In this paper, we present the design, modeling, and real-time nonlinear model predictive control (NMPC) of an autonomous robotic boat. The robot is easy to manufacture, highly maneuverable, and capable of accurate trajectory tracking in both indoor and outdoor environments. In particular, a cross type four-thruster configuration is proposed for the robotic boat to produce efficient holonomic motions. The robot prototype is rapidly 3D-printed and then sealed by adhering several layers of fiberglass. To achieve accurate tracking control, we formulate an NMPC strategy for the four-controlinput boat with control input constraints, where the nonlinear dynamic model includes a Coriolis and centripetal matrix, the hydrodynamic added mass, and damping. By integrating "GPS" modules and an inertial measurement unit (IMU) into the robot, we demonstrate accurate trajectory tracking of the robotic boat along preplanned paths in both a swimming pool and a natural river. Furthermore, the code generation strategy employed in our paper yields a two order of magnitude improvement in the run time of the NMPC algorithm compared to similar systems. The robot is designed to form the basis for surface swarm robotics testbeds, on which collective algorithms for surface transportation and self-assembly of dynamic floating infrastructures can be assessed.
This tutorial article describes a dynamical systems framework rooted in evolutionary game principles to characterize non-cooperative strategic interactions among large populations of bounded rationality agents. It also overviews recent results that use passivity notions to characterize the stability of Nash-like equilibria. In our framework, each agent belongs to a population that prescribes to its members a strategy set and a strategy revision protocol. A so-called social state registers the proportions of agents in every population adopting each strategy and a pre-selected dynamic payoff mechanism, specified by a payoff dynamics model (PDM), determines the payoff as a causal map of the social state. According to the framework, each agent must take up a strategy at a time, which it can repeatedly revise over time based on its current strategy, and information about the payoff and social state available to it. The PDM class considered in our framework can model precisely or approximately prevalent dynamic behaviors such as inertia and delays that are inherent to learning and network effects, which cannot be captured using conventional memoryless payoff mechanisms (often referred to as population games).We organize the article in two main parts. The first introduces basic concepts prevailing in existing approaches in which a population game determines the payoff, while the second considers rather general PDM classes, of which every population game is a particular case. The latter expounds a passivity-based methodology to characterize convergence of the social state to Nash-like equilibria.
This paper investigates an energy conservation and dissipation -passivity -aspect of dynamic models in evolutionary game theory. We define a notion of passivity using the state-space representation of the models, and we devise systematic methods to examine passivity and to identify properties of passive dynamic models. Based on the methods, we describe how passivity is connected to stability in population games and illustrate stability of passive dynamic models using numerical simulations.
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