a particle group in two canonical environments: a square and a circular workspace. Finally, we show how workspaces with linear boundary layers can be used to achieve a more rich set of mean and variance configurations. 

There are driving applications for large populations of tiny robots in robotics, biology, and chemistry. These robots often lack onboard computation, actuation, and communication. Instead, these “robots” are particles carrying some payload and the particle swarm is controlled by a shared control input such as a uniform magnetic gradient or electric field. In previous works, we showed that the 2D position of each particle in such a swarm is controllable if the workspace contains a single obstacle the size of one particle. Requiring a small, rigid obstacle suspended in the middle of the workspace is a strong constraint, especially in 3D. This paper relaxes that constraint, and provides position control algorithms that only require non-slip wall contact in 2D. Both in vivo and artificial environments often have such boundaries. We assume that particles in contact with the boundaries have zero velocity if the shared control input pushes the particle into the wall. This paper provides a shortest-path algorithm for positioning a two-particle swarm, and a generalization to positioning an n-particle swarm. Results are validated with simulations and a hardware demonstration. 

Microrobotics has the potential to revolutionize many applications including targeted material delivery, assembly, and surgery. The same properties that promise breakthrough solutions—small size and large populations—present unique challenges for controlling motion. Robotic manipulation usually assumes intelligent agents, not particle systems manipulated by a global signal. To identify the key parameters for particle manipulation, we used a collection of online games in which players steer swarms of up to 500 particles to complete manipulation challenges. We recorded statistics from more than 10 000 players. Inspired by techniques in which human operators performed well, we investigate controllers that use only the mean and variance of the swarm. We prove that mean position is controllable and provide conditions under which variance is controllable. We next derive automatic controllers for these and a hysteresis-based switching control to regulate the first two moments of the particle distribution. Finally, we employ these controllers as primitives for an object manipulation task and implement all controllers on 100 kilobots controlled by the direction of a global light source.