Hybrid Estimation for Control and Planning

Abstract

Hybrid or switched models are often used in engineering to analyze complex behavior. The hybrid paradigm can be used to design systems that utilize the relationship between discrete and continuous variables. This dissertation presents three examples in which hybrid principles are implemented in order to: 1) reduce the number of models required to establish hard bounds on the state estimate of smooth nonlinear systems, 2) enable the exchange of low-level information between vehicles using movements instead of radio-communication, and 3) improve the cooperative reconnaissance performance of two autonomous aerial vehicles in a leader/follower configuration under strict communication constraints.

First, the problem of establishing hard bounds on the state estimate of a nonlinear system using a switching piecewise linear hybrid estimator is considered. Within an operating region, the proposed hybrid/switched estimator uses a variant of the Extended Set-Membership Filter to select piecewise linear models based on minimizing uncertainty. A priori selection of the base piecewise linear models is achieved by optimizing the placement of operating points over the operating region.

Second, vehicle mode detection in a cooperative environment while minimizing communication is investigated. The behavior of a vehicle is described using a finite number of operating modes. Each mode is defined by a model which describes the vehicle's dynamics as well as a perturbation signature based on Gold codes. A locally most powerful detector is derived based on detection theory in which the test statistic is a function of the Kalman Filter innovations. In order to facilitate real-time implementation, a suboptimal detector that requires less computations is also developed. Monte Carlo simulations of a linear and a nonlinear system are presented and the detection performance of the locally most powerful and the suboptimal detectors are compared.

Finally, the cooperative reconnaissance performance of two unmanned aerial vehicles (leader/follower) in uncertain environments while minimizing communication is investigated. To enable cooperative reconnaissance, the follower estimates the operating mode of the leader vehicle by using video camera measurements. The performance of the overall system is gauged using two metrics: 1) by the length of time required for the two vehicles to collect a certain level of information, and 2) by the amount of information collected in a time interval. Monte Carlo simulations of the system are compared to a decentralized system in which there is no cooperation and a centralized system with full communication.