Implementation of 12 Transition Controls for Rotary Double Inverted Pendulum Using Direct Collocation Topics: Engineering Applications on Intelligent Control Systems and Optimization; Mechatronics Systems; Optimization Algorithms; Real-Time Systems Control; System Modeling In Proceedings of the 21st International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, 92-100, 2024 , Porto, Portugal