Algorithms

Robotics systems rely on a rich toolbox of algorithms for sensing, estimation, control, planning and perception. Below is a comprehensive survey-organized by function-of core methods used in modern robots, with links to further reading.

Filtering & State Estimation

Kalman FIlter

• Kalman Filter: Optimal linear estimator for fusing motion models and noisy measurements (e.g., IMU + odometry) https://www.vaia.com/en-us/explanations/engineering/robotics-engineering/robotics-algorithms/
• Extended Kalman Filter (EKF): Nonlinear extension of the Kalman Filter for mapping and SLAM https://www.mdpi.com/2504-446X/7/6/339
• Unscented Kalman Filter (UKF): Deterministic sampling approach to nonlinear state estimation https://www.mdpi.com/2504-446X/7/6/339
• Particle Filter / Monte Carlo Localization: Uses a set of random samples (particles) to represent arbitrary distributions for robot pose https://arxiv.org/pdf/1301.0607.pdf
• FastSLAM / Rao–Blackwellized Particle Filter: Combines particle filters with per-feature Kalman filters for efficient SLAM https://arxiv.org/pdf/1301.0607.pdf
• Moving Average & Savitzky–Golay Filters: Simple smoothing techniques for sensor signal conditioning

• Butterworth & Chebyshev Filters: Frequency-domain filters for removing high-frequency noise

Control & Trajectory Tracking

PID Based Balancer

• PID (Proportional–Integral–Derivative): Ubiquitous feedback controller for setpoint tracking

• LQR (Linear Quadratic Regulator): Optimal state-feedback controller minimizing a quadratic cost

• MPC (Model Predictive Control): Online optimization of control signals subject to constraints

• H∞ Control: Robust control design against modeling uncertainties

• Feedforward / Inverse Dynamics: Calculates required joint torques for planned accelerations

Path Planning & Navigation

A* Algorithm

• Dijkstra’s Algorithm: Guaranteed shortest paths on weighted graphs

• A★ (A-Star): Heuristic search combining Dijkstra with best-first bias for efficient grid and graph planning https://roboticsbiz.com/path-planning-algorithms-for-robotic-systems/
• D★ / D★ Lite: Incremental replanning in dynamic or partially known environments https://roboticsbiz.com/path-planning-algorithms-for-robotic-systems/
• RRT (Rapidly-Exploring Random Trees): Sampling-based planner for high-dimensional spaces https://roboticsbiz.com/path-planning-algorithms-for-robotic-systems/
• PRM (Probabilistic Roadmap): Builds a graph of collision-free configurations offline for query planning

• RRT★ / PRM★: Asymptotically optimal variants of RRT and PRM

• Genetic Algorithms: Evolutionary search for path optimization in complex cost landscapes

• Ant Colony Optimization: Swarm-intelligence-inspired heuristic for shortest path discovery https://roboticsbiz.com/path-planning-algorithms-for-robotic-systems/
• Firefly & Particle Swarm Optimization: Nature-inspired metaheuristics for global path and parameter tuning

SLAM & Mapping

GRAPH SLAM

ORB SLAM

• EKF-SLAM: Maps landmarks with Gaussian estimates via EKF

• Graph-SLAM: Poses and landmarks jointly optimized in a large factor graph

• FastSLAM: Leverages particle filters for robot pose and separate Kalman filters for landmarks https://arxiv.org/pdf/1301.0607.pdf
• ORB-SLAM / LSD-SLAM: Visual SLAM systems using ORB features or direct image alignment

Optimization & Numerical Methods

• Gauss–Newton & Levenberg–Marquardt: Nonlinear least-squares solvers for bundle adjustment and calibration

• Gradient Descent & Stochastic Gradient Descent: Iterative minimization for learning and control parameter tuning

• Convex Optimization (CVX): Fast solvers for quadratic and semidefinite programs in control and state estimation

Perception & Computer Vision

• SIFT / SURF / ORB: Feature detection and description for landmark recognition and place recognition

• FAST & Shi–Tomasi Corner Detectors: Lightweight keypoint extractors for real-time tracking

• Lucas–Kanade & Horn–Schunck Optical Flow: Dense and sparse methods for image motion estimation

• RANSAC: Robust model fitting (e.g., fundamental matrix estimation) in the presence of outliers

• CNNs (Convolutional Neural Networks): Deep learning models for object detection and semantic segmentation

• YOLO / SSD / Mask R-CNN: Real-time detection and instance segmentation frameworks

Machine Learning & AI

• Reinforcement Learning (Q-Learning, DQN, PPO): Autonomous policy learning from interaction rewards

• Gaussian Processes: Nonparametric models for regression and uncertainty quantification in terrain modeling

• Support Vector Machines (SVM): Classification of sensor or vision data in low-dimensional feature spaces

By combining these algorithms-choosing the right filter for robust sensing, the optimal controller for precise motion, and the most suitable planner for agile navigation-robots can perceive, plan, and act reliably in complex, dynamic environments.