Real-Time Shape Estimation of Tensegrity Structures Using Strut Inclination Angles

ACCEPTED MARCH, 2025 1 Real-Time Shape Estimation of Tensegrity Structures Using Strut Inclination Angles Tufail Ahmad Bhat 1, Y uhei Y oshimitsu 1, Kazuki Wada 1, Shuhei Ikemoto 1 Abstract --T ensegrity structures are becoming widely used in robotics, such as continuously bending soft manipulators and mobile robots to explore unknown and uneven environments dynamically. Estimating their shape, which is the foundation of their state, is essential for establishing control. However, on-board sensor-based shape estimation remains difficult despite its importance, because tensegrity structures lack well-defined joint structures, which makes it challenging to use conventional angle sensors such as potentiometers or encoders for shape estimation. T o our knowledge, no existing work has successfully achieved shape estimation using only onboard sensors such as Inertial Measurement Units (IMUs). This study addresses this issue by proposing a novel approach that uses energy minimization to estimate the shape. We validated our method through experiments on a simple Class 1 tensegrity structure, and the results show that the proposed algorithm can estimate the real-time shape of the structure using onboard sensors, even in the presence of external disturbances. I NTRODUCTION T HE concept of "tensegrity" is coined by the iconoclastic architect R. Buckminster Fuller. It describes structures that achieve stability through a balance of forces: specific components, known as "cables" are always in tension, while others, known as "struts" are constantly under compression [1]. In tensegrity, the cables of the structure are always under continuous tension, a condition known as "prestress".