In this dissertation, we apply the framework of ensemble control theory to derive an approximate steering algorithm for two classical robotic systems---the nonholonomic unicycle and the plate-ball manipulator---in the presence of model perturbation that scales all inputs by an unknown but bounded constant. The basic idea is to maintain the set of all possible configurations and to select inputs that reduce the size of this set and drive it toward some goal configuration. The key insight is that the evolution of this set can be described by a family of control systems that depend continuously on the unknown constant. Ensemble control theory provides conditions under which it is possible to steer this entire family to a neighborhood of the goal configuration with a single open-loop input trajectory. For both the nonholonomic unicycle and the plate-ball manipulator, we show how to construct this trajectory using piecewise-constant inputs. We also validate our approach with hardware experiments, where the nonholonomic unicycle is a differential-drive robot with unknown wheel size, and the plate-ball manipulator is a planar motion stage that uses magnetic actuation to orient a sphere of unknown radius. We conclude by showing how the same framework can be applied to feedback control of multi-robot systems under the constraint that every robot receives exactly the same control input. We focus on the nonholonomic unicycle, instantiated in experiment by a collection of differential-drive robots. Assuming that each robot has a unique wheel size, we derive a globally asymptotically stabilizing feedback control policy. We show that this policy is robust to standard models of noise and scales to an arbitrary number of robots. These results suggest that our approach may have possible future application to control of micro- and nano-scale robotic systems, which are often subject to similar constraints.
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