On Handling Discontinuities in Adjoint-based Optimal Control of Multibody Systems

This paper presents the treatment of artificial discontinuities in a Hamiltonian-based optimal control of holonomically-constrained multibody systems. Discontinuities considered here are defined as artificial. As opposed to, e.g., impacts or unilateral constraints, they do not originate from physical phenomena, but they are the result of a particular action took against possible numerical issues instead. This action transforms the system into a hybrid one in which discrete events have to be considered. In the proposed approach, a general optimal control problem is formulated by approximating the optimal solutions with Chebyshev polynomials of the first kind in order to bound the number of design variables. The optimal control problem is solved by employing an efficient adjoint-based technique. A derivation of jump conditions for both state and adjoint variables are shown. An example showcasing the implementation of the proposed method is included as well. This work presents an intermediate step in deriving a framework, which would directly operate on time functions instead of time-independent parameters.