Human activities like ball bouncing and trampoline jumping demonstrate an intuitive ability to tune into and excite a system’s natural resonant motions. While this sensitivity to resonance has been observed in simple linear systems, it’s more difficult to confirm in complex, nonlinear systems due to their unpredictable dynamics.
However, it has been found that many nonlinear systems still exhibit periodic behaviors that resemble the resonant modes seen in linear systems.
Alin Albu-Schäffer, a professor at the Chair of Sensor-based Robotic Systems and Intelligent Assistance Systems at TUM, has successfully transferred this method to robot movement. They have developed a new tool to make these intrinsic, highly efficient movements calculable. Because of this new tool, they can find out which system movements are particularly economical.
In their research on efficient and versatile legged locomotion, the team uses BERT, a four-legged robot resembling a small dog, designed by Prof. Albu-Schäffer at the German Aerospace Centre (DLR). The EU’s ERC Advanced Grant funds the project and focuses on improving robotic movement.
The researchers identified six movement patterns for BERT, which Prof. Albu-Schäffer described as exceptionally effortless—so effortless that they would require no energy in a frictionless world. These patterns mirror common quadruped gaits, such as walking, trotting, and hopping.
Annika Schmidt from Prof. Albu-Schäffer’s research team. With one difference, it said, “To realize these movements in a natural system with friction, a computer-controlled regulator has now been added that delivers an impulse at the right moment.”
“You can compare it to a child sitting on a playground swing and receiving an energy impulse at the highest point from the parent who is pushing. Humans don’t need a lot of equations in their heads to time their push exactly—they do it intuitively.”
Success is demonstrated in a race between three BERT models, where the robot dog programmed with the intrinsic movement method outperforms its counterparts. This model tends to jump and move much faster and more dynamically than the other BERTs, which use more conventional movement patterns.
Journal References:
- Annika Schmidt, Marion Forano, Arne Sachtler, Davide Calzolari, Bernhard M. Weber, David W. Franklin, Alin Albu-Schäffer; Finding the rhythm: Humans exploit nonlinear intrinsic dynamics of compliant systems in period interaction tasks; PLOS Computational Biology, 2024; DOI: 10.1371/journal.pcbi.1011478
- A. Sachtler et al., “Swing-Up of a Weakly Actuated Double Pendulum via Nonlinear Normal Modes,” 2024 European Control Conference (ECC), Stockholm, Sweden, 2024, pp. 2392-2398, doi: 10.23919/ECC64448.2024.10590854
- D. Calzolari, C. D. Santina, A. M. Giordano, A. Schmidt, and A. Albu-Schäffer, “Embodying Quasi-Passive Modal Trotting and Pronking in a Sagittal Elastic Quadruped,” in IEEE Robotics and Automation Letters, vol. 8, no. 4, pp. 2285-2292, April 2023, DOI: 10.1109/LRA.2023.3249631