Nonlinear dynamical control systems
Nonlinear dynamical control systems
Stabilization of collective motion in a time-invariant flowfield on a rotating sphere
ACC'09 Proceedings of the 2009 conference on American Control Conference
Vision-based estimation of three-dimensional position and pose of multiple underwater vehicles
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
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We provide a Lyapunov-based design of decentralized control laws that stabilize relative equilibria in a model of self-propelled particles that travel on the surface of a sphere. Such control laws have applications in planetary-scale mobile sensing networks in air, sea, and space. Relative equilibria of the closed-loop model include formations in which all of the particles travel around a common circular trajectory. Particle interaction can be time-invariant or time-varying and directed or undirected. The algorithm for time-invariant and undirected particle interaction uses a gradient-like control induced from the associated Laplacian matrix. The algorithm for time-varying and directed interaction replaces average quantities in the control law with dynamic consensus variables. An augmented Laplacian algorithm is also proposed to stabilize symmetric circular formations.