Solving optimal control problems by exploiting inherent dynamical systems structures
The paper proposes a method combining local optimization and motion planning techniques based on exploiting inherent dynamical systems structures, such as symmetries and invariant manifolds. Prior to the optimal control, the dynamical system is analyzed for structural properties that can be used to compute pieces of trajectories that are stored in a motion planning library. In the context of mechanical systems, these motion planning candidates, named primitives, are given by relative equilibria induced by symmetries and motion on stable or unstable manifolds. The existence of controlled relative equilibria is studied with Lagrangian mechanics and symmetry reduction techniques. The approach is illustrated by two numerical examples.
scientific article; zbMATH DE number 6100217
scientific article