  We introduce the novel concept of Spatial Predictive Control (SPC) to solve
the following problem: given a collection of agents (e.g., drones) with
positional low-level controllers (LLCs) and a mission-specific distributed cost
function, how can a distributed controller achieve and maintain cost-function
minimization without a plant model and only positional observations of the
environment? Our fully distributed SPC controller is based strictly on the
position of the agent itself and on those of its neighboring agents. This
information is used in every time-step to compute the gradient of the cost
function and to perform a spatial look-ahead to predict the best next target
position for the LLC. Using a high-fidelity simulation environment, we show
that SPC outperforms the most closely related class of controllers, Potential
Field Controllers, on the drone flocking problem. We also show that SPC is able
to cope with a potential sim-to-real transfer gap by demonstrating its
performance on real hardware, namely our implementation of flocking using nine
Crazyflie 2.1 drones.
