Optimal Control and Coordination of Small UAVs for Vision-based Target Tracking

Small unmanned aerial vehicles (UAVs) are relatively inexpensive mobile sensing platforms capable of reliably and autonomously performing numerous tasks, including mapping, search and rescue, surveillance and tracking, and real-time monitoring. The general problem of interest that we address is that of using small, fixed-wing UAVs to perform vision-based target tracking, which entails that one or more camera-equipped UAVs is responsible for autonomously tracking a moving ground target. In the single-UAV setting, the underactuated UAV must maintain proximity and visibility of an unpredictable ground target while having a limited sensing region. We provide solutions from two different vantage points. The first regards the problem as a two-player zero-sum game and the second as a stochastic optimal control problem. The resulting control policies have been successfully field-tested, thereby verifying the efficacy of both approaches while highlighting the advantages of one approach over the other. When employing two UAVs, one can fuse vision-based measurements to improve the estimate of the target's position. Accordingly, the second part of this dissertation involves determining the optimal control policy for two UAVs to gather the best joint vision-based measurements of a moving ground target, which is first done in a simplified deterministic setting. The results in this setting show that the key optimal control strategy is the coordination of the UAVs' distances to the target and not of the viewing angles as is traditionally assumed, thereby showing the advantage of solving the optimal control problem over using heuristics. To generate a control policy robust to real-world conditions, we formulate the same control objective using higher order stochastic kinematic models. Since grid-based solutions are infeasible for a stochastic optimal control problem of this dimension, we employ a simulation-based dynamic programming technique that relies on regression to form the optimal policy maps, thereby demonstrating an effective solution to a multi-vehicle coordination problem that until recently seemed intractable on account of its dimension. The results show that distance coordination is again the key optimal control strategy and that the policy offers considerable advantages over uncoordinated optimal policies, namely reduced variability in the cost and a reduction in the severity and frequency of high-cost events

Simultaneous Nonlinear Model Predictive Control and State Estimation: Theory and Applications

As computational power increases, online optimization is becoming a ubiquitous approach for solving control and estimation problems in both academia and industry. This widespread popularity of online optimization techniques is largely due to their abilities to solve complex problems in real time and to explicitly accommodate hard constraints. In this dissertation, we discuss an especially popular online optimization control technique called model predictive control (MPC). Specifically, we present a novel output-feedback approach to nonlinear MPC, which combines the problems of state estimation and control into a single min-max optimization. In this way, the control and estimation problems are solved simultaneously providing an output-feedback controller that is robust to worst-case system disturbances and noise. This min-max optimization is subject to the nonlinear system dynamics as well as constraints that come from practical considerations such as actuator limits. Furthermore, we introduce a novel primal-dual interior-point method that can be used to efficiently solve the min-max optimization problem numerically and present several examples showing that the method succeeds even for severely nonlinear and non-convex problems. Unlike other output-feedback nonlinear optimal control approaches that solve the estimation and control problems separately, this combined estimation and control approach facilitates straightforward analysis of the resulting constrained, nonlinear, closed-loop system and yields improved performance over other standard approaches. Under appropriate assumptions that encode controllability and observability of the nonlinear process to be controlled, we show that this approach ensures that the state of the closed-loop system remains bounded. Finally, we investigate the use of this approach in several applications including the coordination of multiple unmanned aerial vehicles for vision-based target tracking of a moving ground vehicle and feedback control of an artificial pancreas system for the treatment of Type 1 Diabetes. We discuss why this novel combined control and estimation approach is especially beneficial for these applications and show promising simulation results for the eventual implementation of this approach in real-life scenarios