Distributed formation tracking control of multiple car-like robots

In this thesis, distributed formation tracking control of multiple car-like robots is studied. Each vehicle can communicate and send or receive states information to or from a portion of other vehicles. The communication topology is characterized by a graph. Each vehicle is considered as a vertex in the graph and each communication link is considered as an edge in the graph. The unicycles are modeled firstly by both kinematic systems. Distributed controllers for vehicle kinematics are designed with the aid of graph theory. Two control algorithms are designed based on the chained-form system and its transformation respectively. Both algorithms achieve exponential convergence to the desired reference states. Then vehicle dynamics is considered and dynamic controllers are designed with the aid of two types of kinematic-based controllers proposed in the first section. Finally, a special case of switching graph is addressed considering the probability of vehicle disability and links breakage

Robust Formation Control for Networked Robotic Systems Using Negative Imaginary Dynamics

This paper proposes a consensus-based formation tracking scheme for multi-robot systems utilizing the Negative Imaginary (NI) theory. The proposed scheme applies to a class of networked robotic systems that can be modelled as a group of single integrator agents with stable uncertainties connected via an undirected graph. NI/SNI property of networked agents facilitates the design of a distributed Strictly Negative Imaginary (SNI) controller to achieve the desired formation tracking. A new theoretical proof of asymptotic convergence of the formation tracking trajectories is derived based on the integral controllability of a networked SNI systems. The proposed scheme is an alternative to the conventional Lyapunov-based formation tracking schemes. It offers robustness to NI/SNI-type model uncertainties and fault-tolerance to a sudden loss of robots due to hardware/communication fault. The feasibility and usefulness of the proposed formation tracking scheme were validated by lab-based real-time hardware experiments involving miniature mobile robots

Distributed Consensus of Linear Multi-Agent Systems with Adaptive Dynamic Protocols

This paper considers the distributed consensus problem of multi-agent systems with general continuous-time linear dynamics. Two distributed adaptive dynamic consensus protocols are proposed, based on the relative output information of neighboring agents. One protocol assigns an adaptive coupling weight to each edge in the communication graph while the other uses an adaptive coupling weight for each node. These two adaptive protocols are designed to ensure that consensus is reached in a fully distributed fashion for any undirected connected communication graphs without using any global information. A sufficient condition for the existence of these adaptive protocols is that each agent is stabilizable and detectable. The cases with leader-follower and switching communication graphs are also studied.Comment: 17 pages, 5 figue

Optimal Control of Vehicular Formations With Nearest Neighbor Interactions

We consider the design of optimal localized feedback gains for one-dimensional formations in which vehicles only use information from their immediate neighbors. The control objective is to enhance coherence of the formation by making it behave like a rigid lattice. For the single-integrator model with symmetric gains, we establish convexity, implying that the globally optimal controller can be computed efficiently. We also identify a class of convex problems for double-integrators by restricting the controller to symmetric position and uniform diagonal velocity gains. To obtain the optimal non-symmetric gains for both the single- and the double-integrator models, we solve a parameterized family of optimal control problems ranging from an easily solvable problem to the problem of interest as the underlying parameter increases. When this parameter is kept small, we employ perturbation analysis to decouple the matrix equations that result from the optimality conditions, thereby rendering the unique optimal feedback gain. This solution is used to initialize a homotopy-based Newton’s method to find the optimal localized gain. To investigate the performance of localized controllers, we examine how the coherence of large-scale stochastically forced formations scales with the number of vehicles. We establish several explicit scaling relationships and show that the best performance is achieved by a localized controller that is both non-symmetric and spatially-varying

Pinning Control of Higher Order Nonlinear Network Systems

In this letter, we study the problem of controlling via pinning the motion of nonlinear network systems of any order whose dynamics are in controllable canonical form. Different from existing works that either focus on spontaneous synchronization, assume linear dynamics or rely on dynamics cancellation, here we provide a constructive method to prove pinning controllability towards the desired trajectory selected by the pinner. We introduce an algorithmic procedure that associates to any connected topology a suitable Lyapunov function for the network system. The approach is demonstrated on an illustrative example

Consensus of Multi-Agent Systems with General Linear and Lipschitz Nonlinear Dynamics Using Distributed Adaptive Protocols

This paper considers the distributed consensus problems for multi-agent systems with general linear and Lipschitz nonlinear dynamics. Distributed relative-state consensus protocols with an adaptive law for adjusting the coupling weights between neighboring agents are designed for both the linear and nonlinear cases, under which consensus is reached for all undirected connected communication graphs. Extensions to the case with a leader-follower communication graph are further studied. In contrast to the existing results in the literature, the adaptive consensus protocols here can be implemented by each agent in a fully distributed fashion without using any global information.Comment: 15 pages, 6 figures, submitted to IEEE TA