RI-Small: Adaptive Parameter and State Estimation on Groups with Application to Sensor-Based Control

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This research seeks to develop adaptive methods that will enable sensor-based systems to learn from their own sensory experience in order to improve their perceptual precision and dexterity. We will investigate the problem of sensor-based parameter estimation and state estimation on groups, with particular focus on the group of rigid body transformations. These group-structured problems naturally arise in three-dimensional sensing (e.g. range scanners such as laser scanners and multi-beam bathymetric sonars; Doppler sonar; and vision based state estimation) and dynamic state estimation (e.g. image-based state estimation; vision based control; and multi-degree-of-freedom vehicle navigation and control). Few identification techniques presently exist for the common problem in which the unknown parameter set or state possesses group structure. This is in contrast to the variety of well-known techniques (i.e. least-squares and adaptive) for parameter and state estimation for the case in which the unknown parameter or state appears linearly in the plant equations and the unknown is an element of a linear vector space. The anticipated impact will be robotic systems capable of adaptively learning to improve their navigation and sensing accuracy. We will apply these approaches to actual real-world problems arising in underwater vehicle sensing and control.