Modeling and Control Design of a Contact-Based, Electrostatically Actuated Rotating Sphere

Abstract

The performance of micromirrors in terms of their maximum deflection is often limited due to mechanical constraints in the design. To increase the range of achievable deflection angles, we present a novel concept in which a free-lying sphere with a flat side as reflector can be rotated. Due to the large forces needed to move the sphere, multiple electrostatic actuators are used to cooperatively rotate the sphere in iterative steps by impacts and friction. A parameterized system-level model of the configuration is derived, which considers arbitrary multi-contact scenarios and can be used for simulation, analysis, and control design purposes. Due to the complex, indirect relation between the actuator voltages and the sphere motion, model-based numerical optimization is applied to obtain suitable system inputs. This results in rotation sequences, which can be understood as a sequence of motion primitives, thus transforming the continuous time model into an abstract discrete time model. Based on this, we propose a feedback control strategy for trajectory following, considering model uncertainties by a learning scheme. High precision is achieved by an extension controlling the angular change of each rotation step. The suitability of the overall approach is demonstrated in simulation for maximum angles of 40°, achieving angular velocities of approximately 10°/s.