Geometric Control of a Constrained System: Cooperative Action with a Coordinated Multiagent System

Abstract In this work we examine a differential geometric approach towards the synthesis of trajectory for each member of a team of autonomous surface vehicles which are cooperating to perform a coordinated act. In this framework the procedure of trajectory planning is done in decentralized fashion as a closed-loop control for each of the agent which is drawing feedback from the state of the consensus point of the team. The coordination/cooperation between the members of the group is minimum and limits to the common objective of the team to drive the consensus point on a predefined trajectory. The problem is formulated as trajectory planning for the agents of the cooperation. The agents are subjected to various holonomic and nonholonomic constraints on their state variables. The holonomic constraints mainly arise from arise from the dynamic of the agents, and the non-holonomic constraints are between the agents participating in the cooperation. With unifying both these seemingly different constraints we concentrate on addressing other difficulties of the problem, such as the hard constraint on the control and speed variables of the system. To embolden the significance of the solution this research proposes we have applied this method for a team consists of several micro Autonomous Surface Vehicles (mASVs) which are to be coordinated to transport a buoyant load. The mASVs have limited dynamic and kinematic capabilities. These limitations are modeled as bounds on the Force and torque inputs and speed and angular velocities of the extended unicycle models which represent each vehicle. The particular formulation of ours provides us with tools to corporate these limitations in the design of the trajectories and come up with a feasible solution to the problem. We exploit the power and flexibility of the mathematical tools that differential geometry provides us to synthesize an optimal solution for this highly constrained problem. We start with examining the holonomic and nonholonomic constraints on the states of the participating vehicles, and continue to design a trajectory for the total system in its kinematic space. At this stage a trajectory is designed for the load, and consequent trajectories are derived for the vehicles. The next step is to introduce dynamics to the model of the agents. This will eliminated the secondary controller which was necessary to implement for each agent to follow the devised kinematic trajectory. Since the dynamics of the agents appears in the formulation, the trajectories are designed such that the actions of the agents are being optimized.Ph.D., Mechanical Engineering and Mechanics -- Drexel University, 201