Showcase Of An Optimal Control Problem In Robotics For Integrating The System Matrices From A Multibody Simulation Code To Generate Adjoint Gradients For Optimization

An implementation in C++ is computationally more efficient than a Python code, especially in case of multibody system matrices. However, the analytical derivation and implementation of system matrices as well as gradients for optimization is elaborate and time consuming. Hence, the combination of C++ for critical performance parts and Python for the overhead and optimization is highly beneficial. A possible interface from ExuDyn to Python modules for optimization and parameter variation is shown e.g. in [1]. Moreover, PyChrono is a Python library that wraps the Chrono C++ multi-physics simulation library [2]. PyChrono can be used together with popular Python libraries, such as optimization or neural networks. The multibody simulation software HOTINT provides an interface to the optimization tool MagOpt allowing a multi-objective optimization [3]. PROPT [4] is a software package for solving highly complex dynamic optimization problems using the pseudo-spectral collocation methods of the TOMLAB solver. The goal of PROPT is to make the formulation of such problem descriptions as seamless as possible without having to worry about the solver. Here, the present work aims to make an important contribution for easy utilization of adjoint gradients. Using adjoint methods in large-scale optimization problems in multibody dynamics brings time efficiency and enables real-time applications, but the analytical derivation of the underlying system matrices is elaborate. Due to a wide upcoming community using the adjoint gradients in multibody dynamics, here a showcase for integrating the system matrices from multibody simulation to generate adjoint gradients for optimization is presented. For this reason, a robotic system for a rest-to-rest maneuver is shown in which matrices are utilized from the multibody simulation software FreeDyn [5] and used in classical Python optimization packages. By using existing system matrices, the effort required to adapt the optimization problem to new examples and tasks can be significantly reduced.

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