In various applications, achieving a complex task using many simple agents as opposed to a single agent, offers properties such as robustness, reconfigurability and maneuverability. Such properties of multi-agent systems have been exploited in the areas of distributed computing, distributed sensing, distributed beamforming, etc. A complex task is shared by multiple agents cooperating with each other. This cooperation could be in the form of agreeing on a variable of the system (consensus), achieving a geometric formation and so on. Motivated by such applications, we consider the cooperative tasks of achieving formations with attitude and velocity synchronisation for a group of nonholonomic mobile robots (unicycles and Mobile Inverted Pendulum (MIP) robots) and achieving consensus on the n-Sphere for driftless bilinear systems. We present control laws that achieve these tasks and validate them through simulations and experimentation on indigenously built robots.

In the implementation of these control laws, resources such as sampling, computation and communication are employed, which have to be judiciously used. Over the years, techniques such as minimum-attention control, event-triggered control, maximum hands-off control etc. have emerged, that utilise these resources optimally. With the same objective, we take up the task of implementing the control laws designed for MIP robots in an event-triggered manner.

The MIP robot presents motivating challenges for event-based control because of it's instability and the presence of a center manifold. A two-loop control architecture is used for the control of the MIP robot, with the inner-loop stabilizing the pitch dynamics and the outer-loop leading to cooperation with neighbors. For the event-based implementation of the inner-loop controller, based on the linearized model of the MIP robot, we present optimized thresholds for time-invariant and state-dependent triggering. The event-based implementation of the position stabilizing controller of the MIP robot, presents us with a setting hitherto unexplored in literature. After exploring the local input-to-state stability of nonlinear systems with center manifolds, we present event-triggering rules for such systems. We also present our attempt at designing the event-based implementation of the cooperative outer-loop.