Optimal control of shape-similar multi-agent systems.
Korde, Rohan Y
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Formation control problems in the field of control theory are not new. They pertain to multiple mobile agents i.e. robots that are placed in a formation of a certain geometric shape and then the endeavor is to find a control that will move this formation in space by maintaining the initial shape. Additional constraints can also be imposed. Researchers have conducted research in this field using different techniques to measure and preserve the shape of the formation of robots using approaches like measuring inter-agent distances and inter-agent angles using SONAR-based, LIDAR-based sensors etc. In this thesis research, we attempt to answer the question - "Is it possible to find an optimal control to move a formation of mobile agents from t=0 to t=T subject to two constraints - a path constraint and a shape constraint - without measuring inter-agent distances and inter-agent angles?". We use Calculus of Variations to formulate this optimal control problem and we then derive the Euler-Lagrange equations that give us the system of partial differential equations. We then use COMSOL Multiphysics software to solve this system of equations. Since this is a two-point boundary value problem (BVP), it was difficult to determine a priori whether this system had zero, one, or more than one solutions for the boundary value conditions we specified in the problem. Fortunately, we did find an optimal control that moved this triangle-shaped formation along a straight line path and the shape was preserved throughout the movement from t=0 to t=T without taking any distance or angle measurements.