Learning Stable Dynamics Via Iterative Quadratic Programming

This paper proposes a novel autonomous dynamic system (ADS) based controller for trajectory learning from demonstration (LfD). We call our method Learning Stable Dynamics via Iterative Quadratic Programming (LSD-IQP). LSD-IQP learns an energy function and an ADS from demon- strations via semi-infinite quadratic programming. Energy function constraints are imposed on the learned ADS to ensure convergence to a single goal position. Unlike other energy-based methods, LSD-IQP allows the energy function to have both local maximums and saddle points. This flexibility enables LSD- IQP to learn a broader class of motions compared to other ADS-based controllers. We demonstrate the capabilities of LSD- IQP via several experiments, including: 1) learning handwritten symbols and comparing the swept error area to several other ADS methods 2) learning a pick-and-place task with novel goal positions for a robot, and 3) learning a point to point motion in the presence of a non-convex obstacle for a robot.