Robustness of a class of three-dimensional curve tracking control laws under time delays and polygonal state constraints

We analyze the robustness of a class of controllers that enable three-dimensional curve tracking of free moving particles. By building a strict Lyapunov function and robustly forwardly invariant sets, we show input-to-state stability under predictable tolerance and safety bounds that guarantee robustness under control uncertainty, input delays, and a class of polygonal state constraints. Such understanding may provide certified performance when the control laws are applied to real life systems. We demonstrate our findings in simulations.