Herbert G. Tanner

Flocking in Fixed and Switching Networks

This note analyzes the stability properties of a group of mobile agents that align their velocity vectors, and stabilize their inter-agent distances, using decentralized, nearest-neighbor interaction rules, exchanging information over networks that change arbitrarily (no dwell time between consecutive switches). These changes introduce discontinuities in the agent control laws. To accommodate for arbitrary switching in the topology of the network of agent interactions we employ nonsmooth analysis. The main result is that regardless of switching, convergence to a common velocity vector and stabilization of inter-agent distances is still guaranteed as long as the network remains connected at all times

Leader-to-formation stability

The paper investigates the stability properties of mobile agent formations which are based on leader following. We derive nonlinear gain estimates that capture how leader behavior affects the interconnection errors observed in the formation. Leader-to-formation stability (LFS) gains quantify error amplification, relate interconnection topology to stability and performance, and offer safety bounds for different formation topologies. Analysis based on the LFS gains provides insight to error propagation and suggests ways to improve the safety, robustness, and performance characteristics of a formation.

Stable flocking of mobile agents, part I: fixed topology

This is the first of a two-part paper that investigates the stability properties of a system of multiple mobile agents with double integrator dynamics. In this first part we generate stable flocking motion for the group using a coordination control scheme which gives rise to smooth control laws for the agents. These control laws are a combination of attractive/repulsive and alignment forces, ensuring collision avoidance and cohesion of the group and an aggregate motion along a common heading direction. In this control scheme the topology of the control interconnections is fixed and time invariant. The control policy ensures that all agents eventually align with each other and have a common heading direction while at the same time avoid collisions and group into a tight formation.

Stable flocking of mobile agents part I: dynamic topology

This is the second of a two-part paper, investigating the stability properties of a system of multiple mobile agents with double integrator dynamics. In this second part, we allow the topology of the control inter-connections between the agents in the group to vary with time. Specifically, the control law of an agent depends on the state of a set of agents that are within a certain neighborhood around it. As the agents move around this set changes, giving rise to a dynamic control interconnection topology and a switching control law. This control law consists of a combination of attractive/repulsive and alignment forces. The former ensure collision avoidance and cohesion of the group and the latter result to all agents attaining a common heading angle, exhibiting flocking motion. Despite the use of only local information and the time varying nature of agent interaction which affects the local controllers, flocking motion is established, as long as connectivity in the neighboring graph is maintained.

On the controllability of nearest neighbor interconnections

In this paper we derive necessary and sufficient conditions for a group of systems interconnected via nearest neighbor rules, to be controllable by one of them acting as a leader. It is indicated that connectivity seems to have an adverse effect on controllability, and it is formally shown why a path is controllable while a complete graph is not. The dependence of the graph controllability property on the size of the graph and its connectivity is investigated in simulation. Results suggest analytical means of selecting the right leader and/or the appropriate topology to be able to control an interconnected system with nearest neighbor interaction rules.

Nonholonomic navigation and control of cooperating mobile manipulators

This paper presents the first motion planning methodology applicable to articulated, nonpoint nonholonomic robots with guaranteed collision avoidance and convergence properties. It is based on a new class of nonsmooth Lyapunov functions and a novel extension of the navigation function method to account for nonpoint articulated robots. The dipolar inverse Lyapunov functions introduced are appropriate for nonholonomic control and offer superior performance characteristics compared to existing tools. The new potential field technique uses diffeomorphic transformations and exploits the resulting point-world topology. The combined approach is applied to the problem of handling deformable material by multiple nonholonomic mobile manipulators in an obstacle environment to yield a centralized coordinating control law. Simulation results verify asymptotic convergence of the robots, obstacle avoidance, boundedness of object deformations, and singularity avoidance for the manipulators.

Hybrid Control for Connectivity Preserving Flocking

In this technical note, we address the combined problem of motion and network topology control in a group of mobile agents with common objective the flocking behavior of the group. Instead of assuming network connectivity, we enforce it by means of distributed topology control that decides on both deletion and creation of communication links between agents, adapting the network to the groups spatial distribution. With this protocol ensuring network connectivity, a decentralized motion controller aligns agent velocity vectors and regulates inter-agent distances to maintain existing network links. The stability of the flocking controller is established in continuous time by means of an observability argument on a quadratic form of the graph Laplacian that exploits the time delay between link deletion and creation caused by the topology control protocol, which induces a dwell time between network switches.

Towards Decentralization of Multi-robot Navigation Functions

We present a navigation function through which a group of mobile agents can be coordinated to achieve a particular formation, both in terms of shape and orientation, while avoiding collisions between themselves and with obstacles in the environment. Convergence is global and complete, subject to the constraints of the navigation function methodology. Algebraic graph theoretic properties associated with the interconnection graph are shown to affect the shape of the navigation function. The approach is centralized but the potential function is constructed in a way that facilitates complete decentralization. The strategy presented will also serve as a point of reference and comparison in quantifying the cost of decentralization in terms of performance.

Nonholonomic motion planning for mobile manipulators

A nonholonomic motion planner for mobile manipulators moving in cluttered environments is presented. The approach is based on a discontinuous feedback law under the influence of a special potential field. Convergence is shown via Lyapunovs direct method. Utilizing redundancy, the methodology allows the system to perform secondary, configuration dependent, objectives such as singularity avoidance. It introduces an efficient feedback scheme for real time navigation of nonholonomic systems.

Formation Stabilization of Multiple Agents Using Decentralized Navigation Functions.

We develop decentralized cooperative controllers, which are based on local navigation functions and yield (almost) global asymptotic stability of a group of mobile agents to a desired formation and simultaneous collision avoidance. The formation could be achieved anywhere in the free space; there are no pre-specified final positions for the agents and is rendered stable both in terms of shape and in terms of orientation. Shape and orientation stabilization is possible because the agents regulate relative positions rather than distances with respect to their network neighbors. Asymptotic stability is provable and guaranteed, once the parameters in the local navigation functions are tuned based on the geometry of the environment and the degree of the interconnection network. Feedback controllers steer the agents away from stationary point-obstacles and into the desired formation using information that can be obtained within their sensing neighborhood and through communication with their network neighbors. The methodology is tested in simulation where groups of three and four mobile agents come into formations of triangles and diamonds, navigating amongst obstacles.