In high-end equipment manufacturing, soft robots show immense potential for delicate tasks thanks to their flexible materials. However, predicting and controlling complex dynamic motions—especially jumping—has long hindered further development. Recently, a research team from Keio University and Osaka University, inspired by simple children's pop-up toys, achieved a key breakthrough, bringing new dawn to soft robotics.

Although soft robots hold great promise, their complex motions are difficult to predict and control, with jumping being a persistent industry challenge. In a study published in Advanced Robotics, the Keio and Osaka University team focused on the fundamental component of jumping soft robots—a thin hemispherical shell—and delved deeply into the physics behind its jumping behavior.

The team conducted detailed analysis of the jumping dynamics of hemispherical shells using a combination of precision experiments, numerical simulations, and theoretical calculations, with particular emphasis on the critical role of contact between the shell and the ground. In experiments, they fabricated various silicone rubber hemispherical shells and used a desktop setup with pneumatic control to induce deformation. Multiple sensors captured real-time rapid shape changes, providing comprehensive data for analysis. For deeper investigation, the team employed the Material Point Method (MPM) to create numerical simulations that accurately reproduced the complex deformations during jumping.

The key breakthrough lies in understanding how the contact area between the shell and the ground changes. When an inverted shell snaps back to its original shape, the contact area transitions from an annular ring to a full disk. This seemingly simple shift is crucial for understanding the energy transfer that propels the shell upward. Based on this insight, the researchers developed a predictive formula for jump height, dividing the process into two critical phases: initial lift-off and final launch. The formula closely matches both experimental and simulation results, providing a reliable basis for predicting jump height in soft robots.

The ability to predict jump height represents a major leap in soft robotics. It eliminates the need for extensive and time-consuming trial-and-error, enabling researchers to precisely design soft robots tailored to specific tasks and environments. This breakthrough will be critical in complex terrain operations such as exploration, search and rescue, and environmental monitoring, helping robots better adapt and complete missions.

Lead researcher Tomohiko Sano stated: "This study highlights the importance of analyzing individual components to understand overall soft robot performance, marking a shift toward theory-driven design and enabling the creation of more complex and efficient soft machines." Co-author Ryuichi Tarumi, Professor at Osaka University, added: "Fundamental understanding of basic building blocks opens the door to designing new soft robots optimized for specific load conditions—without extensive parameter searches."

This research not only advances soft robotics but also provides valuable insights into elastic energy and motion principles, with significant contributions across fields such as biomechanics, materials science, and aerospace engineering. It marks a solid step forward in building robust, predictable, and truly capable soft machines.