Math & Kinematics

Monte Carlo Methods

Monte Carlo methods are computational techniques that estimate quantities by averaging over random samples rather than computing them analytically, with accuracy improving as sample count grows. Robotics applications pervade the stack: particle filters for state estimation, sampling-based motion planners, Monte Carlo return estimates in reinforcement learning, Monte Carlo tree search for decision-making, and randomized rollouts in sampling-based controllers such as MPPI.

Why it matters for physical AI

Uncertainty is irreducible in real-world sensing and dynamics; sampling-based approximations are frequently the only tractable way to propagate that uncertainty through nonlinear models for estimation, planning, and evaluation.