Trajectory optimization is a critical research area in robotics and automation, especially in manufacturing industries where mechanical systems are often required to minimize the execution time or the consumed energy. In this context, the most common mechanical systems are those with a single degree of freedom because of their simplicity and ease of control. In this paper, we present an approach for the online optimization of minimum-time and minimum-energy trajectories for a robotic system with one degree of freedom. Point-to-point motions of the considered linear axis are planned online, without idle times, by leveraging a verified dynamic model of the robotic system, which also includes an accurate identification of friction parameters. Both minimum-time and minimum-energy trajectories are considered, and the performance of the online optimization using a selected open-source optimization tool is verified in different dynamic conditions of the system. The results of extensive experiments on a belt-driven robotic axis demonstrate the feasibility and the energy-saving capabilities of the proposed approach, as well as the flexibility of the online trajectory optimization in different scenarios, while meeting the kinematics and dynamics limits of the system and guaranteeing low computational time.
