Nonlocal control of active agents on a deformable substrate

In an effort to construct a robophysical analog gravity system, we previously studied the dynamics of a 200-gram differential wheeled vehicle driving on a deformable spandex membrane (d=2.4m) with a static central depression (Li et al., 2019). The system displays rich dynamics, including precessing orbits reminiscent of those in general relativity. To take the next step and study how the vehicle dynamics can be manipulated via changes in membrane curvature, we developed an automated gantry system that can control the position and depth of a spherical object. The object creates a deformation on the membrane which influences the dynamics of the vehicle. Experiments reveal that forcing the object in circular orbits on the membrane can lead to “capture” of the moving vehicle depending on the initial orientation and position of the vehicle. Motivated by this, we augmented the vehicle with sensors which measure its instantaneous roll and pitch (tilt). A scheme which decreases the speed with tilt generally enhances capture, whereas, increasing speed with tilt generally prevents capture. In both cases, the trajectories of the vehicle are highly variable with even small changes to initial condition. A numerical model based on Poisson equation rationalizes our experimental observations.