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Multistable structures, known for their ability to rapidly switch between multiple stable states, are increasingly used for various robotic and mechatronic systems (e.g., grippers, swimming, jumping, or crawling robots). However, existing multistable structures generally have a fixed structure after fabrication, leading to a fixed energy profile with respect to deformations, a concept termed as energy landscape (EL) that dictates a structure's stable configurations and dynamic responses. To overcome this limitation, this work investigates how to actively tune the EL of a beam-based mechanism with a linear spring on the fly to enable tunable modules. We consider two tuning strategies to adjust the beam's initial bending angle and the offset of the spring. We establish a forward model to predict the module's EL and conduct experiments to validate this model. We also address the inverse problem to achieve a desired EL by choosing proper values of the initial bending angle and the offset of the spring. Finally, we demonstrate the practical applications of this tunable module with three cases: A kicker, a configurable arm, and a crawling robot. Our research lays the groundwork for advanced robotic and mechatronic systems, enabling them to harness structures with elastic instabilities for tuning their performance on the fly, thereby enhancing their adaptability and functionality.

This article investigates ${H_\infty }$ tracking control problem with a discount factor for two-time-scale systems subject to disturbances. The ${H_\infty }$ controller design is reduced to solving a set of linear matrix inequalities by using Lyapunov functions with two-time-scale structure. Under the obtained controller, the closed-loop system can track the output of a nonasymptotically stable reference model and achieve the ${H_\infty }$ performance for the given attenuation level and discount factor. The stability of the closed-loop system under the developed controller is proven. Compared with the existing discounted tracking control methods, the proposed method is capable of avoiding the complicated process of calculating the upper bound of the discount factor to guarantee the stability of the closed-loop system. The effectiveness of our theoretical results is demonstrated through both simulation and experiment on speed control of permanent magnet synchronous motor.

Tensegrity structures made from rigid rods and elastic cables have unique characteristics, such as being lightweight, easy to fabricate, and high load-carrying to weight capacity. In this article, we leverage tensegrity structures as wheels for a mobile robot that can actively change its shape by expanding or collapsing the wheels. Besides the shape-changing capability, using tensegrity as wheels offers several advantages over traditional wheels of similar sizes, such as a shock-absorbing capability without added mass since tensegrity wheels are both lightweight and highly compliant. We show that a robot with two icosahedron tensegrity wheels can reduce its width from 400 to 180 mm, and simultaneously, increase its height from 75 to 95 mm by changing the expanded tensegrity wheels to collapsed disk-like ones. The tensegrity wheels enable the robot to overcome steps with heights up to 110 and 150 mm with the expanded and collapsed configuration, respectively. We establish design guidelines for robots with tensegrity wheels by analyzing the maximum step height that can be overcome by the robot and the force required to collapse the wheel. The robot can also jump onto obstacles up to 300-mm high with a bistable mechanism that can gradually store but quickly release energy. We demonstrate the robot's locomotion capability in indoor and outdoor environments, including various natural terrains, like sand, grass, rocks, ice, and snow. Our results suggest that using tensegrity structures as wheels for mobile robots can enhance their capability to overcome obstacles, traverse challenging terrains, and survive falls from heights. When combined with other locomotion modes (e.g., jumping), such shape-changing robots can have broad applications for search-and-rescue after disasters or surveillance and monitoring in unstructured environments.