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Robotics & Kinematics

From four-bar linkages to FABRIK inverse kinematics — this category explores the mathematics of machines that move. Each interactive Robotics model runs in your browser, covering joint chains and inverse kinematics, path planning with A*, Dijkstra and BFS, swarm coordination for drones, the chaotic double pendulum, and the alternating gaits of a six-legged hexapod walker. Click targets, drag joints, draw obstacles, and watch constraint solvers and search frontiers respond in real time. You will learn how robot arms reach precise poses, how autonomous agents navigate cluttered space, and how local rules produce emergent group behaviour. The same algorithms power industrial manipulators, warehouse automation, self-driving vehicles and animated game characters — which is why building hands-on intuition for these ideas matters far beyond the classroom.

6 simulations Canvas 2D · Three.js IK · Pathfinding · Pendulum

Category Simulations

Mechanisms, motion planning and manipulator control

Robotics is applied geometry — representing joint chains as rotation matrices, solving position constraints iteratively, and planning collision-free paths through configuration space. The same mathematics drives both industrial arms and animated character skeletons in games.

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★★★ Advanced New
LiDAR Scanning
A rotating 2D LiDAR fires rays that ray-march to walls, building a noisy point cloud and a log-odds occupancy grid. Drag the sensor around rooms and corridors.
LiDARPoint CloudOccupancy GridCanvas 2D
⚙️
★★☆ Moderate
Mechanisms & Linkages
Four-bar linkages, Peaucellier cell, Watt's linkage and Chebyshev's mechanism. Drag joints to see coupler curves — the foundations of mechanical engineering.
Canvas 2D Kinematics Constraints
🗺️
★★☆ Moderate
Pathfinding
A*, Dijkstra and BFS visualised on an interactive grid. Draw walls, set start/goal, and watch the search frontier expand in real time.
Canvas 2D A* Dijkstra
🔗
★★☆ Moderate
Double Pendulum
Chaotic two-link pendulum solved with RK4. Multi-pendulum traces reveal the butterfly-like sensitivity to initial conditions.
Canvas 2D RK4 Lagrangian Mechanics
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★★☆ Moderate
Inverse Kinematics (FABRIK)
Click anywhere to set a target and watch the arm chain reach it using FABRIK's alternating forward-backward passes. Multi-chain branching support.
Canvas 2D FABRIK IK Solver
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★★★ Advanced
Drone Swarm
N quadrotors flock using Boids-style decentralised rules plus formation holding. Four formations: Flock, Circle, Grid, V-Shape.
Canvas 2D Boids Swarm
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★★★ Advanced
Hexapod Walker
Six-legged robot with per-leg 2-link IK and alternating tripod or wave gait. Flat and bumpy terrain modes.
Canvas 2D Gait Planning IK

Key Concepts

The mathematics of machines that move

FABRIK IK
Forward And Backward Reaching Inverse Kinematics. Alternates: forward pass stretches chain from root toward target; backward pass re-anchors root. Converges in O(iterations × N) — no matrix inversion needed. Works for branching chains.
Four-Bar Linkage
Ground + three moving links forming a closed quadrilateral. The coupler point traces a coupler curve: nearly straight lines (Watt), figure-8s, and more. Fundamental building block of mechanical clocks, engines, and articulated robots.
A* Pathfinding
Priority-queue search sorting nodes by f(n) = g(n) + h(n): actual cost + heuristic estimate. Admissible heuristic (never overestimates) guarantees optimal path. Euclidean distance h for grid robots, pre-computed hierarchical maps for games.
Lagrangian Mechanics
L = T − V (kinetic minus potential energy). Euler-Lagrange equations give equations of motion for any joint-chain system. Avoids Newton's vector force analysis — only scalar energy expressions needed. Standard derivation for robots and double pendulums.

Learning Resources

Articles and tutorials about robotics algorithms

Article IK FABRIK: From Scratch in JavaScript Full walkthrough: link chain, forward pass, backward pass, angle limits, branching. Live canvas demo included. →
All articles →

About Robotics & Automation Simulations

Pathfinding, kinematics, swarm control, and autonomous agents — live

Robotics and automation simulations model the algorithms that allow machines to perceive space, plan paths, and execute tasks. Pathfinding simulations visualise A*, Dijkstra, and RRT algorithms navigating a robot arm or autonomous vehicle through obstacle fields. Swarm robotics simulations place dozens of agents in a shared environment and implement flocking, formation control, and collective task allocation using only local sensor information.

Inverse kinematics solvers animate multi-link robot arms reaching toward targets using Jacobian gradient methods. These models are directly relevant to the algorithms running in industrial manipulators, autonomous delivery robots, warehouse automation systems, and drone swarms. By interacting with cost functions, sensor noise levels, and obstacle layouts you discover the trade-offs between path optimality, computational cost, and real-time performance.

Each simulation in this category is built with accuracy and interactivity in mind. The underlying mathematical models are the same ones used in academic research and professional engineering — just made accessible through a web browser. Changing parameters in real time and observing the results is one of the most effective ways to build intuition for complex scientific and engineering concepts.

Key Concepts

Topics and algorithms you'll explore in this category

Interactive ModelReal-time browser simulation with live parameter controls
WebGL / Canvas 2DHardware-accelerated rendering in the browser
Mathematical FoundationDifferential equations and numerical integration
Open SourceMIT-licensed code — inspect, fork, and learn
No Install RequiredRuns directly in Chrome, Firefox, Safari, Edge
Educational FocusBuilt to explain the underlying science clearly

🤖 Test Your Robotics Knowledge

Five quick questions to check your understanding of robotics and autonomous systems

Robotics Quiz

Frequently Asked Questions

Common questions about this simulation category

How does the FABRIK inverse kinematics algorithm work?
FABRIK (Forward And Backward Reaching Inverse Kinematics) solves joint-chain positioning without matrix inversion. The forward pass stretches each link from root toward the target; the backward pass re-anchors the root and propagates back. Repeating these two passes converges in O(iterations × N) time and handles joint angle constraints and branching chains. Click anywhere in the Inverse Kinematics simulation to see the arm reach.
What path planning algorithms are simulated?
The Pathfinding simulation lets you compare A*, Dijkstra, and BFS side by side on an interactive obstacle grid. A* is generally fastest because it uses a heuristic h(n) to focus the search toward the goal. Dijkstra explores uniformly and guarantees the shortest path. BFS finds the fewest-hop path on unweighted grids. All three are visualised with open/closed sets shown live.
How does the drone swarm maintain formation?
Each drone in the swarm applies three forces: a Boids-style local force (separation, alignment, cohesion with nearby drones) and a formation-holding force pulling it toward its assigned slot in the target pattern. The balance between these forces creates stable formations (Flock, Circle, Grid, V-Shape) while still allowing organic swarm behaviour when drones are disturbed.
What makes the double pendulum chaotic?
The double pendulum's equations of motion (derived from the Lagrangian L = T − V) are coupled and nonlinear. Two trajectories that start with nearly identical initial conditions diverge exponentially — a hallmark of chaos. The Lyapunov exponent measures this divergence rate. In the simulation you can launch multiple pendulums with tiny angle differences and watch them quickly diverge into completely different trajectories.

Other Categories

Every Robotics simulation on this page is free, open-source and runs instantly in any modern browser — there is no better way to learn Robotics online than to experiment with the algorithms yourself. Each interactive Robotics model exposes live parameters so you can adjust joint limits, obstacle layouts, swarm sizes and gait patterns and immediately see the effect. These same techniques — inverse kinematics, motion planning and decentralised swarm control — underpin real-world applications such as warehouse picking robots, autonomous delivery drones and robotic surgical assistants, making this a practical foundation for students, engineers and curious tinkerers alike.