Featherstone Articulated Body Physics Engine

A C++ articulated body physics engine for interactive demos and experiments.

Features

Featherstone-based forward dynamics

Implements RNEA (Recursive Newton–Euler Algorithm) and CRBA (Composite Rigid Body Algorithm), as described in Rigid Body Dynamics Algorithms by Featherstone, at the core of the solver.

Closed-loop constraint support

Supports closed-loop systems using simple joints as loop-closure constraints. Loop closure is enforced at the acceleration level, with Baumgarte-stabilized velocity and position terms.

Joint and DoF coupling

Supports coupling across joints and degrees of freedom by modeling coupling as linear constraints between DoFs. Constraints are resolved by parameterizing joint accelerations using the orthogonal complement basis of the constraint matrix.

Impulse-based contact resolution

Solves contacts using an impulse-based approach, implementing Projected Gauss–Seidel (PGS) with Sequential Impulses (SI) and impulse warm starting. Impulses transmitted across loop-closure joints are also accounted for during collision handling.

Springs

Solves spring forces using a semi-implicit Euler integration scheme, improving numerical stability and preventing blow-up for stiff springs.

glTF-based physics asset pipeline

Streamlines physics asset creation and the simulation pipeline by supporting construction of a physics world from glTF physics assets exported from Blender.

Supported Joints

| Joint Type | Dynamics Model | Support Loop Closure | Support Spring | |----|---|---|---| | Revolute | Motion subspace | ✅ | ✅ | | Prismatic | Motion subspace | ✅ | ✅ | | Cylindrical | Motion subspace | ✅ | ✅ *both DoFs | | Spherical | Motion subspace | ✅ | ❌ | | Gear | Coupling 2 revolutes | ❌ | ✅ *both joints | | Rack and Pinion | Coupling a revolute and a prismatic | ❌ | ✅ *both joints | | Screw | Coupling the 2 DoFs of a cylindrical | ❌ | ✅ *both DoFs | | Worm | Coupling linear DoF of a cylindrical and a revolute | ❌ | ✅ *all DoFs and joints |

• A spring cannot be applied to a joint when the joint is a loop closure.

Demos

YouTube link

What each of these demos demonstrates | Name | Demo | Articulated | Loop Closure | Spring | Coupling | Spherical Joint | Trivial PID Control | |---|---|---|---|---|---|---|---| | Scissor Lift | <img src="media/scissor_lift.gif" width="200"/> | ✅ | ✅ | ❌ | ❌ | ❌ | ❌ | | Worm Screw Jack | <img src="media/worm_screw_jack.gif" width="200"/> | ✅ | ✅ | ❌ | ✅*heavy | ❌ | ✅ | | Spring Scale | <img src="media/spring_scale.gif" width="200"/> | ✅ | ❌ | ✅*stiff | ✅ | ❌ | ❌ | | Double Wishbone Suspension | <img src="media/double_wishbone.gif" width="200"/> | ✅ | ✅ | ✅ | ❌ | ✅ | ✅ | | Collision and Scene Test | <img src="media/wrecking_ball.gif" width="200"/> | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | | Spring Test | <img src="media/spring_test.gif" width="200"/> | ✅ | ✅ | ✅*stiff | ❌ | ❌ | ❌ | | Spherical Joint Test | <img src="media/spherical_test.gif" width="200"/> | ✅ | ✅ | ❌ | ❌ | ✅ | ❌ |

Dependencies

• BulletCollision, Bullet v3.25
  Only the collision detection components are used. Collision resolution is implemented separately within this project.
  Refer to third_party/bullet for build instructions.

• nlohmann/json v3.12.0

• raylib v5.5

• tinygltf v2.9.5

• Eigen v3.4.0
  Used for core Featherstone dynamics.

• glm v1.0.1
  Used alongside raylib for rendering utilities.

• glTF_Physics_Blender_Exporter v0.5.4
  Install this exporter in Blender if you need to generate physics-enabled assets.
  Note that there are certain limitations and caveats in the asset generation process. These will either be resolved in future updates or documented separately in an instruction guide.

  glTF Physics is not an official feature supported by the glTF specification.

Build

Required CMake Parameters

The following CMake cache variables must be specified if the libraries are not installed system-wide:

• EIGEN3_INCLUDE_DIR — Path to the Eigen include directory
• GLM_INCLUDE_DIR — Path to the GLM include directory

Example (Windows – Visual Studio 2022)

cmake -DEIGEN3_INCLUDE_DIR=[your Eigen directory] -DGLM_INCLUDE_DIR=[your GLM directory]  .. -G "Visual Studio 17 2022"

Tested On

• Windows 10 / Visual Studio 2022

Next Steps

• Expand joint types (e.g., fixed joints, 6-DoF joints)
• Inverse dynamics and inverse kinematics for more sophisticated control
• Contact block solver for improved convergence and performance
• Coulomb friction formulated as a linear complementarity problem (LCP)
• Joint limits with impulse-based enforcement
• Rotational friction models at contact points
• CCD (Continuous Collision Detection)