Physics

Iterative method

Relaxation (psychology)

Dynamic relaxation

Mathematics

Algorithm

Mathematical optimization

Epistemology

Dynamics (music)

Bisection method

Mathematical analysis

Philosophy

Iterated function

Artificial intelligence

Psychology

Gauss

Acoustics

Programming language

Geometry

Solver

Computer science

Simple (philosophy)

Quantum mechanics

Simulation

Computational science

Social psychology

Robot

IEEE Robotics and Automation Letters

This letter introduces a new iterative method for contact dynamics problems. The proposed method is based on an efficient bisection method which iterates over each contact. We compared our approach to two existing ones for the same model and found that it is about twice as fast as the existing ones. We also introduce four different robotic simulation experiments and compare the proposed method to the most common contact solver, the projected Gauss-Seidel (PGS) method. We show that, while both methods are very efficient in solving simple problems, the proposed method significantly outperforms the PGS method in more complicated contact scenarios. Simulating one time step of an 18-DOF quadruped robot with multiple contacts took less than 20 μs with a single core of a CPU. This is at least an order of magnitude faster than many other simulators which employ multiple relaxation methods to the major dynamic principles in order to boost their computational speed. The proposed simulation method is also stable at 50 Hz due to its strict adherence to the dynamical principles. Although the accuracy might be compromised at such a low update rate, this means that we can simulate an 18-DOF robot more than thousand times faster than the real time.

Per-Contact Iteration Method for Solving Contact Dynamics