
SLAM is a computational method for a device to simultaneously construct a map of its environment and locate itself within that map.SLAM is a mathematical framework that enables a moving platform (robot, drone, car) to simultaneously refine its own position in space and build a map of the environment. It is based on a probabilistic approach: the robot doesn't store a single exact position, but rather a whole fan of possible positions with varying degrees of confidence. Each new sensor measurement — from a laser rangefinder (lidar), inertial sensors, cameras — updates this distribution. The key idea is loop closure: when the robot returns to a previously visited place, it recognizes it and sharply reduces the accumulated error.
The concept of SLAM was formalized by Hugh Durrant-Whyte and John J. Leonard in 1991, although earlier works (e.g., Cheyne, 1986) had already tackled similar problems. Early implementations relied on the extended Kalman filter (EKF) and worked with radar or sonar data. A turning point came in 2002, when Montemerlo and Thrun introduced FastSLAM — a particle filter-based algorithm capable of processing thousands of landmarks in real time. Modern approaches, such as ORB-SLAM, use multi-sensor fusion and graph architectures, achieving high accuracy at large scales.
Probabilistic SLAM models the joint distribution P(x_{1:t}, m | z_{1:t}, u_{1:t}), where x is the trajectory, m is the map, z are observations, and u are control inputs. Recursive Bayesian filtering is commonly used: prediction based on a motion model, correction using sensor data. In Graph SLAM, the problem is transformed into a sparse graph where nodes are robot poses and landmarks, and edges are constraints from odometry and observations. Optimizing the graph using Newton-Gauss or Levenberg-Marquardt methods yields the best estimate of the entire history. For loop closure, place recognition methods are used — often based on visual bags of words (BoW) for camera systems. Particle filters, in turn, represent the distribution with a set of hypotheses (particles), each with its own map; this approach is effective for nonlinear models and non-normal noise.
A self-driving car doesn't drive blindly — it builds a 3D model of the street and knows where it is. Robot vacuums memorize the layout of an apartment so they don't miss corners.
Some SLAM systems use multiple cameras and inertial sensors at once, similar to how a person orients themselves by looking with their eyes and sensing the tilt of their body.

















