Calculus & Optimization
Gradients, Lagrangians, convexity — how robots decide.
Why it matters in robotics
Almost every decision a robot makes — a trajectory, a grasp, a control input, a sensor-fusion estimate — is the solution to an optimization problem, so interviewers probe whether you can set up an objective, encode constraints, and reason about gradients and convexity. Expect questions on Lagrange multipliers and KKT conditions, why convex problems are tractable while non-convex ones get stuck in local minima, and how gradient descent and its variants actually converge. Being fluent here signals you can move from a planning/control idea to a solvable formulation, which is the daily work of a robotics engineer.
Application focus
The same topic, tailored to the robot you're building. Your choice is remembered across the roadmap and every topic.
At a glance
How an optimization-based robot decides: a cost and constraints become a Lagrangian, whose stationary (KKT) conditions a convex/gradient solver drives to the optimal action.
What to study
- ✓Gradients, Jacobians, and Hessians; gradient descent and its convergence behavior (step size, conditioning, local vs. global minima)
- ✓Constrained optimization: Lagrange multipliers, the Lagrangian, and KKT conditions for equality/inequality constraints
- ✓Convexity: convex sets and functions, why convex problems have a global optimum, and recognizing LP/QP/SOCP/SDP standard forms
- ✓Applying it in robotics: formulating trajectory optimization and convex MPC, and solving problems with tools like CVXPY
Study by time budget
Pick the path that fits the time you have before your interview.