Planar Orientation Control and Torque Maximization Using a Swarm With Global Inputs

This paper studies the torque applied by a large number of particles on a long aspect-ratio rod. The particles are all pushed in the same direction by a global signal. We calculate the force and torque generated by three canonical position distributions of a swarm: uniform, triangular, and normal. The model shows that for a pivoted rod the uniform distribution produces the maximum torque for small swarm standard deviations, but the normal distribution maximizes torque for large standard deviations. In the simulation, we use these results to design proportional-derivative controllers to orient rigid objects. We conclude showing the experiments with up to 97 hardware robots to evaluate our theory in practice. Note to Practitioners—Workspace clutter can prevent large steered particles from being able to manipulate objects and maneuver, while smaller particles can pass through this clutter. A small particle produces less force than a big particle, so to produce the same force, more are needed. Their small size makes onboard sensing and computation hard. Therefore, they are often controlled by a shared control input. Manipulating objects with a swarm of particles actuated by a shared control input is a challenging task, but it is even more challenging when the object’s final orientation needs to be set. Many applications including assembly and delivery require a specific orientation of the object. Torque control with only one steered particle is easy: maximize torque by pushing on the object at a location as far from the pivot point as possible. However, a swarm of particles contributes force at different places on the object. This paper studies how to maximize torque using a swarm of particles shaped in three canonical position distributions. The work is limited by assuming each particle touching the object transmits equal force, but hardware experiments validate the necessity to consider swarm distribution when applying torque. In the future work, we will investigate how stochastic contacts between particles effects force and torque transmission, and examine control in 3-D space.