Abstract
In this letter, we introduce a decentralized, nonlinear, discontinuous, and computationally simple control law for large scale multiagent navigation systems. The control is based on extending Gauss's principle of least constraint with a dynamic incorporation of inequality constraints, actuator saturation, and actuator dynamics. With no individual path planner, each agent executes its motion and generates its control actions by reacting solely to the evolution of its constrained dynamics, which is equivalent to solving a linear matrix equation with a dimension up to around 20 without iteration at each time instant. Numerical experiments are conducted on hundreds of two-dimensional (2-D) double integrators subjected to path and collision constraints, demonstrating the promise of the proposed method.
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