Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

   

2009 Research Summary

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

View Current Project Information

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.

[1]
M. Arcak, "Passivity as a Design Tool for Group Coordination," IEEE Transactions on Automatic Control, Vol. 52, No. 8, 2007, pp. 1380-1390.
[2]
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.
[3]
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.
[4]
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.
[5]
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.