AFIT - ENY - 14 - M - 20 Continuous Control Artificial Potential Function

Artificial potential function methods (APFMs) are a class of computationally inexpensive control methods for driving a system to a desired goal while avoiding obstacles. Although APFMs have been applied successfully to a wide range of systems since the late 1980s, these control methods do have notable drawbacks. The general suboptimality of APFM results is one of these drawbacks, which is due to the fact that APFMs contain no cost function in their formulation. This thesis first develops a new continuous control APFM for fully actuated systems called the Velocity Artificial Potential Function (VAPF) Method, which causes the system velocity to converge to the negative gradient of an artificial potential function. Then, methods for increasing APFM optimality are studied. First, an investigation is undertaken to determine if placing an APFM into an optimal control framework is a practical way of addressing the suboptimality of APFMs. While effective at increasing optimality of APFM results, this approach proves to be too computationally expensive to be practical. Finally, the Adaptive Artificial Potential Function developed by Muñoz is studied and implemented via the VAPF Method. This approach produces results with higher optimality than traditional APFMs but with negligibly greater computational expense.