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IEEE Robotics and Automation Letters

Date of Publication: 12 January 2018 

https://doi.org/10.1109/LRA.2018.2792536

■  Researchers

Jemin Hwangbo, Joonho Lee, Marco Hutter

Robotic Systems Lab, ETH Zurich

■  Abstract

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.

■  Conclusion

We introduced the bisection method for solving contact dynamics which accounts for the non-diagonal dominant nature of the inverse apparent mass matrix. We found that it outperforms the two existing methods for a single contact problem at least by a factor of two. In addition, we fairly compared it against the PGS method on four robotic simulation tasks. The proposed method showed fast and consistent performance on all tasks whereas the PGS became significantly slow on complicated tasks. Our result shows that the proposed method can be a promising alternative to the existing contact solvers which employ many relaxations of the physical principles.

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