**James Bern**

Postdoctoral Associate

MIT CSAIL

Distributed Robotics Lab

jbern@mit.edu

he / him / his

**Research:**Soft-Rigid Robot Design, Modeling, and Control

> Undergraduate Research Opportunities

**Draw Robots:**Data-Oriented Introduction to Graphics × Robotics

This is a short course to help undergraduate and early graduate researchers pick up the practical skills needed to do novel research at the intersection of computer graphics and robotics.

*click to enlarge sample slides*

**Optimization Glossary**

Notation: *E_x = dE / dx*, *E_xx = d ^{2}E / dx^{2}*.

*Gradient descent:* The first order Taylor expansion of the energy *E(x + dx) ≈ E(x) + E_x(x) dx**dx ← -E_x*

*Newton's method:* The first order Taylor expansion of the gradient *E_x(x + dx) ≈ E_x(x) + E_xx(x) dx**dx ← -inv(E_xx) E_x*

*Basic backtracking line search:*
Given current best guess *x* and search direction *dx**α**E(x + αdx) < E(x)**α = 1**α = 1/2**1/4**15**α*

*Direct sensitivity analysis:* Given control *u*, the resulting state *x(u)**C(u, x) = 0**C(u, x(u)) = 0**C_u + C_x x_u = 0**x_u = -inv(C_x) C_u*