Real-Time Generation of Near Minimum-Energy Trajectories via Constraint-Informed Residual Learning: A Paradigm for Learning From Optimal Solutions

Industrial robotics demands significant energy to operate, making energy-reduction methodologies increasingly important. Strategies for planning minimum-energy trajectories typically involve solving nonlinear optimal control problems (OCPs), which rarely cope with real-time (RT) requirements. In this article, we propose a paradigm for generating near minimum-energy trajectories for manipulators by learning from optimal solutions. Our paradigm leverages a residual learning approach, which embeds boundary conditions (BCs) while focusing on learning only the adjustments needed to steer a standard solution to an optimal one. Compared to a computationally expensive OCP-based planner, our paradigm achieves 87.3% of the performance near the training dataset and 50.8% far from the dataset, while being two to three orders-of-magnitude faster.