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Proprioceptive Shape Estimation of Tensegrity Manipulators Using Energy Minimisation

Tufail Ahmad Bhat, Shuhei Ikemoto

Abstract

Shape estimation is fundamental for controlling continuously bending tensegrity manipulators, yet achieving it remains a challenge. Although using exteroceptive sensors makes the implementation straightforward, it is costly and limited to specific environments. Proprioceptive approaches, by contrast, do not suffer from these limitations. So far, several methods have been proposed; however, to our knowledge, there are no proven examples of large-scale tensegrity structures used as manipulators. This paper demonstrates that shape estimation of the entire tensegrity manipulator can be achieved using only the inclination angle information relative to gravity for each strut. Inclination angle information is intrinsic sensory data that can be obtained simply by attaching an inertial measurement unit (IMU) to each strut. Experiments conducted on a five-layer tensegrity manipulator with 20 struts and a total length of 1160 mm demonstrate that the proposed method can estimate the shape with an accuracy of 2.1 \% of the total manipulator length, from arbitrary initial conditions under both static conditions and maintains stable shape estimation under external disturbances.

Proprioceptive Shape Estimation of Tensegrity Manipulators Using Energy Minimisation

Abstract

Shape estimation is fundamental for controlling continuously bending tensegrity manipulators, yet achieving it remains a challenge. Although using exteroceptive sensors makes the implementation straightforward, it is costly and limited to specific environments. Proprioceptive approaches, by contrast, do not suffer from these limitations. So far, several methods have been proposed; however, to our knowledge, there are no proven examples of large-scale tensegrity structures used as manipulators. This paper demonstrates that shape estimation of the entire tensegrity manipulator can be achieved using only the inclination angle information relative to gravity for each strut. Inclination angle information is intrinsic sensory data that can be obtained simply by attaching an inertial measurement unit (IMU) to each strut. Experiments conducted on a five-layer tensegrity manipulator with 20 struts and a total length of 1160 mm demonstrate that the proposed method can estimate the shape with an accuracy of 2.1 \% of the total manipulator length, from arbitrary initial conditions under both static conditions and maintains stable shape estimation under external disturbances.
Paper Structure (14 sections, 18 equations, 10 figures, 1 table)

This paper contains 14 sections, 18 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Elastic Energy of the Cables
  4. Shape Reconstruction Objective Function
  5. Experimental Setup
  6. Description of Tensegrity Manipulator-TM40
  7. Inclination Angle Sensor Module
  8. Experimental results and discussion
  9. System Configuration
  10. Static Case
  11. Collapsed state
  12. Expanded state
  13. External Deformation
  14. Conclusion

Figures (10)

  • Figure 1: Tensegrity manipulator with self-shape awareness a) The tensegrity manipulator provides a balance between rigidity and flexibility. b) TM40: a highly redundant five-layer tensegrity manipulator. c) Schematic of the three-dimensional TM40 tensegrity structure with the proprioceptive sensors, used for the energy minimisation algorithm. d) Estimated nodal positions. e) Full-scale estimated shape of the tensegrity manipulator determined from the spatial nodal positions.
  • Figure 2: Schematic representation of the tensegrity manipulator. a) Geometric representation of the nodal positions, centre positions, and orientations of the strut elements. b) Transformation of the strut orientation from spherical to Cartesian coordinates.
  • Figure 3: The figure shows the visualisation of the optimisation process in RViz2. Given the inclination angles of the strut elements, the method estimates the spatial nodal positions of the structure by minimising the energy function.
  • Figure 4: Five-Layer tensegrity manipulator: Each module is stacked with alternating twist direction to form a five-layer tensegrity manipulator. The structure consists of 80 active and passive tension elements and 20 rigid struts. Each pneumatic cylinder is controlled independently, and the system has a ROS2-compatible embedded AD/DA module to actuate the 40 pneumatic cylinders.
  • Figure 5: Sensor module for inclination angles: a) The manipulator consists of 20 struts. b) Each is equipped with a 6-axis IMU sensor. c) The inclination angles are measured from the longitudinal axis direction of each strut element and the gravitational vector.
  • ...and 5 more figures