Kalman Filter SLAM

Simultaneous localization and mapping using the Extended Kalman Filter to jointly estimate robot pose and landmark positions.

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Motion Planning

Algorithms for finding collision-free, dynamically feasible, and optimally smooth robot trajectories from start to goal.

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Occupancy Grid Mapping

Bayesian grid-based environment representation where each cell independently tracks its probability of being occupied.

bayes theorem probability theory information theory

Optimal Control in Robotics

Optimal control finds inputs that minimize a cost functional over a trajectory, from LQR for linear systems to MPC and iLQR for nonlinear robots.

control theory optimization variational calculus

PID Control

The proportional-integral-derivative controller — the most widely deployed feedback control law in engineering.

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Particle Filter

Monte Carlo localization represents robot belief as a set of weighted particles, enabling non-Gaussian, multi-modal distributions over robot pose.

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Probabilistic Roadmaps

Sampling-based motion planning algorithms that construct roadmaps in configuration space to find collision-free paths.

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Robot Dynamics

Equations of motion for rigid-body robot manipulators derived via Lagrangian mechanics and computed efficiently with the Newton-Euler algorithm.

differential equations linear algebra variational calculus

Robot Kinematics

Forward and inverse kinematics for serial manipulators using homogeneous transforms, DH parameters, and the geometric Jacobian.

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Visual Odometry

Estimating ego-motion from camera images by tracking visual features across frames using epipolar geometry and PnP solvers.

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