Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences


UC Berkeley


2009 Research Summary

Passivity and Time-Scale Decomposition Techniques for Robust and Adaptive Cooperative Control

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Murat Arcak

Air Force Office of Scientific Research FA9550-07-1-0308

The goal of this project is developing a new approach to decentralized cooperative control design using passivity techniques, assisted by singular perturbation and averaging methods for enhanced robustness and adaptivity features. The advantages of this approach include: (1) the ability to allow high-order, nonlinear, and heterogenous agent dynamics; (2) modularity of the design procedure in which the internal control of an agent relies on very little information about the external interconnection structure; and (3) broad applicability to various coordination problems, including synchronization and agreement for sensor networks, formation stabilization, gradient climbing, and synchronized path-following for distributed UAVs.

As we have shown in [1], when the information flow between neighboring members is bidirectional, the closed-loop system exhibits a special interconnection structure that inherits the passivity properties of its components. By exploiting this structure we have developed a passivity-based design which results in a broad class of feedback rules that encompass as special cases some of the existing formation stabilization and group agreement designs in the literature. This design technique has been extended in [2] below to path following control where the only information that is exchanged between the vehicles is a path variable that parameterizes the prescribed path for each vehicle.

A key advantage of the passivity-based approach developed in this project is the design flexibility it offers. We have demonstrated this flexibility in [3] with an adaptive redesign applicable when the reference velocity for the group is available only to a leader and the others have access to the relative distance and relative orientation with respect to their neighbors. In [4] we have reported an application of this adaptive paradigm to a gradient climbing problem in which the leader performs extremum seeking to reach the minima or maxima of a field distribution and the other vehicles maintain a formation with respect to the leader. As depicted in Figure 1 below, the leader performs a dither motion from which it collects samples of the field and generates finite-difference approximations for the gradient and the Hessian. This information is then used to determine the next Newton direction.

A further advantage of the passivity-based approach is that complex agent dynamic models can be allowed in this design framework thanks to their inherent passivity properties. We are currently developing a design in which the agents are modeled as rigid bodies, and attitude coordination is achieved with local feedback rules that do not require inertial frame information. A complementary research direction pursued in this project is model reduction of vehicle swarms via time-scale decomposition techniques as presented in [5].

Figure 1
Figure 1: Gradient climbing by extremum seeking. The arrows represent the slow Newton motion. Triangular paths represent the fast dither motion with the samples taken at positions marked by dots.

M. Arcak, "Passivity as a Design Tool for Group Coordination," IEEE Transactions on Automatic Control, Vol. 52, No. 8, 2007, pp. 1380-1390.
I.-A. F. Ihle, M. Arcak, and T. I. Fossen, "Passivity-based Designs for Synchronized Path Following," Automatica, Vol. 43, No. 9, 2007, pp. 1508-1518.
H. Bai, M. Arcak, and J. T. Wen, "Adaptive Design for Reference Velocity Recovery in Motion Coordination," Systems and Control Letters, Vol. 57, No. 8, 2008, pp. 602-610.
E. Biyik and M. Arcak, "Gradient Climbing in Formation via Extremum Seeking and Passivity-based Coordination Rules," Asian Journal of Control, Vol. 10, No. 2 (Special Issue on Collective Behavior and Control of Multi-Agent Systems), 2008, pp. 201-211.
E. Biyik and M. Arcak, "Area Aggregation and Time-Scale Modeling for Sparse Nonlinear Networks," Systems and Control Letters, Vol. 57, No. 2, 2008, pp. 142-149.