(Georgia Institute of Technology, 2019-12)
Chen, Jiaqi
Chinese calligraphy is unique and has great artistic value but is difficult to master. In this paper, we make robots write calligraphy. Learning methods could teach robots to write, but may not be able to generalize to new characters. As such, we formulate the calligraphy writing problem as a trajectory optimization problem, and propose a new virtual brush model for simulating the dynamic writing process.Our optimization approach is taken from pseudospectral optimal control, where the proposed dynamic virtual brush model plays a key role in formulating the objective function to be optimized. We also propose a stroke-level optimization to achieve better performance compared to the character-level optimization proposed in previous work. Our methodology shows good performance in drawing aesthetically pleasing characters.
(Georgia Institute of Technology, 2016-12)
Jimenez Rodriguez, Ivan Dario Dario
Several problems in robotics can be solved using constrained optimization. For example, solutions in areas like control and planning frequently use it. Meanwhile, the Georgia Tech Smoothing and Mapping (GTSAM) toolbox provides a straight forward way to represent sparse least-square optimization problems as factor graphs. Factor graphs, are a popular graphical model to represent a factorization of a probability distribution allowing for efficient computations. This paper demonstrates the use of the GTSAM and factor graphs to solve linear and quadratic constrained optimization programs using the active set method. It also includes an implementation of a line search method for sequential quadratic programming that can solve nonlinear equality constrained problems. The result is a constrained optimization framework that allows the user to think of optimization problems as solving a series of factor graphs and is open-source.