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This thesis developed guidance laws to optimally position a relay Micro-UAV (MAV) to provide an operator with real-time Intelligence, Surveillance, and Suboptimal solutions are also analyzed to aid in solving the TPBVP which yields the solution of the differential game. One suboptimal approach is based upon the geometry of the ISR system. Another suboptimal approach envisions a stationary Rover and solves for the optimal path for the Relay. Both suboptimal approaches showed that the optimal path for the Relay is to head straight toward the midpoint between the Rover and the Base.iv

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This paper developed guidance laws to optimally and autonomously position a relay Micro Aerial Vehicle (MAV) to provide an operator with real-time Intelligence, Surveillance, and Reconnaissance (ISR) by relaying communication and video signals from a rover MAV to the base, thus extending the rover's reach. The ISR system is comprised of two MAVs, the Relay and the Rover, and a Base. The Relay strives to position itself so as to minimize the radio frequency (RF) power required for maintaining communications between the Rover and the Base, while the Rover performs the ISR mission, which may maximize the required RF power. The optimal control of the Relay MAV then entails the solution of a differential game. Applying Pontryagin's Maximum Principle yields a standard, albeit nonlinear, Two-Point Boundary Value Problem (TPBVP). Suboptimal solutions are first obtained as an aid in solving the TPBVP which yields the solution of the differential game. One suboptimal approach is based upon the geometry of the ISR system: The midpoint between the Rover and the Base is the ideal location which minimizes the RF power required, so the Relay heads toward that pointassuming that the Rover is stationary. At the same time, to maximize the rate of required RF power, the Rover moves in the opposite direction of the Relay-assuming the Relay is stationary. These are optimal strategies in the end-game, but it is suboptimal to use them throughout the game. Another suboptimal approach investigated envisions the Rover to remain stationary and solves for the optimal path for the Relay to minimize the RF power requirement. This one-sided optimization problem is analyzed using a Matlabbased optimization program, GPOCS, which uses the Gauss pseudospectral method of discretization. The results from GPOCS corroborated with the geometry-based suboptimal Relay strategy of heading straight toward the midpoint between the Rover and the Base. The suboptimal solutions are readily implementable for real-time operation and are used to facilitate the solutions of the TPBVP. In order to maintain communications/connectivity/controllability with deployed ISR MAVs/Rovers a relay is used to extend the line-of-sight distance between the Rover and the Base station. This paper focuses on developing guidance laws to optimally position an autonomous Relay MAV to provide the operator at the Base with real-time ISR by relaying communication and sensor data between the operator at the Base and the Rover.The cooperative control of networked MAVs is an area of significant interest [5,6,7,8,9]. Recent studies have applied various mobility control laws as a means of optimizing network communications for reliability and robustness. For example, in [1], Dixon and Frew use an extremum seeking controller for mobile communication nodes in order to maximize the signal-to-noise ratio of a network; in [2], Goldenberg et al. have shown that communication nodes should be evenly spaced on the line between the source and destination in order to minimize the energy cost of ...