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		✅	✅	❌	❌	❌	❌
Worm Screw Jack		✅	✅	❌	✅*heavy	❌	✅
Spring Scale		✅	❌	✅*stiff	✅	❌	❌
Double Wishbone Suspension		✅	✅	✅	❌	✅	✅
Collision and Scene Test		❌	❌	❌	❌	❌	❌
Spring Test		✅	✅	✅*stiff	❌	❌	❌
Spherical Joint Test		✅	✅	❌	❌	✅	❌

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