Doctor of Philosophy (PhD)
Department of Mechanical and Industrial Engineering
This dissertation is concerned with the formation control problem of multiple agents modeled as nonholonomic wheeled mobile robots. Both kinematic and dynamic robot models are considered. Solutions are presented for a class of formation problems that include formation, maneuvering, and flocking. Graph theory and nonlinear systems theory are the key tools used in the design and stability analysis of the proposed control schemes. Simulation and/or experimental results are presented to illustrate the performance of the controllers.
In the first part, we present a leader-follower type solution to the formation maneuvering problem. The solution is based on the graph that models the coordination among the robots being a spanning tree. Our control law incorporates two types of position errors: individual tracking errors and coordination errors for leader-follower pairs in the spanning tree. The control ensures that the robots globally acquire a given planar formation while the formation as a whole globally tracks a desired trajectory, both with uniformly ultimately bounded errors. The control law is first designed at the kinematic level and then extended to the dynamic level. In the latter, we consider that parametric uncertainty exists in the equations of motion. These uncertainties are accounted for by employing an adaptive control scheme.
In the second part, we design a distance-based control scheme for the flocking of the nonholonomic agents under the assumption that the desired flocking velocity is known to all agents. The control law is designed at the kinematic level and is based on the rigidity properties of the graph modeling the sensing/control interactions among the robots. A simple input transformation is used to facilitate the control design by converting the nonholonomic model into the single-integrator equation. The resulting control ensures exponential convergence to the desired formation while the formation maneuvers according to a desired, time-varying translational velocity.
In the third part, we extend the previous flocking control framework to the case where only a subset of the agents know the desired flocking velocity. The resulting controllers include distributed observers to estimate the unknown quantities. The theory of interconnected systems is used to analyze the stability of the observer-controller system.
Khaledyan, Milad, "Formation Control of Nonholonomic Multi-Agent Systems" (2018). LSU Doctoral Dissertations. 4609.
de Queiroz, Marcio