A learning approach to the FOM problem

Hogan recently provided an heuristic technique called family of modes (FOM) to solve model predictive control (MPC) problems under hybrid constraints and underactuation. The goal of this study is to further develop this new method and to expand its usage in the robotics manipulation community. With that objective in mind, we address some of the method's weaknesses, we provide comparison tools to try to compare the method with traditional MPC solving techniques and we provide a simple and systematic technique to set-up the method's parameters. We conclude the study by presenting our the future lines of research, which consist in generalizing the method for more complex systems and testing it's robustness.Outgoin

Extension of the SWIFT option pricing scheme for european options calibration under Heston stochastic volatility model

A Heston model calibration technique is presented for European options under the Heston model. The novel Shannon Wavelets Inverse Fourier Technique (SWIFT) is extended for European option price calibration (previously it was used only for pricing European, Asian, barrier, and Bermudan options). This method has different expressions and speed-up techniques, adequate to different set-ups. These are discussed and new expressions and properties are presented for the gradient computation and option calibration. The Heston characteristic function expression recently proposed by \cite{cui17} is used in the SWIFT implementation due to its analytic gradient and its continuity properties. The time performance, robustness, and convergence under set-ups representative of real markets is studied for different implementations of the SWIFT technique and compared with the option calibration scheme presented by \cite{cui17} The SWIFT implementations are coded in C++ and uploaded to a public GitHub repository. The libray implements several of the different SWIFT expressions for GBM and Heston European options

Reactive Planar Manipulation with Convex Hybrid MPC

This paper presents a reactive controller for planar manipulation tasks that leverages machine learning to achieve real-time performance. The approach is based on a Model Predictive Control (MPC) formulation, where the goal is to find an optimal sequence of robot motions to achieve a desired object motion. Due to the multiple contact modes associated with frictional interactions, the resulting optimization program suffers from combinatorial complexity when tasked with determining the optimal sequence of modes. To overcome this difficulty, we formulate the search for the optimal mode sequences offline, separately from the search for optimal control inputs online. Using tools from machine learning, this leads to a convex hybrid MPC program that can be solved in real-time. We validate our algorithm on a planar manipulation experimental setup where results show that the convex hybrid MPC formulation with learned modes achieves good closed-loop performance on a trajectory tracking problem

A learning approach to the FOM problem

Hogan recently provided an heuristic technique called family of modes (FOM) to solve model predictive control (MPC) problems under hybrid constraints and underactuation. The goal of this study is to further develop this new method and to expand its usage in the robotics manipulation community. With that objective in mind, we address some of the method's weaknesses, we provide comparison tools to try to compare the method with traditional MPC solving techniques and we provide a simple and systematic technique to set-up the method's parameters. We conclude the study by presenting our the future lines of research, which consist in generalizing the method for more complex systems and testing it's robustness.Outgoin

Reactive Planar Manipulation with Convex Hybrid MPC

NSF (Award IIS-1637753