Certifying non-existence of undesired locally stable equilibria in formation shape control problems

A fundamental control problem for autonomous vehicle formations is formation shape control, in which the agents must maintain a prescribed formation shape using only information measured or communicated from neighboring agents. While a large and growing literature has recently emerged on distance-based formation shape control, global stability properties remain a significant open problem. Even in four-agent formations, the basic question of whether or not there can exist locally stable incorrect equilibrium shapes remains open. This paper shows how this question can be answered for any size formation in principle using semidefinite programming techniques for semialgebraic problems, involving solutions sets of polynomial equations, inequations, and inequalities.Comment: 6 pages; to appear in the 2013 IEEE Multiconference on Systems and Contro

Robust Distance-Based Formation Control of Multiple Rigid Bodies with Orientation Alignment

This paper addresses the problem of distance- and orientation-based formation control of a class of second-order nonlinear multi-agent systems in 3D space, under static and undirected communication topologies. More specifically, we design a decentralized model-free control protocol in the sense that each agent uses only local information from its neighbors to calculate its own control signal, without incorporating any knowledge of the model nonlinearities and exogenous disturbances. Moreover, the transient and steady state response is solely determined by certain designer-specified performance functions and is fully decoupled by the agents' dynamic model, the control gain selection, the underlying graph topology as well as the initial conditions. Additionally, by introducing certain inter-agent distance constraints, we guarantee collision avoidance and connectivity maintenance between neighboring agents. Finally, simulation results verify the performance of the proposed controllers.Comment: IFAC Word Congress 201

Unmanned vehicles formation control in 3D space and cooperative search

The first problem considered in this dissertation is the decentralized non-planar formation control of multiple unmanned vehicles using graph rigidity. The three-dimensional formation control problem consists of n vehicles operating in a plane Q and r vehicles that operate in an upper layer outside of the plane Q. This can be referred to as a layered formation control where the objective is for all vehicles to cooperatively acquire a predefined formation shape using a decentralized control law. The proposed control strategy is based on regulating the inter-vehicle distances and uses backstepping and Lyapunov approaches. Three different models, with increasing level of complexity are considered for the multi-vehicle system: the single integrator vehicle model, the double integrator vehicle model, and a model that represents the dynamics of a class of robotics vehicles including wheeled mobile robots, underwater vehicles with constant depth, aircraft with constant altitude, and marine vessels. A rigorous stability analysis is presented that guarantees convergence of the inter-vehicle distances to desired values. Additionally, a new Neural Network (NN)-based control algorithm that uses graph rigidity and relative positions of the vehicles is proposed to solve the formation control problem of unmanned vehicles in 3D space. The control law for each vehicle consists of a nonlinear component that is dependent on the closed-loop error dynamics plus a NN component that is linear in the output weights (a one-tunable layer NN is used). A Lyapunov analysis shows that the proposed distance-based control strategy achieves the uniformly ultimately bounded stability of the desired infinitesimally and minimally rigid formation and that NN weights remain bounded. Simulation results are included to demonstrate the performance of the proposed method. The second problem addressed in this dissertation is the cooperative unmanned vehicles search. In search and surveillance operations, deploying a team of unmanned vehicles provides a robust solution that has multiple advantages over using a single vehicle in efficiency and minimizing exploration time. The cooperative search problem addresses the challenge of identifying target(s) in a given environment when using a team of unmarried vehicles by proposing a novel method of mapping and movement of vehicle teams in a cooperative manner. The approach consists of two parts. First, the region is partitioned into a hexagonal beehive structure in order to provide equidistant movements in every direction and to allow for more natural and flexible environment mapping. Additionally, in search environments that are partitioned into hexagons, the vehicles have an efficient travel path while performing searches due to this partitioning approach. Second, a team of unmanned vehicles that move in a cooperative manner and utilize the Tabu Random algorithm is used to search for target(s). Due to the ever-increasing use of robotics and unmanned systems, the field of cooperative multi-vehicle search has developed many applications recently that would benefit from the use of the approach presented in this dissertation, including: search and rescue operations, surveillance, data collection, and border patrol. Simulation results are presented that show the performance of the Tabu Random search algorithm method in combination with hexagonal partitioning

Control of Formations with Non-rigid and Hybrid Graphs

This thesis studies the problem of control of multi-agent formations, of which the interaction architectures can be modeled by undirected and directed graphs or a mixture of the two (hybrid graphs). The algorithms proposed in this thesis can be applied to control the architectures of multi-agent systems or sensor networks, and the developed control laws can be employed in the autonomous agents of various types within multi-agent systems. This thesis discusses two major issues. The first tackles formations with undirected and directed underlying graphs, more specifically, the problems of rigidity restoration and persistence verification for multi-agent formations are studied. The second discusses the control of formations with both undirected and directed interaction architectures (hybrid formations) by distance-based control methods. The main contributions of this thesis are: definition of spindle agent and basic graphs for non-rigid undirected graphs, development of new operations for the constructions of undirected and directed graphs, design of graph rigidity restoration strategy by merging two or more non-rigid graphs, development of new persistence analysis strategy for arbitrary directed graphs, definition and investigation of hybrid formations and the underlying hybrid graphs, verification of persistence and minimal persistence for hybrid graphs, as well as the control of persistent hybrid formations by distance-based approaches

Distributed multi-UAV shield formation based on virtual surface constraints

This paper proposes a method for the deployment of a multi-agent system of unmanned aerial vehicles (UAVs) as a shield with potential applications in the protection of infrastructures. For this purpose, a distributed control law based on the gradient of a potential function is proposed to acquire the desired shield shape, which is modeled as a quadric surface in the 3D space. The graph of the formation is a Delaunay triangulation, which guarantees the formation to be rigid. An algorithm is proposed to design the formation (target distances between agents and interconnections) to distribute the agents over the virtual surface, where the input parameters are just the parametrization of the quadric and the number of agents of the system. Proofs of system stability with the proposed control law are provided, as well as a new method to guarantee that the resulting triangulation over the surface is Delaunay, which can be executed locally. Simulation and experimental results illustrate the effectiveness of the proposed approach