About Me

I am a researcher with a focus on designing serial and parallel robotic mechanisms and manipulators for various workspace requirements. I accomplish this through the development of non-convex global optimization algorithms for engineering applications that deal with structured polynomial systems. I have contributed to the development of algorithms in numerical algebraic geometry that exploit the phenomenon of monodromy and have applied them to solving problems in robotics. My research encompasses aspects of kinematics, algebraic geometry, combinatorics, complex analysis, ordinary differential equations, and data science. Using these techniques, I have solved an open research problem in computational kinematics, that of the general optimal path synthesis of four-bar mechanisms, which is a nonlinear least squares regression that can admit a maximum of around 1.8 million critical points. I have used manifold learning techniques to organize large sets of design candidates, and developed dimensional reduction techniques to visualize these higher dimensional optimization design spaces in 2D network graphs based on Morse-Smale complexes. I have also built GUI tools based on this dimensional reduction to aid engineers in designing planar and spatial mechanisms for applications such as humanoid fingers, legged robots, and deployable wing mechanisms for UAVs.

Up for a game of chess? Drop me a challenge here.

External Links

Video Highlights

Graphics

I. An atlas of four-bar linkages visualized using Uniform Manifold Approximation and Projection (UMAP). These ‘coupler curves’ generate approximately unit straight line segments within one-hundredth of a unit error deviation.

II. Views of the configuration spaces of a serial 2R (left half) and a parallel five-bar (right half).

1st row: The output workspace for each manipulator.

2nd row: The 2R admits two IK solutions, the five-bar admits four.

3rd row: The input actuator space for each manipulator, with holes visible for the five-bar.

4th row: An (x, y, ψ) view of the configuration manifold. The skewering line shows the locations of the IK solutions for a set (x, y).

III. Topological data analysis

PhD Summary

Optimal Kinematic Synthesis via Saddle Graphs Computed by Monodromy Loops

Adviser: Mark Plecnik

This thesis focuses on developing tools for designing closed chain robotic mechanisms through optimization of structured polynomial systems. A primary contribution of my work is the development of a heuristic technique in numerical algebraic geometry called random monodromy loops which can compute complete solutions to highly nonlinear polynomial system of equations (or function) with millions of roots (or critical points) significantly faster than classical continuation methods. A generalized optimization framework which can handle any number of design positions is proposed for the approximate kinematic synthesis of rigid-body mechanisms. Random monodromy loops is used to fully characterize the design space of polynomial objectives in the form of graph networks which identify minima of the objective function as vertices and connections between them via saddle points as edges. Such graphs are interactively presented to a designer, whereby edges are continuously traversed to navigate families of design candidates in between minima. Candidates can be further evaluated continuously across the graph according to auxiliary considerations for the exploration of design trade-offs. Graph-based representations and unsupervised machine learning can be used to process and visualize the large yield of design candidates which arise in the aforementioned design systems.