2021/03/04 by Logan E. Beaver, Beaver, Logan E., Andreas A. Malikopoulos +1 · 5 citations
Computer Science · Decision Sciences · Engineering · #Dynamics and Control of Mechanical Systems #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Robotic Path Planning Algorithms #Robotics (cs.RO) #Simulation Techniques and Applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2103.03339
openalex publication_date 2021/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal control problems for a class of CPS with nonlinear dynamics. We exploit the property of differential flatness to simplify the Euler-Lagrange equations that arise during optimization, and this simplification eliminates the numerical instabilities that plague optimal control in general. We also present an explicit differential equation that describes the evolution of the optimal state trajectory, and we extend our results to consider both the unconstrained and constrained cases. Furthermore, we demonstrate the performance of our approach by generating the optimal trajectory for a planar manipulator with two revolute joints. We show in simulation that our approach is able to generate the constrained optimal trajectory in 4.5 ms while respecting workspace constraints and switching between a `left' and `right' bend in the elbow joint.