Math & Kinematics
Nonlinear Optimization
Nonlinear optimization is the minimization of a nonlinear objective subject to nonlinear constraints, the mathematical core of trajectory optimization, inverse kinematics, calibration, and SLAM back-ends. Robotics problems are typically solved with local gradient-based methods, sequential quadratic programming or interior-point solvers such as IPOPT and SNOPT, which find locally optimal solutions given a good initial guess.
Why it matters for physical AI
Most planning and estimation problems in robotics reduce to nonlinear programs, so solver speed, convergence behavior, and initialization strategies directly bound what runs on a real robot.
Build physical AI
Put these concepts to work on real hardware
Axol is a dual-arm robot built for physical AI — teleoperate it, collect demonstrations, and deploy learned policies out of the box.