An overview of Forward Dynamics Algorithms and their use in Open Source Dynamics Engines

Simulation of real-world dynamics is of major importance in testing and verifying developed industrial concepts and solutions, developing and verifying potential control paradigms, scientific research, learning and training tools, or the entertainment industry as a basis for a game engine. The module of the 3D virtual simulator that achieves simulation of the real-world behaviour such as rigid and elastic body dynamics, particle dynamics, fluid dynamics, electrodynamics, magnetism, etc., is often referred to as a dynamics engine or physics engine. The core of the rigid body dynamics (physics) engine is the solution to the forward dynamics problem, which is defined as finding a rigid body's path, velocity, and acceleration for a given input actuating torque and external forces. The past few decades saw a considerable amount of research in robot dynamics modelling, and there are many methods for robot dynamic model development available in the literature. The most commonly used algorithms for solving robot forward dynamics problem are the Composite-Rigid-Body Algorithm (CRBA) [1] and the Articulated-Body Algorithm (ABA) [2]. CRBA and ABA are reduced coordinate methods where known constraints, such as joints, are embedded in the formulation of the equations of motion. Besides reduced coordinate methods, there are maximal coordinate methods using Lagrange multipliers [3-4] to enforce constraints using constraint reaction forces.